From 7573bd6b897e2024099832a732a265195fecc758 Mon Sep 17 00:00:00 2001 From: Yeseo Jang Date: Mon, 28 Feb 2022 21:13:04 +0900 Subject: [PATCH 01/20] updata curriculum --- README.md | 31 +++++++++++++++++++++++++++++-- 1 file changed, 29 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index 7664941..0fa0641 100644 --- a/README.md +++ b/README.md @@ -1,2 +1,29 @@ -# 2022-1-Euron-Study-Assignments -Euron 2기 스터디팀 예습·복습 과제 제출 +# Euron 2기 예습·복습 과제 제출 + +### ▶ [Computer Vision](https://github.com/Ewha-Euron/2022-1-Euron-CV) +### ▶ [Natural Language Processing](https://github.com/Ewha-Euron/2022-1-Euron-NLP) +### ▶ [Data Analysis](https://github.com/Ewha-Euron/2022-1-Euron-DA) + +## Curriculum + +| 주차 | 날짜 | CV | NLP | DA | +|---|---|---|---|---| +|1|22/03/08|cs231n 1주차|cs224n 1강|파이썬 머신러닝 완벽가이드 1~3장| +|2|22/03/15|cs231n 2주차|cs224n 2강|파이썬 머신러닝 완벽가이드 4장(1)| +|3|22/03/22|cs231n 3주차|cs224n 3강|파이썬 머신러닝 완벽가이드 4장(2)| +|4|22/03/29|cs231n 4주차|cs224n 4강|4장 관련 필사| +|5|22/04/05|cs231n 5주차|cs224n 5강|파이썬 머신러닝 완벽가이드 5장| +|6|22/04/12|cs231n 6주차|cs224n 6강|5장 관련 필사| +|7|22/04/19|cs231n 7주차|cs224n 7강|파이썬 머신러닝 완벽가이드 6장| +|8|22/05/03|cs231n 8주차|cs224n 8강|6장 관련 필사| +|9|22/05/10|cs231n 9주차|cs224n 9강|파이썬 머신러닝 완벽가이드 7장| +|10|22/05/17|cs231n 10주차|cs224n 10강|7장 관련 필사| +|11|22/05/24|cs231n 11주차|cs224n 11강|파이썬 머신러닝 완벽가이드 9장| +|12|22/05/31|cs231n 12주차|cs224n 12강|9장 관련 필사| +|13|22/06/07|cs231n 13주차|cs224n 13강|캐글 필사 1| +|14|22/06/21|cs231n 14주차|cs224n 14강|캐글 필사 2| +|15|22/06/28|논문 스터디 1|cs224n 15강|캐글 필사 2| +|16|22/07/05|논문 스터디 2|cs224n 18강|| +|17|22/07/12|논문 스터디 3|cs224n 20강|| +|18|22/07/19||cs224n 21강|| +|19|22/07/26||cs224n 22강|| From 2620a723e21b531a4c4363f86b215f613329b7f1 Mon Sep 17 00:00:00 2001 From: MSY99 <101084413+MSY99@users.noreply.github.com> Date: Mon, 7 Mar 2022 23:08:27 +0900 Subject: [PATCH 02/20] Create preview.md --- preview.md | 23 +++++++++++++++++++++++ 1 file changed, 23 insertions(+) create mode 100644 preview.md diff --git a/preview.md b/preview.md new file mode 100644 index 0000000..bc68e64 --- /dev/null +++ b/preview.md @@ -0,0 +1,23 @@ +생각보다 컴퓨터 비전은 알아야 하는 분야가 많은 과목이었다. +인간의 시각 체계는 복잡하고 중요한 감각처리로 이에 대한 연구도 오래 전 부터 진행되어왔다. + +CV 분야에서 큰 영향을 준 연구들은 다음과 같다. + +1959: Hubel, Wiesel 포유류의 시각 메커니즘이 어떻게 될 것인지에 대해 연구 +1963: Larry Roberts 우리가 보는 사진을 특징점으로 재구성하는 방법에 대해 연구 +1970년대: Davide Marr Vision이라는 책을 통해 CV가 어떤 방식으로 발전해야하는지 제시 +Input Image가 들어왔을 때, 이미지의 특징을 추출, 특징에 따라 depth나 surface를 추출한다. 이렇게 추출한 정보를 바탕으로 3D modeling하는 방법을 제시 + +Object Detection 분야는 굉장히 어렵기 때문에 객체 분할을 먼저 시도하는 연구가 있었다 (= Object segmentation) +시간이 흘러, 90년도 후반에서 2010년도 까지는 특징을 기반으로 한 객체 인식 알고리즘이 대세를 이루었다. 이 흐름에 영향을 준 논문이 SIFT 알고리즘이다. +객체의 모양은 카메라의 각도에 따라, 조도의 영향에 따라 달라질 수 있지만 불변하는 특징을 찾아 매칭하는 것이 main idea이다. + +이후 Spatial Pyramid Matching, HOG algorithm 등등 여러 논문이 CV에 영향을 미쳤다. + +2000년대 초: SVM, Adaboost 같은 기계학습 알고리즘을 Training 하는 과정에서 overfitting이 일어나는데 그 이유는 시각 데이터가 복잡하고, 학습 데이터가 부족하기 때문이다. 따라서 Classificaiton 분야에서는 세상의 모든 객체를 인식하고 overfitting을 줄인다는 목표를 세운다. + +위의 목표를 가지고 ImageNet이라는 데이터셋을 만들게 된다. 이는 22K의 카테고리와 14M의 이미지 사진이 들어있으며 이를 가지고 Image Classification 대회를 열기도 한다. (=ILSVRC) + +이 대회에서 2012년에 오차율이 10%로 줄어든 혁신적인 알고리즘이 제안되었고 그것이 CNN 구조를 기반으로한 ALexNet이다. 그 이후로 CNN을 변형해서 성능을 좋게 하려는 연구가 계속되고 있으며 이 수업에서는 CNN이 무엇인지 배우게 될 것이다. + +1988년에 이미 제안되었던 CNN은 데이터의 양이 적었거나 연산 속도가 굉장히 느렸다는 단점에 의해 발전이 느렸었다. 하지만 최근에는 여러 기술들이 발전하면서 한계를 극복해나가는 중이다. From 22abcce1ca71b6d7b85690c51c07f9e93e4820dd Mon Sep 17 00:00:00 2001 From: Yeseo Jang Date: Thu, 10 Mar 2022 01:09:18 -0500 Subject: [PATCH 03/20] update cp link --- README.md | 1 + 1 file changed, 1 insertion(+) diff --git a/README.md b/README.md index 0fa0641..4a1056b 100644 --- a/README.md +++ b/README.md @@ -3,6 +3,7 @@ ### ▶ [Computer Vision](https://github.com/Ewha-Euron/2022-1-Euron-CV) ### ▶ [Natural Language Processing](https://github.com/Ewha-Euron/2022-1-Euron-NLP) ### ▶ [Data Analysis](https://github.com/Ewha-Euron/2022-1-Euron-DA) +### ▶ [Competition](https://github.com/Ewha-Euron/2022-1-Euron-CP) ## Curriculum From 8cceb1f57cfc8564267785823d823e4d45afe17c Mon Sep 17 00:00:00 2001 From: MSY99 <101084413+MSY99@users.noreply.github.com> Date: Mon, 21 Mar 2022 12:50:47 +0900 Subject: [PATCH 04/20] =?UTF-8?q?Create=20Week3=5FCV=5F=EC=98=88=EC=8A=B5?= =?UTF-8?q?=EA=B3=BC=EC=A0=9C=5F=EB=AF=BC=EC=86=8C=EC=97=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- ...\234_\353\257\274\354\206\214\354\227\260" | 125 ++++++++++++++++++ 1 file changed, 125 insertions(+) create mode 100644 "Week3_CV_\354\230\210\354\212\265\352\263\274\354\240\234_\353\257\274\354\206\214\354\227\260" diff --git "a/Week3_CV_\354\230\210\354\212\265\352\263\274\354\240\234_\353\257\274\354\206\214\354\227\260" "b/Week3_CV_\354\230\210\354\212\265\352\263\274\354\240\234_\353\257\274\354\206\214\354\227\260" new file mode 100644 index 0000000..0de57b8 --- /dev/null +++ "b/Week3_CV_\354\230\210\354\212\265\352\263\274\354\240\234_\353\257\274\354\206\214\354\227\260" @@ -0,0 +1,125 @@ +Linear Classifier에서 어떤 가중치(w) 값을 사용하느냐에 따라 정확도가 달라진 다는 것을 배웠다. +그렇다면 어떻게 최적의 가중치 값을 찾아야 하는지 알아야 하는데 이를 위해서 사용하는 정량화 방법이 loss function이다. +loss fuction은 어느 가중치 값이 얼마나 "안 좋은지"를 알려주는 지표이다. +그리고 이 안 좋은 가중치를 좋은 가중치로 바꿔나가는 과정을 optimization이라고 한다. +f(x, W) = Wx + b +이 식에서 x는 이미지, W는 가중치, b는 편향값이다. +이 식에서 loss를 구하는 방법은 각 카테고리 (고양이 자동차 개구리 등)별로 loss를 각각 구해서 그걸 모두 더한 후 평균을 내는 것이다. +강의 자료에서 제시된 고양이 자동차 개구리 이미지를 통해 loss를 구한 값들은 다음과 같다. + +- SVM loss (= hinge loss) +sj는 정답이 아닌 클래스의 score이고 syi는 정답 클래스의 score 값이다. +만약, syi > sj + safety margin(강의자료에서는 1)이면 loss = 0이고, +syi < sj + safety margin 이면 loss = sj - syi + safety margin이다. +SVM loss = SUM(j != y_i) { max (0, sj-syi+1) } +강의 자료의 고양이 자동차 개구리의 케이스로 계산한 SVM loss = 5.27이다. +고양이 자동차의 경우는 loss 값이 작지만 개구리에서 12.9의 loss 값이 나온다. + +Q1. 그런데 이 때 자동차의 score 값을 조금 변경해서 loss 값을 계산해도 loss 값이 크게 변동하지 않는 것을 볼 수 있다. +따라서, SVM hinge loss는 데이터에 민감하지 않다는 특성이 있음을 알 수 있다. +Q2. 그럼 최소 최댓값은 어떻게 될까? +loss의 최소값은 0이다. 그리고 최대값은 무한대이다. +Q3. 만약 W가 매우 작아져서 score가 0에 근사해지면 어떻게 되나? +계산해보면, 클래스 3개니까 (2+2+2)/3 = 2가 나오고 만일 클래스가 9개라면 (9+9+9+~+9)/10 = 9가 나올 것이다. +따라서 그럴 경우 loss = 클래스 갯수 -1이 된다. 이 계산은 디버그 용으로 사용한다. +0으로 해주었을 때 loss가 클래수 갯수 -1의 값으로 나오는지 검사하는 것이다. +이걸 sanity check라고 부른다. +Q4. 지금까지 계산하면서 정답 클래스 값을 제외하고 계산했는데 그 이유는? +정답 클래스 값을 포함해서 계산하게 되면 모든 경우에서 loss 값이 +1 증가하게 된다. +그러나 우리는 loss 값이 0에 근사하게 되길 바라기 때문에 정답 클래스 값을 제외하는 것이다. +Q5. 만약 sum 대신 평균을 이용하면 어떻게 되나? +계산해보면 딱히 상관은 없다. 단지 평균을 사용했기 때문에 scale만 작아질 뿐이다. +다만, loss가 0에 가까워지도록 하길 바라기 때문에 scale을 크게 해서 변화를 관찰하는 것이 좋은 방법일 수 있다! +Q6. 그럼 max 값에 제곱승을 해서 계산하면? +제곱승을 해서 계산하게 되면 nonlinear한 결과가 나오고, 답이 달라지게 된다. +이렇게 계산하는 방식을 squared hinge loss라고 하는데 때에 따라서는 이 방식이 잘 먹힐 때도 있다. +그래서 "아주 좋다"와 "아주 나쁘다"를 따질 때 유용한 방식이다. (그러나 잘 사용하지는 않음) + +그런데 이렇게 구하는 W 값은 과연 유일한 걸까? -> 아님 +각각의 score 값을 2배 혹은 3배 증가시켜도 똑같은 loss 값이 나올 수 있다. 따라서 W는 여러 개가 나올 수 있다. +유일하지 않는 W값이 문제가 되는 이유는 +-> 우리는 새로운 값에 대해서 예측을 하기 위해 model을 만들기 때문에 test set에 더 관심이 많고 따라서 정확도도 test set을 통해서 추출한다. +그런데 지금까지 구한 W값은 train set에 맞춰서 나온 것들이기 때문에 최적값도 train set에 맞춰져서 나오게 된다. +그래서 그 최적값은 test set에는 맞지 않을 수도 있다는 문제가 있다. +-> overfitting의 문제가 생길 수도 있다는 것이다. + +따라서 test set에도 맞을 수 있는 W값을 찾아야 하는데 이를 위해 사용하는 방식이 regularization이다. +L(W) = 1/N * SUM^N_(i=1) { Li(f(xi, W), yi) } + lamda R(W) +이 식에서 왼쪽의 항은 data loss이고 오른쪽의 항은 regularization이다. +data loss는 train set의 입장에서, regularazation은 test set의 입장에 있기 때문에 +이 식에 따르면, 매 loss 값을 계산할 때 마다 train에만 맞는 것을 학습하려고 하면 regularization에서 패널티를 부여하게 된다. +이 과정을 통해서 test set에도 맞는 W 값을 찾아나갈 수 있다. + +* 여기서 lamda R(W)가 무엇이길래 패널티를 부여하는 것일까? +일단 다항식이 너무 깊어지게 되면 복잡한 계산을 하게 되기 때문에 이를 방지하는 효과가 있다. +그리고 L1 regularization, L2 regularization이 있는데 +전자는 실제로 차수 값이 0이 되도록하고, 후자는 전체 차수의 값이 0에 가깝도록 유도한다. +따라서 L1은 원하는 특성이 제거될 수 있기 때문에 L2가 모든 것을 고려한다는 점에서 비교우위를 가지게 된다. +그리고 lamda 값은 규제의 강도 값이고, 높으면 모델이 단순해지며 underfitting / 낮으면 모델이 복잡해지며 overfitting이 된다는 문제가 있다. + +위와 같은 특성들 때문에 L1은 가중치 값 중 0이 있는 경우를, L2는 전체적으로 0에 가깝게 퍼진 가중치 값을 선호한다. + +어쨋든 우리의 목적에 더 부합하는 것은 L2 regularization이기 때문에 이를 더 많이 사용하고 이는 dropout, batch normalization에서도 많이 사용한다. + +- softmax classifier (=cross entropy) +모든 스코어에 exp를 취하고 그걸 모두 더한 뒤 원하는 클래스의 점수에 exp를 취해서 나눈다. +이렇게 계산한 것은 확률 값으로 도출되며, 이 때 원하는 정답 클래스에 -log를 취해 loss를 구하게 된다. +softmax는 multinomial logistic regression이다. (logistic regression = sigmoid function) +위와 같은 정의에 따라 위의 계산 방식에서 exp를 취해주는 것이다. +그리고 우리는 얼마나 "안" 좋은지를 판단하고자 하는데 +x축을 확률, y축을 loss라고 했을 때, -log의 함수가 확률이 1에 가까워질 수록 0에 가까워지기 때문에 -log를 취해 최종 loss를 구하게 되는 것이다. + +Q1. 이런 방식을 취했을 때 min, max는? +이론적으로 최소는 0, 최대는 무한대이다. (feat. -log graph) +Q2. 만약 score가 0에 가까워지면? +-log(1/클래스 갯수)가 되고 이 또한 디버깅 용으로 사용하며, sanity check라고 불린다. + +강의자료에서는 예시 자료를 통해 svm과 softmax를 비교하고 있다. +1. max값을 취해서 loss를 구하는 것과 exp를 취해서 확률 값으로 loss를 구하는 것의 차이가 있다. +2. 만약 data point를 흔들어 주게 되면? +SVM의 경우에는 딱히 영향이 없었고 둔감하다는 결론이 나왔으나, +cross-entropy loss의 경우에는 조금만 데이터가 바뀌어도 확률에 영향이 있었고 매우 민감하다는 결론이 나온다. + ++) Full loss라는 것은 언제가 regularization을 추가한다. + +위와 같은 방식들을 통해서 얻은 결론은 "어떤 W값이 얼마나 안좋은지"이다. +그렇다면 좋은 W값은? -> Optimization을 통해 구할 수 있다. +optimization은 쉽게 말하면 산 골짜기의 가장 깊은 곳으로 내려가는 것과 같으며 이 과정이 곧 loss가 0에 가까워지도록 하는 것이다. +몇 가지 방법이 소개되고 있는데 그 중에서 Random search는 사용하지 말아야 한다. (연산 오래 걸릴 수 있음.) +보통은 Follow the slope (gradient descent)경사 하강법을 사용한다. + +1-dimension, the derivative of a function +d f(x) / d x = lim_(h->0) { ( f(x+h) - f(x) ) / h } (* 만약 다차원이면 편미분 형태의 식) +이렇게 수식으로 하나하나 계산해서 사용하는 방법 -> numerical 방법 (수치적 방법) +이 방식은 모든 가중치 W 값에 조금씩 변화를 줘가면서 loss 값의 변화를 관찰하는 것인데 이렇게 하면 너무 연산이 오래 걸린다. +단지 W가 변화할 때의 loss 값을 알고 싶을 뿐이라면? +미분을 이용한 analytic gradient(해석적 방법)을 사용한다. 이 방식을 사용하면 일일이 계산할 필요없이 딱! 원하는 값이 나오게 된다. +요약하자면, +numerical gradient: 정확하지 않고 느리지만 간편한 연산 방식 (오류가 덜 나는 편) +analytic gradient: 정확하고 빠르지만 복잡한 연산 방식 (오류가 날 가능성이 있음) +이다. 보통은 해석적 방법을 더 많이 사용하지만 디버깅을 할 때는 수치적 방법을 사용하기도 한다. 이를 gradient check라고 한다. + +위와 같이 gradient 계산한 것들은 앞에 -가 붙으면 음의 기울기이기 때문에 +방향으로 이동하고 +앞에 +가 붙으면 - 방향으로 이동하면서 그래프에서 가장 낮은 지점으로 이동한다. +여기서 한 번 이동할 때 이동하는 거리를 step size (=learning rate)라고 부른다. 이 값도 적절한 값을 찾아서 적용시키는 것이 중요하다. +그래서 임의의 w 위치에서 가운데 빨간색 지점으로 가는 것, 즉 기울기가 0에 가까운 지점으로 가는 것이 목표이다. + ++) 지금까지 계산한 방식들은 N을 한 번에 올려서 계산했는데, 만약 N이 굉장히 큰 값이라면 매우 비효율적인 결과가 나올 것이다. +그래서 이 N을 나눠서 계산하는 stochastic gradient descent (SGD)를 많이 사용한다. +mini batch를 두어서 데이터 갯수를 잘라 사용하는 것인데 보통 2의 제곱수 만큼 잘라서 사용한다. +(256개를 가지고 W를 업데이트하고 그 다음 256개를 가지고 W를 업데이트하는 것을 반복하는 식이다.) + +그냥 이미지를 그대로 넣어버리는 식으로 사용하는 것은 성능이 그닥 좋지 않았다. (이전 강의록의 말 머리가 2개 있는 식이라던가..) +그래서 CNN이 연구 되기 전까지는 이미지의 특징을 뽑아내고 이 특징을 합쳐서 linear regression에 넣는 방식을 사용해왔다. +이전에 linear classification으로 해결할 수 없는 것들의 예시를 보여주었었는데 이 때 극좌표계로 변환함으로써 직선으로 구분 가능한 형태로 바뀌는 경우가 있었다. +이미지를 활용할 때는 이렇게 하지 않지만 여기서 동기 부여를 받아 특징을 추출하는 방식으로 이어지게 된 것이다. +특징 추출의 한 가지 방법이 바로 color histogram이다. 컬러 hue 값이 있는데 여기에 어떤 컬러가 많이 나오는지 count 해서 특징을 추출하는 것이다. +2번 째 방법은 HoG(Historam of Oriented Gradients)이다. 방향 값을 히스토 그램으로 표현하는 것이다. +전체 이미지 내에서 어느 방향으로의 각도가 많은지 히스토그램으로 나타내 특징을 추출하는 것이다. +3번 째 방법은 bag of words이다. 자연어 처리에서 많이 사용하는 방법인데 +먼저 이미지를 여러 개로 잘라낸 뒤, 비지도 학습과 같이 클러스터링을 돌려 각도, 색 등의 특징을 추출한다. +이 후 새로운 이미지가 들어오면 이 이미지를 잘라내서 클러스터와 비교해 어떤 특징이 있는지 비교한다. + +그러나 CNN 연구 방식이 도입된 후 특징을 미리 뽑아내는 것이 아니라 입력된 이미지에서 스스로 특징을 추출하도록 하여 사용하고 있다. + +(-> 다음 강의: neural network & backpropagation) From 8aaab2ac9770abcb1544a1cdfdcf569bbacbb293 Mon Sep 17 00:00:00 2001 From: MSY99 Date: Mon, 21 Mar 2022 16:10:47 +0900 Subject: [PATCH 05/20] =?UTF-8?q?CV=5FWeek3=5F=EC=98=88=EC=8A=B5=EA=B3=BC?= =?UTF-8?q?=EC=A0=9C=5F=EB=AF=BC=EC=86=8C=EC=97=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- ...0\354\212\265\352\263\274\354\240\234.txt" | 125 ++++++++++++++++++ 1 file changed, 125 insertions(+) create mode 100644 "Week3_\354\230\210\354\212\265\352\263\274\354\240\234.txt" diff --git "a/Week3_\354\230\210\354\212\265\352\263\274\354\240\234.txt" "b/Week3_\354\230\210\354\212\265\352\263\274\354\240\234.txt" new file mode 100644 index 0000000..1e6a436 --- /dev/null +++ "b/Week3_\354\230\210\354\212\265\352\263\274\354\240\234.txt" @@ -0,0 +1,125 @@ +Linear Classifier에서 어떤 가중치(w) 값을 사용하느냐에 따라 정확도가 달라진 다는 것을 배웠다. +그렇다면 어떻게 최적의 가중치 값을 찾아야 하는지 알아야 하는데 이를 위해서 사용하는 정량화 방법이 loss function이다. +loss fuction은 어느 가중치 값이 얼마나 "안 좋은지"를 알려주는 지표이다. +그리고 이 안 좋은 가중치를 좋은 가중치로 바꿔나가는 과정을 optimization이라고 한다. +f(x, W) = Wx + b +이 식에서 x는 이미지, W는 가중치, b는 편향값이다. +이 식에서 loss를 구하는 방법은 각 카테고리 (고양이 자동차 개구리 등)별로 loss를 각각 구해서 그걸 모두 더한 후 평균을 내는 것이다. +강의 자료에서 제시된 고양이 자동차 개구리 이미지를 통해 loss를 구한 값들은 다음과 같다. + +- SVM loss (= hinge loss) +sj는 정답이 아닌 클래스의 score이고 syi는 정답 클래스의 score 값이다. +만약, syi > sj + safety margin(강의자료에서는 1)이면 loss = 0이고, +syi < sj + safety margin 이면 loss = sj - syi + safety margin이다. +SVM loss = SUM(j != y_i) { max (0, sj-syi+1) } +강의 자료의 고양이 자동차 개구리의 케이스로 계산한 SVM loss = 5.27이다. +고양이 자동차의 경우는 loss 값이 작지만 개구리에서 12.9의 loss 값이 나온다. + +Q1. 그런데 이 때 자동차의 score 값을 조금 변경해서 loss 값을 계산해도 loss 값이 크게 변동하지 않는 것을 볼 수 있다. +따라서, SVM hinge loss는 데이터에 민감하지 않다는 특성이 있음을 알 수 있다. +Q2. 그럼 최소 최댓값은 어떻게 될까? +loss의 최소값은 0이다. 그리고 최대값은 무한대이다. +Q3. 만약 W가 매우 작아져서 score가 0에 근사해지면 어떻게 되나? +계산해보면, 클래스 3개니까 (2+2+2)/3 = 2가 나오고 만일 클래스가 9개라면 (9+9+9+~+9)/10 = 9가 나올 것이다. +따라서 그럴 경우 loss = 클래스 갯수 -1이 된다. 이 계산은 디버그 용으로 사용한다. +0으로 해주었을 때 loss가 클래수 갯수 -1의 값으로 나오는지 검사하는 것이다. +이걸 sanity check라고 부른다. +Q4. 지금까지 계산하면서 정답 클래스 값을 제외하고 계산했는데 그 이유는? +정답 클래스 값을 포함해서 계산하게 되면 모든 경우에서 loss 값이 +1 증가하게 된다. +그러나 우리는 loss 값이 0에 근사하게 되길 바라기 때문에 정답 클래스 값을 제외하는 것이다. +Q5. 만약 sum 대신 평균을 이용하면 어떻게 되나? +계산해보면 딱히 상관은 없다. 단지 평균을 사용했기 때문에 scale만 작아질 뿐이다. +다만, loss가 0에 가까워지도록 하길 바라기 때문에 scale을 크게 해서 변화를 관찰하는 것이 좋은 방법일 수 있다! +Q6. 그럼 max 값에 제곱승을 해서 계산하면? +제곱승을 해서 계산하게 되면 nonlinear한 결과가 나오고, 답이 달라지게 된다. +이렇게 계산하는 방식을 squared hinge loss라고 하는데 때에 따라서는 이 방식이 잘 먹힐 때도 있다. +그래서 "아주 좋다"와 "아주 나쁘다"를 따질 때 유용한 방식이다. (그러나 잘 사용하지는 않음) + +그런데 이렇게 구하는 W 값은 과연 유일한 걸까? -> 아님 +각각의 score 값을 2배 혹은 3배 증가시켜도 똑같은 loss 값이 나올 수 있다. 따라서 W는 여러 개가 나올 수 있다. +유일하지 않는 W값이 문제가 되는 이유는 +-> 우리는 새로운 값에 대해서 예측을 하기 위해 model을 만들기 때문에 test set에 더 관심이 많고 따라서 정확도도 test set을 통해서 추출한다. +그런데 지금까지 구한 W값은 train set에 맞춰서 나온 것들이기 때문에 최적값도 train set에 맞춰져서 나오게 된다. +그래서 그 최적값은 test set에는 맞지 않을 수도 있다는 문제가 있다. +-> overfitting의 문제가 생길 수도 있다는 것이다. + +따라서 test set에도 맞을 수 있는 W값을 찾아야 하는데 이를 위해 사용하는 방식이 regularization이다. +L(W) = 1/N * SUM^N_(i=1) { Li(f(xi, W), yi) } + lamda R(W) +이 식에서 왼쪽의 항은 data loss이고 오른쪽의 항은 regularization이다. +data loss는 train set의 입장에서, regularazation은 test set의 입장에 있기 때문에 +이 식에 따르면, 매 loss 값을 계산할 때 마다 train에만 맞는 것을 학습하려고 하면 regularization에서 패널티를 부여하게 된다. +이 과정을 통해서 test set에도 맞는 W 값을 찾아나갈 수 있다. + +* 여기서 lamda R(W)가 무엇이길래 패널티를 부여하는 것일까? +일단 다항식이 너무 깊어지게 되면 복잡한 계산을 하게 되기 때문에 이를 방지하는 효과가 있다. +그리고 L1 regularization, L2 regularization이 있는데 +전자는 실제로 차수 값이 0이 되도록하고, 후자는 전체 차수의 값이 0에 가깝도록 유도한다. +따라서 L1은 원하는 특성이 제거될 수 있기 때문에 L2가 모든 것을 고려한다는 점에서 비교우위를 가지게 된다. +그리고 lamda 값은 규제의 강도 값이고, 높으면 모델이 단순해지며 underfitting / 낮으면 모델이 복잡해지며 overfitting이 된다는 문제가 있다. + +위와 같은 특성들 때문에 L1은 가중치 값 중 0이 있는 경우를, L2는 전체적으로 0에 가깝게 퍼진 가중치 값을 선호한다. + +어쨋든 우리의 목적에 더 부합하는 것은 L2 regularization이기 때문에 이를 더 많이 사용하고 이는 dropout, batch normalization에서도 많이 사용한다. + +- softmax classifier (=cross entropy) +모든 스코어에 exp를 취하고 그걸 모두 더한 뒤 원하는 클래스의 점수에 exp를 취해서 나눈다. +이렇게 계산한 것은 확률 값으로 도출되며, 이 때 원하는 정답 클래스에 -log를 취해 loss를 구하게 된다. +softmax는 multinomial logistic regression이다. (logistic regression = sigmoid function) +위와 같은 정의에 따라 위의 계산 방식에서 exp를 취해주는 것이다. +그리고 우리는 얼마나 "안" 좋은지를 판단하고자 하는데 +x축을 확률, y축을 loss라고 했을 때, -log의 함수가 확률이 1에 가까워질 수록 0에 가까워지기 때문에 -log를 취해 최종 loss를 구하게 되는 것이다. + +Q1. 이런 방식을 취했을 때 min, max는? +이론적으로 최소는 0, 최대는 무한대이다. (feat. -log graph) +Q2. 만약 score가 0에 가까워지면? +-log(1/클래스 갯수)가 되고 이 또한 디버깅 용으로 사용하며, sanity check라고 불린다. + +강의자료에서는 예시 자료를 통해 svm과 softmax를 비교하고 있다. +1. max값을 취해서 loss를 구하는 것과 exp를 취해서 확률 값으로 loss를 구하는 것의 차이가 있다. +2. 만약 data point를 흔들어 주게 되면? +SVM의 경우에는 딱히 영향이 없었고 둔감하다는 결론이 나왔으나, +cross-entropy loss의 경우에는 조금만 데이터가 바뀌어도 확률에 영향이 있었고 매우 민감하다는 결론이 나온다. + ++) Full loss라는 것은 언제가 regularization을 추가한다. + +위와 같은 방식들을 통해서 얻은 결론은 "어떤 W값이 얼마나 안좋은지"이다. +그렇다면 좋은 W값은? -> Optimization을 통해 구할 수 있다. +optimization은 쉽게 말하면 산 골짜기의 가장 깊은 곳으로 내려가는 것과 같으며 이 과정이 곧 loss가 0에 가까워지도록 하는 것이다. +몇 가지 방법이 소개되고 있는데 그 중에서 Random search는 사용하지 말아야 한다. (연산 오래 걸릴 수 있음.) +보통은 Follow the slope (gradient descent)경사 하강법을 사용한다. + +1-dimension, the derivative of a function +d f(x) / d x = lim_(h->0) { ( f(x+h) - f(x) ) / h } (* 만약 다차원이면 편미분 형태의 식) +이렇게 수식으로 하나하나 계산해서 사용하는 방법 -> numerical 방법 (수치적 방법) +이 방식은 모든 가중치 W 값에 조금씩 변화를 줘가면서 loss 값의 변화를 관찰하는 것인데 이렇게 하면 너무 연산이 오래 걸린다. +단지 W가 변화할 때의 loss 값을 알고 싶을 뿐이라면? +미분을 이용한 analytic gradient(해석적 방법)을 사용한다. 이 방식을 사용하면 일일이 계산할 필요없이 딱! 원하는 값이 나오게 된다. +요약하자면, +numerical gradient: 정확하지 않고 느리지만 간편한 연산 방식 (오류가 덜 나는 편) +analytic gradient: 정확하고 빠르지만 복잡한 연산 방식 (오류가 날 가능성이 있음) +이다. 보통은 해석적 방법을 더 많이 사용하지만 디버깅을 할 때는 수치적 방법을 사용하기도 한다. 이를 gradient check라고 한다. + +위와 같이 gradient 계산한 것들은 앞에 -가 붙으면 음의 기울기이기 때문에 +방향으로 이동하고 +앞에 +가 붙으면 - 방향으로 이동하면서 그래프에서 가장 낮은 지점으로 이동한다. +여기서 한 번 이동할 때 이동하는 거리를 step size (=learning rate)라고 부른다. 이 값도 적절한 값을 찾아서 적용시키는 것이 중요하다. +그래서 임의의 w 위치에서 가운데 빨간색 지점으로 가는 것, 즉 기울기가 0에 가까운 지점으로 가는 것이 목표이다. + ++) 지금까지 계산한 방식들은 N을 한 번에 올려서 계산했는데, 만약 N이 굉장히 큰 값이라면 매우 비효율적인 결과가 나올 것이다. +그래서 이 N을 나눠서 계산하는 stochastic gradient descent (SGD)를 많이 사용한다. +mini batch를 두어서 데이터 갯수를 잘라 사용하는 것인데 보통 2의 제곱수 만큼 잘라서 사용한다. +(256개를 가지고 W를 업데이트하고 그 다음 256개를 가지고 W를 업데이트하는 것을 반복하는 식이다.) + +그냥 이미지를 그대로 넣어버리는 식으로 사용하는 것은 성능이 그닥 좋지 않았다. (이전 강의록의 말 머리가 2개 있는 식이라던가..) +그래서 CNN이 연구 되기 전까지는 이미지의 특징을 뽑아내고 이 특징을 합쳐서 linear regression에 넣는 방식을 사용해왔다. +이전에 linear classification으로 해결할 수 없는 것들의 예시를 보여주었었는데 이 때 극좌표계로 변환함으로써 직선으로 구분 가능한 형태로 바뀌는 경우가 있었다. +이미지를 활용할 때는 이렇게 하지 않지만 여기서 동기 부여를 받아 특징을 추출하는 방식으로 이어지게 된 것이다. +특징 추출의 한 가지 방법이 바로 color histogram이다. 컬러 hue 값이 있는데 여기에 어떤 컬러가 많이 나오는지 count 해서 특징을 추출하는 것이다. +2번 째 방법은 HoG(Historam of Oriented Gradients)이다. 방향 값을 히스토 그램으로 표현하는 것이다. +전체 이미지 내에서 어느 방향으로의 각도가 많은지 히스토그램으로 나타내 특징을 추출하는 것이다. +3번 째 방법은 bag of words이다. 자연어 처리에서 많이 사용하는 방법인데 +먼저 이미지를 여러 개로 잘라낸 뒤, 비지도 학습과 같이 클러스터링을 돌려 각도, 색 등의 특징을 추출한다. +이 후 새로운 이미지가 들어오면 이 이미지를 잘라내서 클러스터와 비교해 어떤 특징이 있는지 비교한다. + +그러나 CNN 연구 방식이 도입된 후 특징을 미리 뽑아내는 것이 아니라 입력된 이미지에서 스스로 특징을 추출하도록 하여 사용하고 있다. + +(-> 다음 강의: neural network & backpropagation) \ No newline at end of file From 63b0145e96185c7a59e7ff08d36657f53143213d Mon Sep 17 00:00:00 2001 From: MSY99 Date: Mon, 21 Mar 2022 16:20:46 +0900 Subject: [PATCH 06/20] =?UTF-8?q?Revert=20"CV=5FWeek3=5F=EC=98=88=EC=8A=B5?= =?UTF-8?q?=EA=B3=BC=EC=A0=9C=5F=EB=AF=BC=EC=86=8C=EC=97=B0"?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit This reverts commit 8aaab2ac9770abcb1544a1cdfdcf569bbacbb293. --- ...0\354\212\265\352\263\274\354\240\234.txt" | 125 ------------------ 1 file changed, 125 deletions(-) delete mode 100644 "Week3_\354\230\210\354\212\265\352\263\274\354\240\234.txt" diff --git "a/Week3_\354\230\210\354\212\265\352\263\274\354\240\234.txt" "b/Week3_\354\230\210\354\212\265\352\263\274\354\240\234.txt" deleted file mode 100644 index 1e6a436..0000000 --- "a/Week3_\354\230\210\354\212\265\352\263\274\354\240\234.txt" +++ /dev/null @@ -1,125 +0,0 @@ -Linear Classifier에서 어떤 가중치(w) 값을 사용하느냐에 따라 정확도가 달라진 다는 것을 배웠다. -그렇다면 어떻게 최적의 가중치 값을 찾아야 하는지 알아야 하는데 이를 위해서 사용하는 정량화 방법이 loss function이다. -loss fuction은 어느 가중치 값이 얼마나 "안 좋은지"를 알려주는 지표이다. -그리고 이 안 좋은 가중치를 좋은 가중치로 바꿔나가는 과정을 optimization이라고 한다. -f(x, W) = Wx + b -이 식에서 x는 이미지, W는 가중치, b는 편향값이다. -이 식에서 loss를 구하는 방법은 각 카테고리 (고양이 자동차 개구리 등)별로 loss를 각각 구해서 그걸 모두 더한 후 평균을 내는 것이다. -강의 자료에서 제시된 고양이 자동차 개구리 이미지를 통해 loss를 구한 값들은 다음과 같다. - -- SVM loss (= hinge loss) -sj는 정답이 아닌 클래스의 score이고 syi는 정답 클래스의 score 값이다. -만약, syi > sj + safety margin(강의자료에서는 1)이면 loss = 0이고, -syi < sj + safety margin 이면 loss = sj - syi + safety margin이다. -SVM loss = SUM(j != y_i) { max (0, sj-syi+1) } -강의 자료의 고양이 자동차 개구리의 케이스로 계산한 SVM loss = 5.27이다. -고양이 자동차의 경우는 loss 값이 작지만 개구리에서 12.9의 loss 값이 나온다. - -Q1. 그런데 이 때 자동차의 score 값을 조금 변경해서 loss 값을 계산해도 loss 값이 크게 변동하지 않는 것을 볼 수 있다. -따라서, SVM hinge loss는 데이터에 민감하지 않다는 특성이 있음을 알 수 있다. -Q2. 그럼 최소 최댓값은 어떻게 될까? -loss의 최소값은 0이다. 그리고 최대값은 무한대이다. -Q3. 만약 W가 매우 작아져서 score가 0에 근사해지면 어떻게 되나? -계산해보면, 클래스 3개니까 (2+2+2)/3 = 2가 나오고 만일 클래스가 9개라면 (9+9+9+~+9)/10 = 9가 나올 것이다. -따라서 그럴 경우 loss = 클래스 갯수 -1이 된다. 이 계산은 디버그 용으로 사용한다. -0으로 해주었을 때 loss가 클래수 갯수 -1의 값으로 나오는지 검사하는 것이다. -이걸 sanity check라고 부른다. -Q4. 지금까지 계산하면서 정답 클래스 값을 제외하고 계산했는데 그 이유는? -정답 클래스 값을 포함해서 계산하게 되면 모든 경우에서 loss 값이 +1 증가하게 된다. -그러나 우리는 loss 값이 0에 근사하게 되길 바라기 때문에 정답 클래스 값을 제외하는 것이다. -Q5. 만약 sum 대신 평균을 이용하면 어떻게 되나? -계산해보면 딱히 상관은 없다. 단지 평균을 사용했기 때문에 scale만 작아질 뿐이다. -다만, loss가 0에 가까워지도록 하길 바라기 때문에 scale을 크게 해서 변화를 관찰하는 것이 좋은 방법일 수 있다! -Q6. 그럼 max 값에 제곱승을 해서 계산하면? -제곱승을 해서 계산하게 되면 nonlinear한 결과가 나오고, 답이 달라지게 된다. -이렇게 계산하는 방식을 squared hinge loss라고 하는데 때에 따라서는 이 방식이 잘 먹힐 때도 있다. -그래서 "아주 좋다"와 "아주 나쁘다"를 따질 때 유용한 방식이다. (그러나 잘 사용하지는 않음) - -그런데 이렇게 구하는 W 값은 과연 유일한 걸까? -> 아님 -각각의 score 값을 2배 혹은 3배 증가시켜도 똑같은 loss 값이 나올 수 있다. 따라서 W는 여러 개가 나올 수 있다. -유일하지 않는 W값이 문제가 되는 이유는 --> 우리는 새로운 값에 대해서 예측을 하기 위해 model을 만들기 때문에 test set에 더 관심이 많고 따라서 정확도도 test set을 통해서 추출한다. -그런데 지금까지 구한 W값은 train set에 맞춰서 나온 것들이기 때문에 최적값도 train set에 맞춰져서 나오게 된다. -그래서 그 최적값은 test set에는 맞지 않을 수도 있다는 문제가 있다. --> overfitting의 문제가 생길 수도 있다는 것이다. - -따라서 test set에도 맞을 수 있는 W값을 찾아야 하는데 이를 위해 사용하는 방식이 regularization이다. -L(W) = 1/N * SUM^N_(i=1) { Li(f(xi, W), yi) } + lamda R(W) -이 식에서 왼쪽의 항은 data loss이고 오른쪽의 항은 regularization이다. -data loss는 train set의 입장에서, regularazation은 test set의 입장에 있기 때문에 -이 식에 따르면, 매 loss 값을 계산할 때 마다 train에만 맞는 것을 학습하려고 하면 regularization에서 패널티를 부여하게 된다. -이 과정을 통해서 test set에도 맞는 W 값을 찾아나갈 수 있다. - -* 여기서 lamda R(W)가 무엇이길래 패널티를 부여하는 것일까? -일단 다항식이 너무 깊어지게 되면 복잡한 계산을 하게 되기 때문에 이를 방지하는 효과가 있다. -그리고 L1 regularization, L2 regularization이 있는데 -전자는 실제로 차수 값이 0이 되도록하고, 후자는 전체 차수의 값이 0에 가깝도록 유도한다. -따라서 L1은 원하는 특성이 제거될 수 있기 때문에 L2가 모든 것을 고려한다는 점에서 비교우위를 가지게 된다. -그리고 lamda 값은 규제의 강도 값이고, 높으면 모델이 단순해지며 underfitting / 낮으면 모델이 복잡해지며 overfitting이 된다는 문제가 있다. - -위와 같은 특성들 때문에 L1은 가중치 값 중 0이 있는 경우를, L2는 전체적으로 0에 가깝게 퍼진 가중치 값을 선호한다. - -어쨋든 우리의 목적에 더 부합하는 것은 L2 regularization이기 때문에 이를 더 많이 사용하고 이는 dropout, batch normalization에서도 많이 사용한다. - -- softmax classifier (=cross entropy) -모든 스코어에 exp를 취하고 그걸 모두 더한 뒤 원하는 클래스의 점수에 exp를 취해서 나눈다. -이렇게 계산한 것은 확률 값으로 도출되며, 이 때 원하는 정답 클래스에 -log를 취해 loss를 구하게 된다. -softmax는 multinomial logistic regression이다. (logistic regression = sigmoid function) -위와 같은 정의에 따라 위의 계산 방식에서 exp를 취해주는 것이다. -그리고 우리는 얼마나 "안" 좋은지를 판단하고자 하는데 -x축을 확률, y축을 loss라고 했을 때, -log의 함수가 확률이 1에 가까워질 수록 0에 가까워지기 때문에 -log를 취해 최종 loss를 구하게 되는 것이다. - -Q1. 이런 방식을 취했을 때 min, max는? -이론적으로 최소는 0, 최대는 무한대이다. (feat. -log graph) -Q2. 만약 score가 0에 가까워지면? --log(1/클래스 갯수)가 되고 이 또한 디버깅 용으로 사용하며, sanity check라고 불린다. - -강의자료에서는 예시 자료를 통해 svm과 softmax를 비교하고 있다. -1. max값을 취해서 loss를 구하는 것과 exp를 취해서 확률 값으로 loss를 구하는 것의 차이가 있다. -2. 만약 data point를 흔들어 주게 되면? -SVM의 경우에는 딱히 영향이 없었고 둔감하다는 결론이 나왔으나, -cross-entropy loss의 경우에는 조금만 데이터가 바뀌어도 확률에 영향이 있었고 매우 민감하다는 결론이 나온다. - -+) Full loss라는 것은 언제가 regularization을 추가한다. - -위와 같은 방식들을 통해서 얻은 결론은 "어떤 W값이 얼마나 안좋은지"이다. -그렇다면 좋은 W값은? -> Optimization을 통해 구할 수 있다. -optimization은 쉽게 말하면 산 골짜기의 가장 깊은 곳으로 내려가는 것과 같으며 이 과정이 곧 loss가 0에 가까워지도록 하는 것이다. -몇 가지 방법이 소개되고 있는데 그 중에서 Random search는 사용하지 말아야 한다. (연산 오래 걸릴 수 있음.) -보통은 Follow the slope (gradient descent)경사 하강법을 사용한다. - -1-dimension, the derivative of a function -d f(x) / d x = lim_(h->0) { ( f(x+h) - f(x) ) / h } (* 만약 다차원이면 편미분 형태의 식) -이렇게 수식으로 하나하나 계산해서 사용하는 방법 -> numerical 방법 (수치적 방법) -이 방식은 모든 가중치 W 값에 조금씩 변화를 줘가면서 loss 값의 변화를 관찰하는 것인데 이렇게 하면 너무 연산이 오래 걸린다. -단지 W가 변화할 때의 loss 값을 알고 싶을 뿐이라면? -미분을 이용한 analytic gradient(해석적 방법)을 사용한다. 이 방식을 사용하면 일일이 계산할 필요없이 딱! 원하는 값이 나오게 된다. -요약하자면, -numerical gradient: 정확하지 않고 느리지만 간편한 연산 방식 (오류가 덜 나는 편) -analytic gradient: 정확하고 빠르지만 복잡한 연산 방식 (오류가 날 가능성이 있음) -이다. 보통은 해석적 방법을 더 많이 사용하지만 디버깅을 할 때는 수치적 방법을 사용하기도 한다. 이를 gradient check라고 한다. - -위와 같이 gradient 계산한 것들은 앞에 -가 붙으면 음의 기울기이기 때문에 +방향으로 이동하고 -앞에 +가 붙으면 - 방향으로 이동하면서 그래프에서 가장 낮은 지점으로 이동한다. -여기서 한 번 이동할 때 이동하는 거리를 step size (=learning rate)라고 부른다. 이 값도 적절한 값을 찾아서 적용시키는 것이 중요하다. -그래서 임의의 w 위치에서 가운데 빨간색 지점으로 가는 것, 즉 기울기가 0에 가까운 지점으로 가는 것이 목표이다. - -+) 지금까지 계산한 방식들은 N을 한 번에 올려서 계산했는데, 만약 N이 굉장히 큰 값이라면 매우 비효율적인 결과가 나올 것이다. -그래서 이 N을 나눠서 계산하는 stochastic gradient descent (SGD)를 많이 사용한다. -mini batch를 두어서 데이터 갯수를 잘라 사용하는 것인데 보통 2의 제곱수 만큼 잘라서 사용한다. -(256개를 가지고 W를 업데이트하고 그 다음 256개를 가지고 W를 업데이트하는 것을 반복하는 식이다.) - -그냥 이미지를 그대로 넣어버리는 식으로 사용하는 것은 성능이 그닥 좋지 않았다. (이전 강의록의 말 머리가 2개 있는 식이라던가..) -그래서 CNN이 연구 되기 전까지는 이미지의 특징을 뽑아내고 이 특징을 합쳐서 linear regression에 넣는 방식을 사용해왔다. -이전에 linear classification으로 해결할 수 없는 것들의 예시를 보여주었었는데 이 때 극좌표계로 변환함으로써 직선으로 구분 가능한 형태로 바뀌는 경우가 있었다. -이미지를 활용할 때는 이렇게 하지 않지만 여기서 동기 부여를 받아 특징을 추출하는 방식으로 이어지게 된 것이다. -특징 추출의 한 가지 방법이 바로 color histogram이다. 컬러 hue 값이 있는데 여기에 어떤 컬러가 많이 나오는지 count 해서 특징을 추출하는 것이다. -2번 째 방법은 HoG(Historam of Oriented Gradients)이다. 방향 값을 히스토 그램으로 표현하는 것이다. -전체 이미지 내에서 어느 방향으로의 각도가 많은지 히스토그램으로 나타내 특징을 추출하는 것이다. -3번 째 방법은 bag of words이다. 자연어 처리에서 많이 사용하는 방법인데 -먼저 이미지를 여러 개로 잘라낸 뒤, 비지도 학습과 같이 클러스터링을 돌려 각도, 색 등의 특징을 추출한다. -이 후 새로운 이미지가 들어오면 이 이미지를 잘라내서 클러스터와 비교해 어떤 특징이 있는지 비교한다. - -그러나 CNN 연구 방식이 도입된 후 특징을 미리 뽑아내는 것이 아니라 입력된 이미지에서 스스로 특징을 추출하도록 하여 사용하고 있다. - -(-> 다음 강의: neural network & backpropagation) \ No newline at end of file From afe6b16d673b40c97383aaed1d4f82cf64341fb0 Mon Sep 17 00:00:00 2001 From: MSY99 Date: Mon, 21 Mar 2022 16:20:54 +0900 Subject: [PATCH 07/20] =?UTF-8?q?Revert=20"Create=20Week3=5FCV=5F=EC=98=88?= =?UTF-8?q?=EC=8A=B5=EA=B3=BC=EC=A0=9C=5F=EB=AF=BC=EC=86=8C=EC=97=B0"?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit This reverts commit 8cceb1f57cfc8564267785823d823e4d45afe17c. --- ...\234_\353\257\274\354\206\214\354\227\260" | 125 ------------------ 1 file changed, 125 deletions(-) delete mode 100644 "Week3_CV_\354\230\210\354\212\265\352\263\274\354\240\234_\353\257\274\354\206\214\354\227\260" diff --git "a/Week3_CV_\354\230\210\354\212\265\352\263\274\354\240\234_\353\257\274\354\206\214\354\227\260" "b/Week3_CV_\354\230\210\354\212\265\352\263\274\354\240\234_\353\257\274\354\206\214\354\227\260" deleted file mode 100644 index 0de57b8..0000000 --- "a/Week3_CV_\354\230\210\354\212\265\352\263\274\354\240\234_\353\257\274\354\206\214\354\227\260" +++ /dev/null @@ -1,125 +0,0 @@ -Linear Classifier에서 어떤 가중치(w) 값을 사용하느냐에 따라 정확도가 달라진 다는 것을 배웠다. -그렇다면 어떻게 최적의 가중치 값을 찾아야 하는지 알아야 하는데 이를 위해서 사용하는 정량화 방법이 loss function이다. -loss fuction은 어느 가중치 값이 얼마나 "안 좋은지"를 알려주는 지표이다. -그리고 이 안 좋은 가중치를 좋은 가중치로 바꿔나가는 과정을 optimization이라고 한다. -f(x, W) = Wx + b -이 식에서 x는 이미지, W는 가중치, b는 편향값이다. -이 식에서 loss를 구하는 방법은 각 카테고리 (고양이 자동차 개구리 등)별로 loss를 각각 구해서 그걸 모두 더한 후 평균을 내는 것이다. -강의 자료에서 제시된 고양이 자동차 개구리 이미지를 통해 loss를 구한 값들은 다음과 같다. - -- SVM loss (= hinge loss) -sj는 정답이 아닌 클래스의 score이고 syi는 정답 클래스의 score 값이다. -만약, syi > sj + safety margin(강의자료에서는 1)이면 loss = 0이고, -syi < sj + safety margin 이면 loss = sj - syi + safety margin이다. -SVM loss = SUM(j != y_i) { max (0, sj-syi+1) } -강의 자료의 고양이 자동차 개구리의 케이스로 계산한 SVM loss = 5.27이다. -고양이 자동차의 경우는 loss 값이 작지만 개구리에서 12.9의 loss 값이 나온다. - -Q1. 그런데 이 때 자동차의 score 값을 조금 변경해서 loss 값을 계산해도 loss 값이 크게 변동하지 않는 것을 볼 수 있다. -따라서, SVM hinge loss는 데이터에 민감하지 않다는 특성이 있음을 알 수 있다. -Q2. 그럼 최소 최댓값은 어떻게 될까? -loss의 최소값은 0이다. 그리고 최대값은 무한대이다. -Q3. 만약 W가 매우 작아져서 score가 0에 근사해지면 어떻게 되나? -계산해보면, 클래스 3개니까 (2+2+2)/3 = 2가 나오고 만일 클래스가 9개라면 (9+9+9+~+9)/10 = 9가 나올 것이다. -따라서 그럴 경우 loss = 클래스 갯수 -1이 된다. 이 계산은 디버그 용으로 사용한다. -0으로 해주었을 때 loss가 클래수 갯수 -1의 값으로 나오는지 검사하는 것이다. -이걸 sanity check라고 부른다. -Q4. 지금까지 계산하면서 정답 클래스 값을 제외하고 계산했는데 그 이유는? -정답 클래스 값을 포함해서 계산하게 되면 모든 경우에서 loss 값이 +1 증가하게 된다. -그러나 우리는 loss 값이 0에 근사하게 되길 바라기 때문에 정답 클래스 값을 제외하는 것이다. -Q5. 만약 sum 대신 평균을 이용하면 어떻게 되나? -계산해보면 딱히 상관은 없다. 단지 평균을 사용했기 때문에 scale만 작아질 뿐이다. -다만, loss가 0에 가까워지도록 하길 바라기 때문에 scale을 크게 해서 변화를 관찰하는 것이 좋은 방법일 수 있다! -Q6. 그럼 max 값에 제곱승을 해서 계산하면? -제곱승을 해서 계산하게 되면 nonlinear한 결과가 나오고, 답이 달라지게 된다. -이렇게 계산하는 방식을 squared hinge loss라고 하는데 때에 따라서는 이 방식이 잘 먹힐 때도 있다. -그래서 "아주 좋다"와 "아주 나쁘다"를 따질 때 유용한 방식이다. (그러나 잘 사용하지는 않음) - -그런데 이렇게 구하는 W 값은 과연 유일한 걸까? -> 아님 -각각의 score 값을 2배 혹은 3배 증가시켜도 똑같은 loss 값이 나올 수 있다. 따라서 W는 여러 개가 나올 수 있다. -유일하지 않는 W값이 문제가 되는 이유는 --> 우리는 새로운 값에 대해서 예측을 하기 위해 model을 만들기 때문에 test set에 더 관심이 많고 따라서 정확도도 test set을 통해서 추출한다. -그런데 지금까지 구한 W값은 train set에 맞춰서 나온 것들이기 때문에 최적값도 train set에 맞춰져서 나오게 된다. -그래서 그 최적값은 test set에는 맞지 않을 수도 있다는 문제가 있다. --> overfitting의 문제가 생길 수도 있다는 것이다. - -따라서 test set에도 맞을 수 있는 W값을 찾아야 하는데 이를 위해 사용하는 방식이 regularization이다. -L(W) = 1/N * SUM^N_(i=1) { Li(f(xi, W), yi) } + lamda R(W) -이 식에서 왼쪽의 항은 data loss이고 오른쪽의 항은 regularization이다. -data loss는 train set의 입장에서, regularazation은 test set의 입장에 있기 때문에 -이 식에 따르면, 매 loss 값을 계산할 때 마다 train에만 맞는 것을 학습하려고 하면 regularization에서 패널티를 부여하게 된다. -이 과정을 통해서 test set에도 맞는 W 값을 찾아나갈 수 있다. - -* 여기서 lamda R(W)가 무엇이길래 패널티를 부여하는 것일까? -일단 다항식이 너무 깊어지게 되면 복잡한 계산을 하게 되기 때문에 이를 방지하는 효과가 있다. -그리고 L1 regularization, L2 regularization이 있는데 -전자는 실제로 차수 값이 0이 되도록하고, 후자는 전체 차수의 값이 0에 가깝도록 유도한다. -따라서 L1은 원하는 특성이 제거될 수 있기 때문에 L2가 모든 것을 고려한다는 점에서 비교우위를 가지게 된다. -그리고 lamda 값은 규제의 강도 값이고, 높으면 모델이 단순해지며 underfitting / 낮으면 모델이 복잡해지며 overfitting이 된다는 문제가 있다. - -위와 같은 특성들 때문에 L1은 가중치 값 중 0이 있는 경우를, L2는 전체적으로 0에 가깝게 퍼진 가중치 값을 선호한다. - -어쨋든 우리의 목적에 더 부합하는 것은 L2 regularization이기 때문에 이를 더 많이 사용하고 이는 dropout, batch normalization에서도 많이 사용한다. - -- softmax classifier (=cross entropy) -모든 스코어에 exp를 취하고 그걸 모두 더한 뒤 원하는 클래스의 점수에 exp를 취해서 나눈다. -이렇게 계산한 것은 확률 값으로 도출되며, 이 때 원하는 정답 클래스에 -log를 취해 loss를 구하게 된다. -softmax는 multinomial logistic regression이다. (logistic regression = sigmoid function) -위와 같은 정의에 따라 위의 계산 방식에서 exp를 취해주는 것이다. -그리고 우리는 얼마나 "안" 좋은지를 판단하고자 하는데 -x축을 확률, y축을 loss라고 했을 때, -log의 함수가 확률이 1에 가까워질 수록 0에 가까워지기 때문에 -log를 취해 최종 loss를 구하게 되는 것이다. - -Q1. 이런 방식을 취했을 때 min, max는? -이론적으로 최소는 0, 최대는 무한대이다. (feat. -log graph) -Q2. 만약 score가 0에 가까워지면? --log(1/클래스 갯수)가 되고 이 또한 디버깅 용으로 사용하며, sanity check라고 불린다. - -강의자료에서는 예시 자료를 통해 svm과 softmax를 비교하고 있다. -1. max값을 취해서 loss를 구하는 것과 exp를 취해서 확률 값으로 loss를 구하는 것의 차이가 있다. -2. 만약 data point를 흔들어 주게 되면? -SVM의 경우에는 딱히 영향이 없었고 둔감하다는 결론이 나왔으나, -cross-entropy loss의 경우에는 조금만 데이터가 바뀌어도 확률에 영향이 있었고 매우 민감하다는 결론이 나온다. - -+) Full loss라는 것은 언제가 regularization을 추가한다. - -위와 같은 방식들을 통해서 얻은 결론은 "어떤 W값이 얼마나 안좋은지"이다. -그렇다면 좋은 W값은? -> Optimization을 통해 구할 수 있다. -optimization은 쉽게 말하면 산 골짜기의 가장 깊은 곳으로 내려가는 것과 같으며 이 과정이 곧 loss가 0에 가까워지도록 하는 것이다. -몇 가지 방법이 소개되고 있는데 그 중에서 Random search는 사용하지 말아야 한다. (연산 오래 걸릴 수 있음.) -보통은 Follow the slope (gradient descent)경사 하강법을 사용한다. - -1-dimension, the derivative of a function -d f(x) / d x = lim_(h->0) { ( f(x+h) - f(x) ) / h } (* 만약 다차원이면 편미분 형태의 식) -이렇게 수식으로 하나하나 계산해서 사용하는 방법 -> numerical 방법 (수치적 방법) -이 방식은 모든 가중치 W 값에 조금씩 변화를 줘가면서 loss 값의 변화를 관찰하는 것인데 이렇게 하면 너무 연산이 오래 걸린다. -단지 W가 변화할 때의 loss 값을 알고 싶을 뿐이라면? -미분을 이용한 analytic gradient(해석적 방법)을 사용한다. 이 방식을 사용하면 일일이 계산할 필요없이 딱! 원하는 값이 나오게 된다. -요약하자면, -numerical gradient: 정확하지 않고 느리지만 간편한 연산 방식 (오류가 덜 나는 편) -analytic gradient: 정확하고 빠르지만 복잡한 연산 방식 (오류가 날 가능성이 있음) -이다. 보통은 해석적 방법을 더 많이 사용하지만 디버깅을 할 때는 수치적 방법을 사용하기도 한다. 이를 gradient check라고 한다. - -위와 같이 gradient 계산한 것들은 앞에 -가 붙으면 음의 기울기이기 때문에 +방향으로 이동하고 -앞에 +가 붙으면 - 방향으로 이동하면서 그래프에서 가장 낮은 지점으로 이동한다. -여기서 한 번 이동할 때 이동하는 거리를 step size (=learning rate)라고 부른다. 이 값도 적절한 값을 찾아서 적용시키는 것이 중요하다. -그래서 임의의 w 위치에서 가운데 빨간색 지점으로 가는 것, 즉 기울기가 0에 가까운 지점으로 가는 것이 목표이다. - -+) 지금까지 계산한 방식들은 N을 한 번에 올려서 계산했는데, 만약 N이 굉장히 큰 값이라면 매우 비효율적인 결과가 나올 것이다. -그래서 이 N을 나눠서 계산하는 stochastic gradient descent (SGD)를 많이 사용한다. -mini batch를 두어서 데이터 갯수를 잘라 사용하는 것인데 보통 2의 제곱수 만큼 잘라서 사용한다. -(256개를 가지고 W를 업데이트하고 그 다음 256개를 가지고 W를 업데이트하는 것을 반복하는 식이다.) - -그냥 이미지를 그대로 넣어버리는 식으로 사용하는 것은 성능이 그닥 좋지 않았다. (이전 강의록의 말 머리가 2개 있는 식이라던가..) -그래서 CNN이 연구 되기 전까지는 이미지의 특징을 뽑아내고 이 특징을 합쳐서 linear regression에 넣는 방식을 사용해왔다. -이전에 linear classification으로 해결할 수 없는 것들의 예시를 보여주었었는데 이 때 극좌표계로 변환함으로써 직선으로 구분 가능한 형태로 바뀌는 경우가 있었다. -이미지를 활용할 때는 이렇게 하지 않지만 여기서 동기 부여를 받아 특징을 추출하는 방식으로 이어지게 된 것이다. -특징 추출의 한 가지 방법이 바로 color histogram이다. 컬러 hue 값이 있는데 여기에 어떤 컬러가 많이 나오는지 count 해서 특징을 추출하는 것이다. -2번 째 방법은 HoG(Historam of Oriented Gradients)이다. 방향 값을 히스토 그램으로 표현하는 것이다. -전체 이미지 내에서 어느 방향으로의 각도가 많은지 히스토그램으로 나타내 특징을 추출하는 것이다. -3번 째 방법은 bag of words이다. 자연어 처리에서 많이 사용하는 방법인데 -먼저 이미지를 여러 개로 잘라낸 뒤, 비지도 학습과 같이 클러스터링을 돌려 각도, 색 등의 특징을 추출한다. -이 후 새로운 이미지가 들어오면 이 이미지를 잘라내서 클러스터와 비교해 어떤 특징이 있는지 비교한다. - -그러나 CNN 연구 방식이 도입된 후 특징을 미리 뽑아내는 것이 아니라 입력된 이미지에서 스스로 특징을 추출하도록 하여 사용하고 있다. - -(-> 다음 강의: neural network & backpropagation) From c9d07149ddd57b6a9d76c04bd87c818e48fb494c Mon Sep 17 00:00:00 2001 From: MSY99 Date: Mon, 21 Mar 2022 16:23:05 +0900 Subject: [PATCH 08/20] =?UTF-8?q?CV=5FWeek3=5F=EC=98=88=EC=8A=B5=EA=B3=BC?= =?UTF-8?q?=EC=A0=9C=5F=EB=AF=BC=EC=86=8C=EC=97=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- ...0\354\212\265\352\263\274\354\240\234.txt" | 125 ++++++++++++++++++ 1 file changed, 125 insertions(+) create mode 100644 "Week3_\354\230\210\354\212\265\352\263\274\354\240\234.txt" diff --git "a/Week3_\354\230\210\354\212\265\352\263\274\354\240\234.txt" "b/Week3_\354\230\210\354\212\265\352\263\274\354\240\234.txt" new file mode 100644 index 0000000..1e6a436 --- /dev/null +++ "b/Week3_\354\230\210\354\212\265\352\263\274\354\240\234.txt" @@ -0,0 +1,125 @@ +Linear Classifier에서 어떤 가중치(w) 값을 사용하느냐에 따라 정확도가 달라진 다는 것을 배웠다. +그렇다면 어떻게 최적의 가중치 값을 찾아야 하는지 알아야 하는데 이를 위해서 사용하는 정량화 방법이 loss function이다. +loss fuction은 어느 가중치 값이 얼마나 "안 좋은지"를 알려주는 지표이다. +그리고 이 안 좋은 가중치를 좋은 가중치로 바꿔나가는 과정을 optimization이라고 한다. +f(x, W) = Wx + b +이 식에서 x는 이미지, W는 가중치, b는 편향값이다. +이 식에서 loss를 구하는 방법은 각 카테고리 (고양이 자동차 개구리 등)별로 loss를 각각 구해서 그걸 모두 더한 후 평균을 내는 것이다. +강의 자료에서 제시된 고양이 자동차 개구리 이미지를 통해 loss를 구한 값들은 다음과 같다. + +- SVM loss (= hinge loss) +sj는 정답이 아닌 클래스의 score이고 syi는 정답 클래스의 score 값이다. +만약, syi > sj + safety margin(강의자료에서는 1)이면 loss = 0이고, +syi < sj + safety margin 이면 loss = sj - syi + safety margin이다. +SVM loss = SUM(j != y_i) { max (0, sj-syi+1) } +강의 자료의 고양이 자동차 개구리의 케이스로 계산한 SVM loss = 5.27이다. +고양이 자동차의 경우는 loss 값이 작지만 개구리에서 12.9의 loss 값이 나온다. + +Q1. 그런데 이 때 자동차의 score 값을 조금 변경해서 loss 값을 계산해도 loss 값이 크게 변동하지 않는 것을 볼 수 있다. +따라서, SVM hinge loss는 데이터에 민감하지 않다는 특성이 있음을 알 수 있다. +Q2. 그럼 최소 최댓값은 어떻게 될까? +loss의 최소값은 0이다. 그리고 최대값은 무한대이다. +Q3. 만약 W가 매우 작아져서 score가 0에 근사해지면 어떻게 되나? +계산해보면, 클래스 3개니까 (2+2+2)/3 = 2가 나오고 만일 클래스가 9개라면 (9+9+9+~+9)/10 = 9가 나올 것이다. +따라서 그럴 경우 loss = 클래스 갯수 -1이 된다. 이 계산은 디버그 용으로 사용한다. +0으로 해주었을 때 loss가 클래수 갯수 -1의 값으로 나오는지 검사하는 것이다. +이걸 sanity check라고 부른다. +Q4. 지금까지 계산하면서 정답 클래스 값을 제외하고 계산했는데 그 이유는? +정답 클래스 값을 포함해서 계산하게 되면 모든 경우에서 loss 값이 +1 증가하게 된다. +그러나 우리는 loss 값이 0에 근사하게 되길 바라기 때문에 정답 클래스 값을 제외하는 것이다. +Q5. 만약 sum 대신 평균을 이용하면 어떻게 되나? +계산해보면 딱히 상관은 없다. 단지 평균을 사용했기 때문에 scale만 작아질 뿐이다. +다만, loss가 0에 가까워지도록 하길 바라기 때문에 scale을 크게 해서 변화를 관찰하는 것이 좋은 방법일 수 있다! +Q6. 그럼 max 값에 제곱승을 해서 계산하면? +제곱승을 해서 계산하게 되면 nonlinear한 결과가 나오고, 답이 달라지게 된다. +이렇게 계산하는 방식을 squared hinge loss라고 하는데 때에 따라서는 이 방식이 잘 먹힐 때도 있다. +그래서 "아주 좋다"와 "아주 나쁘다"를 따질 때 유용한 방식이다. (그러나 잘 사용하지는 않음) + +그런데 이렇게 구하는 W 값은 과연 유일한 걸까? -> 아님 +각각의 score 값을 2배 혹은 3배 증가시켜도 똑같은 loss 값이 나올 수 있다. 따라서 W는 여러 개가 나올 수 있다. +유일하지 않는 W값이 문제가 되는 이유는 +-> 우리는 새로운 값에 대해서 예측을 하기 위해 model을 만들기 때문에 test set에 더 관심이 많고 따라서 정확도도 test set을 통해서 추출한다. +그런데 지금까지 구한 W값은 train set에 맞춰서 나온 것들이기 때문에 최적값도 train set에 맞춰져서 나오게 된다. +그래서 그 최적값은 test set에는 맞지 않을 수도 있다는 문제가 있다. +-> overfitting의 문제가 생길 수도 있다는 것이다. + +따라서 test set에도 맞을 수 있는 W값을 찾아야 하는데 이를 위해 사용하는 방식이 regularization이다. +L(W) = 1/N * SUM^N_(i=1) { Li(f(xi, W), yi) } + lamda R(W) +이 식에서 왼쪽의 항은 data loss이고 오른쪽의 항은 regularization이다. +data loss는 train set의 입장에서, regularazation은 test set의 입장에 있기 때문에 +이 식에 따르면, 매 loss 값을 계산할 때 마다 train에만 맞는 것을 학습하려고 하면 regularization에서 패널티를 부여하게 된다. +이 과정을 통해서 test set에도 맞는 W 값을 찾아나갈 수 있다. + +* 여기서 lamda R(W)가 무엇이길래 패널티를 부여하는 것일까? +일단 다항식이 너무 깊어지게 되면 복잡한 계산을 하게 되기 때문에 이를 방지하는 효과가 있다. +그리고 L1 regularization, L2 regularization이 있는데 +전자는 실제로 차수 값이 0이 되도록하고, 후자는 전체 차수의 값이 0에 가깝도록 유도한다. +따라서 L1은 원하는 특성이 제거될 수 있기 때문에 L2가 모든 것을 고려한다는 점에서 비교우위를 가지게 된다. +그리고 lamda 값은 규제의 강도 값이고, 높으면 모델이 단순해지며 underfitting / 낮으면 모델이 복잡해지며 overfitting이 된다는 문제가 있다. + +위와 같은 특성들 때문에 L1은 가중치 값 중 0이 있는 경우를, L2는 전체적으로 0에 가깝게 퍼진 가중치 값을 선호한다. + +어쨋든 우리의 목적에 더 부합하는 것은 L2 regularization이기 때문에 이를 더 많이 사용하고 이는 dropout, batch normalization에서도 많이 사용한다. + +- softmax classifier (=cross entropy) +모든 스코어에 exp를 취하고 그걸 모두 더한 뒤 원하는 클래스의 점수에 exp를 취해서 나눈다. +이렇게 계산한 것은 확률 값으로 도출되며, 이 때 원하는 정답 클래스에 -log를 취해 loss를 구하게 된다. +softmax는 multinomial logistic regression이다. (logistic regression = sigmoid function) +위와 같은 정의에 따라 위의 계산 방식에서 exp를 취해주는 것이다. +그리고 우리는 얼마나 "안" 좋은지를 판단하고자 하는데 +x축을 확률, y축을 loss라고 했을 때, -log의 함수가 확률이 1에 가까워질 수록 0에 가까워지기 때문에 -log를 취해 최종 loss를 구하게 되는 것이다. + +Q1. 이런 방식을 취했을 때 min, max는? +이론적으로 최소는 0, 최대는 무한대이다. (feat. -log graph) +Q2. 만약 score가 0에 가까워지면? +-log(1/클래스 갯수)가 되고 이 또한 디버깅 용으로 사용하며, sanity check라고 불린다. + +강의자료에서는 예시 자료를 통해 svm과 softmax를 비교하고 있다. +1. max값을 취해서 loss를 구하는 것과 exp를 취해서 확률 값으로 loss를 구하는 것의 차이가 있다. +2. 만약 data point를 흔들어 주게 되면? +SVM의 경우에는 딱히 영향이 없었고 둔감하다는 결론이 나왔으나, +cross-entropy loss의 경우에는 조금만 데이터가 바뀌어도 확률에 영향이 있었고 매우 민감하다는 결론이 나온다. + ++) Full loss라는 것은 언제가 regularization을 추가한다. + +위와 같은 방식들을 통해서 얻은 결론은 "어떤 W값이 얼마나 안좋은지"이다. +그렇다면 좋은 W값은? -> Optimization을 통해 구할 수 있다. +optimization은 쉽게 말하면 산 골짜기의 가장 깊은 곳으로 내려가는 것과 같으며 이 과정이 곧 loss가 0에 가까워지도록 하는 것이다. +몇 가지 방법이 소개되고 있는데 그 중에서 Random search는 사용하지 말아야 한다. (연산 오래 걸릴 수 있음.) +보통은 Follow the slope (gradient descent)경사 하강법을 사용한다. + +1-dimension, the derivative of a function +d f(x) / d x = lim_(h->0) { ( f(x+h) - f(x) ) / h } (* 만약 다차원이면 편미분 형태의 식) +이렇게 수식으로 하나하나 계산해서 사용하는 방법 -> numerical 방법 (수치적 방법) +이 방식은 모든 가중치 W 값에 조금씩 변화를 줘가면서 loss 값의 변화를 관찰하는 것인데 이렇게 하면 너무 연산이 오래 걸린다. +단지 W가 변화할 때의 loss 값을 알고 싶을 뿐이라면? +미분을 이용한 analytic gradient(해석적 방법)을 사용한다. 이 방식을 사용하면 일일이 계산할 필요없이 딱! 원하는 값이 나오게 된다. +요약하자면, +numerical gradient: 정확하지 않고 느리지만 간편한 연산 방식 (오류가 덜 나는 편) +analytic gradient: 정확하고 빠르지만 복잡한 연산 방식 (오류가 날 가능성이 있음) +이다. 보통은 해석적 방법을 더 많이 사용하지만 디버깅을 할 때는 수치적 방법을 사용하기도 한다. 이를 gradient check라고 한다. + +위와 같이 gradient 계산한 것들은 앞에 -가 붙으면 음의 기울기이기 때문에 +방향으로 이동하고 +앞에 +가 붙으면 - 방향으로 이동하면서 그래프에서 가장 낮은 지점으로 이동한다. +여기서 한 번 이동할 때 이동하는 거리를 step size (=learning rate)라고 부른다. 이 값도 적절한 값을 찾아서 적용시키는 것이 중요하다. +그래서 임의의 w 위치에서 가운데 빨간색 지점으로 가는 것, 즉 기울기가 0에 가까운 지점으로 가는 것이 목표이다. + ++) 지금까지 계산한 방식들은 N을 한 번에 올려서 계산했는데, 만약 N이 굉장히 큰 값이라면 매우 비효율적인 결과가 나올 것이다. +그래서 이 N을 나눠서 계산하는 stochastic gradient descent (SGD)를 많이 사용한다. +mini batch를 두어서 데이터 갯수를 잘라 사용하는 것인데 보통 2의 제곱수 만큼 잘라서 사용한다. +(256개를 가지고 W를 업데이트하고 그 다음 256개를 가지고 W를 업데이트하는 것을 반복하는 식이다.) + +그냥 이미지를 그대로 넣어버리는 식으로 사용하는 것은 성능이 그닥 좋지 않았다. (이전 강의록의 말 머리가 2개 있는 식이라던가..) +그래서 CNN이 연구 되기 전까지는 이미지의 특징을 뽑아내고 이 특징을 합쳐서 linear regression에 넣는 방식을 사용해왔다. +이전에 linear classification으로 해결할 수 없는 것들의 예시를 보여주었었는데 이 때 극좌표계로 변환함으로써 직선으로 구분 가능한 형태로 바뀌는 경우가 있었다. +이미지를 활용할 때는 이렇게 하지 않지만 여기서 동기 부여를 받아 특징을 추출하는 방식으로 이어지게 된 것이다. +특징 추출의 한 가지 방법이 바로 color histogram이다. 컬러 hue 값이 있는데 여기에 어떤 컬러가 많이 나오는지 count 해서 특징을 추출하는 것이다. +2번 째 방법은 HoG(Historam of Oriented Gradients)이다. 방향 값을 히스토 그램으로 표현하는 것이다. +전체 이미지 내에서 어느 방향으로의 각도가 많은지 히스토그램으로 나타내 특징을 추출하는 것이다. +3번 째 방법은 bag of words이다. 자연어 처리에서 많이 사용하는 방법인데 +먼저 이미지를 여러 개로 잘라낸 뒤, 비지도 학습과 같이 클러스터링을 돌려 각도, 색 등의 특징을 추출한다. +이 후 새로운 이미지가 들어오면 이 이미지를 잘라내서 클러스터와 비교해 어떤 특징이 있는지 비교한다. + +그러나 CNN 연구 방식이 도입된 후 특징을 미리 뽑아내는 것이 아니라 입력된 이미지에서 스스로 특징을 추출하도록 하여 사용하고 있다. + +(-> 다음 강의: neural network & backpropagation) \ No newline at end of file From 03184abd9b33a6ca76aad08b2c072f56919f638c Mon Sep 17 00:00:00 2001 From: MSY99 <101084413+MSY99@users.noreply.github.com> Date: Mon, 21 Mar 2022 16:24:32 +0900 Subject: [PATCH 09/20] =?UTF-8?q?CV=5FWeek3=5F=EC=98=88=EC=8A=B5=EA=B3=BC?= =?UTF-8?q?=EC=A0=9C=5F=EB=AF=BC=EC=86=8C=EC=97=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 제발 PR 좀 돼라 --- ...0\354\212\265\352\263\274\354\240\234.txt" | 248 +++++++++--------- 1 file changed, 124 insertions(+), 124 deletions(-) diff --git "a/Week3_\354\230\210\354\212\265\352\263\274\354\240\234.txt" "b/Week3_\354\230\210\354\212\265\352\263\274\354\240\234.txt" index 1e6a436..eff9664 100644 --- "a/Week3_\354\230\210\354\212\265\352\263\274\354\240\234.txt" +++ "b/Week3_\354\230\210\354\212\265\352\263\274\354\240\234.txt" @@ -1,125 +1,125 @@ -Linear Classifier에서 어떤 가중치(w) 값을 사용하느냐에 따라 정확도가 달라진 다는 것을 배웠다. -그렇다면 어떻게 최적의 가중치 값을 찾아야 하는지 알아야 하는데 이를 위해서 사용하는 정량화 방법이 loss function이다. -loss fuction은 어느 가중치 값이 얼마나 "안 좋은지"를 알려주는 지표이다. -그리고 이 안 좋은 가중치를 좋은 가중치로 바꿔나가는 과정을 optimization이라고 한다. -f(x, W) = Wx + b -이 식에서 x는 이미지, W는 가중치, b는 편향값이다. -이 식에서 loss를 구하는 방법은 각 카테고리 (고양이 자동차 개구리 등)별로 loss를 각각 구해서 그걸 모두 더한 후 평균을 내는 것이다. -강의 자료에서 제시된 고양이 자동차 개구리 이미지를 통해 loss를 구한 값들은 다음과 같다. - -- SVM loss (= hinge loss) -sj는 정답이 아닌 클래스의 score이고 syi는 정답 클래스의 score 값이다. -만약, syi > sj + safety margin(강의자료에서는 1)이면 loss = 0이고, -syi < sj + safety margin 이면 loss = sj - syi + safety margin이다. -SVM loss = SUM(j != y_i) { max (0, sj-syi+1) } -강의 자료의 고양이 자동차 개구리의 케이스로 계산한 SVM loss = 5.27이다. -고양이 자동차의 경우는 loss 값이 작지만 개구리에서 12.9의 loss 값이 나온다. - -Q1. 그런데 이 때 자동차의 score 값을 조금 변경해서 loss 값을 계산해도 loss 값이 크게 변동하지 않는 것을 볼 수 있다. -따라서, SVM hinge loss는 데이터에 민감하지 않다는 특성이 있음을 알 수 있다. -Q2. 그럼 최소 최댓값은 어떻게 될까? -loss의 최소값은 0이다. 그리고 최대값은 무한대이다. -Q3. 만약 W가 매우 작아져서 score가 0에 근사해지면 어떻게 되나? -계산해보면, 클래스 3개니까 (2+2+2)/3 = 2가 나오고 만일 클래스가 9개라면 (9+9+9+~+9)/10 = 9가 나올 것이다. -따라서 그럴 경우 loss = 클래스 갯수 -1이 된다. 이 계산은 디버그 용으로 사용한다. -0으로 해주었을 때 loss가 클래수 갯수 -1의 값으로 나오는지 검사하는 것이다. -이걸 sanity check라고 부른다. -Q4. 지금까지 계산하면서 정답 클래스 값을 제외하고 계산했는데 그 이유는? -정답 클래스 값을 포함해서 계산하게 되면 모든 경우에서 loss 값이 +1 증가하게 된다. -그러나 우리는 loss 값이 0에 근사하게 되길 바라기 때문에 정답 클래스 값을 제외하는 것이다. -Q5. 만약 sum 대신 평균을 이용하면 어떻게 되나? -계산해보면 딱히 상관은 없다. 단지 평균을 사용했기 때문에 scale만 작아질 뿐이다. -다만, loss가 0에 가까워지도록 하길 바라기 때문에 scale을 크게 해서 변화를 관찰하는 것이 좋은 방법일 수 있다! -Q6. 그럼 max 값에 제곱승을 해서 계산하면? -제곱승을 해서 계산하게 되면 nonlinear한 결과가 나오고, 답이 달라지게 된다. -이렇게 계산하는 방식을 squared hinge loss라고 하는데 때에 따라서는 이 방식이 잘 먹힐 때도 있다. -그래서 "아주 좋다"와 "아주 나쁘다"를 따질 때 유용한 방식이다. (그러나 잘 사용하지는 않음) - -그런데 이렇게 구하는 W 값은 과연 유일한 걸까? -> 아님 -각각의 score 값을 2배 혹은 3배 증가시켜도 똑같은 loss 값이 나올 수 있다. 따라서 W는 여러 개가 나올 수 있다. -유일하지 않는 W값이 문제가 되는 이유는 --> 우리는 새로운 값에 대해서 예측을 하기 위해 model을 만들기 때문에 test set에 더 관심이 많고 따라서 정확도도 test set을 통해서 추출한다. -그런데 지금까지 구한 W값은 train set에 맞춰서 나온 것들이기 때문에 최적값도 train set에 맞춰져서 나오게 된다. -그래서 그 최적값은 test set에는 맞지 않을 수도 있다는 문제가 있다. --> overfitting의 문제가 생길 수도 있다는 것이다. - -따라서 test set에도 맞을 수 있는 W값을 찾아야 하는데 이를 위해 사용하는 방식이 regularization이다. -L(W) = 1/N * SUM^N_(i=1) { Li(f(xi, W), yi) } + lamda R(W) -이 식에서 왼쪽의 항은 data loss이고 오른쪽의 항은 regularization이다. -data loss는 train set의 입장에서, regularazation은 test set의 입장에 있기 때문에 -이 식에 따르면, 매 loss 값을 계산할 때 마다 train에만 맞는 것을 학습하려고 하면 regularization에서 패널티를 부여하게 된다. -이 과정을 통해서 test set에도 맞는 W 값을 찾아나갈 수 있다. - -* 여기서 lamda R(W)가 무엇이길래 패널티를 부여하는 것일까? -일단 다항식이 너무 깊어지게 되면 복잡한 계산을 하게 되기 때문에 이를 방지하는 효과가 있다. -그리고 L1 regularization, L2 regularization이 있는데 -전자는 실제로 차수 값이 0이 되도록하고, 후자는 전체 차수의 값이 0에 가깝도록 유도한다. -따라서 L1은 원하는 특성이 제거될 수 있기 때문에 L2가 모든 것을 고려한다는 점에서 비교우위를 가지게 된다. -그리고 lamda 값은 규제의 강도 값이고, 높으면 모델이 단순해지며 underfitting / 낮으면 모델이 복잡해지며 overfitting이 된다는 문제가 있다. - -위와 같은 특성들 때문에 L1은 가중치 값 중 0이 있는 경우를, L2는 전체적으로 0에 가깝게 퍼진 가중치 값을 선호한다. - -어쨋든 우리의 목적에 더 부합하는 것은 L2 regularization이기 때문에 이를 더 많이 사용하고 이는 dropout, batch normalization에서도 많이 사용한다. - -- softmax classifier (=cross entropy) -모든 스코어에 exp를 취하고 그걸 모두 더한 뒤 원하는 클래스의 점수에 exp를 취해서 나눈다. -이렇게 계산한 것은 확률 값으로 도출되며, 이 때 원하는 정답 클래스에 -log를 취해 loss를 구하게 된다. -softmax는 multinomial logistic regression이다. (logistic regression = sigmoid function) -위와 같은 정의에 따라 위의 계산 방식에서 exp를 취해주는 것이다. -그리고 우리는 얼마나 "안" 좋은지를 판단하고자 하는데 -x축을 확률, y축을 loss라고 했을 때, -log의 함수가 확률이 1에 가까워질 수록 0에 가까워지기 때문에 -log를 취해 최종 loss를 구하게 되는 것이다. - -Q1. 이런 방식을 취했을 때 min, max는? -이론적으로 최소는 0, 최대는 무한대이다. (feat. -log graph) -Q2. 만약 score가 0에 가까워지면? --log(1/클래스 갯수)가 되고 이 또한 디버깅 용으로 사용하며, sanity check라고 불린다. - -강의자료에서는 예시 자료를 통해 svm과 softmax를 비교하고 있다. -1. max값을 취해서 loss를 구하는 것과 exp를 취해서 확률 값으로 loss를 구하는 것의 차이가 있다. -2. 만약 data point를 흔들어 주게 되면? -SVM의 경우에는 딱히 영향이 없었고 둔감하다는 결론이 나왔으나, -cross-entropy loss의 경우에는 조금만 데이터가 바뀌어도 확률에 영향이 있었고 매우 민감하다는 결론이 나온다. - -+) Full loss라는 것은 언제가 regularization을 추가한다. - -위와 같은 방식들을 통해서 얻은 결론은 "어떤 W값이 얼마나 안좋은지"이다. -그렇다면 좋은 W값은? -> Optimization을 통해 구할 수 있다. -optimization은 쉽게 말하면 산 골짜기의 가장 깊은 곳으로 내려가는 것과 같으며 이 과정이 곧 loss가 0에 가까워지도록 하는 것이다. -몇 가지 방법이 소개되고 있는데 그 중에서 Random search는 사용하지 말아야 한다. (연산 오래 걸릴 수 있음.) -보통은 Follow the slope (gradient descent)경사 하강법을 사용한다. - -1-dimension, the derivative of a function -d f(x) / d x = lim_(h->0) { ( f(x+h) - f(x) ) / h } (* 만약 다차원이면 편미분 형태의 식) -이렇게 수식으로 하나하나 계산해서 사용하는 방법 -> numerical 방법 (수치적 방법) -이 방식은 모든 가중치 W 값에 조금씩 변화를 줘가면서 loss 값의 변화를 관찰하는 것인데 이렇게 하면 너무 연산이 오래 걸린다. -단지 W가 변화할 때의 loss 값을 알고 싶을 뿐이라면? -미분을 이용한 analytic gradient(해석적 방법)을 사용한다. 이 방식을 사용하면 일일이 계산할 필요없이 딱! 원하는 값이 나오게 된다. -요약하자면, -numerical gradient: 정확하지 않고 느리지만 간편한 연산 방식 (오류가 덜 나는 편) -analytic gradient: 정확하고 빠르지만 복잡한 연산 방식 (오류가 날 가능성이 있음) -이다. 보통은 해석적 방법을 더 많이 사용하지만 디버깅을 할 때는 수치적 방법을 사용하기도 한다. 이를 gradient check라고 한다. - -위와 같이 gradient 계산한 것들은 앞에 -가 붙으면 음의 기울기이기 때문에 +방향으로 이동하고 -앞에 +가 붙으면 - 방향으로 이동하면서 그래프에서 가장 낮은 지점으로 이동한다. -여기서 한 번 이동할 때 이동하는 거리를 step size (=learning rate)라고 부른다. 이 값도 적절한 값을 찾아서 적용시키는 것이 중요하다. -그래서 임의의 w 위치에서 가운데 빨간색 지점으로 가는 것, 즉 기울기가 0에 가까운 지점으로 가는 것이 목표이다. - -+) 지금까지 계산한 방식들은 N을 한 번에 올려서 계산했는데, 만약 N이 굉장히 큰 값이라면 매우 비효율적인 결과가 나올 것이다. -그래서 이 N을 나눠서 계산하는 stochastic gradient descent (SGD)를 많이 사용한다. -mini batch를 두어서 데이터 갯수를 잘라 사용하는 것인데 보통 2의 제곱수 만큼 잘라서 사용한다. -(256개를 가지고 W를 업데이트하고 그 다음 256개를 가지고 W를 업데이트하는 것을 반복하는 식이다.) - -그냥 이미지를 그대로 넣어버리는 식으로 사용하는 것은 성능이 그닥 좋지 않았다. (이전 강의록의 말 머리가 2개 있는 식이라던가..) -그래서 CNN이 연구 되기 전까지는 이미지의 특징을 뽑아내고 이 특징을 합쳐서 linear regression에 넣는 방식을 사용해왔다. -이전에 linear classification으로 해결할 수 없는 것들의 예시를 보여주었었는데 이 때 극좌표계로 변환함으로써 직선으로 구분 가능한 형태로 바뀌는 경우가 있었다. -이미지를 활용할 때는 이렇게 하지 않지만 여기서 동기 부여를 받아 특징을 추출하는 방식으로 이어지게 된 것이다. -특징 추출의 한 가지 방법이 바로 color histogram이다. 컬러 hue 값이 있는데 여기에 어떤 컬러가 많이 나오는지 count 해서 특징을 추출하는 것이다. -2번 째 방법은 HoG(Historam of Oriented Gradients)이다. 방향 값을 히스토 그램으로 표현하는 것이다. -전체 이미지 내에서 어느 방향으로의 각도가 많은지 히스토그램으로 나타내 특징을 추출하는 것이다. -3번 째 방법은 bag of words이다. 자연어 처리에서 많이 사용하는 방법인데 -먼저 이미지를 여러 개로 잘라낸 뒤, 비지도 학습과 같이 클러스터링을 돌려 각도, 색 등의 특징을 추출한다. -이 후 새로운 이미지가 들어오면 이 이미지를 잘라내서 클러스터와 비교해 어떤 특징이 있는지 비교한다. - -그러나 CNN 연구 방식이 도입된 후 특징을 미리 뽑아내는 것이 아니라 입력된 이미지에서 스스로 특징을 추출하도록 하여 사용하고 있다. - +Linear Classifier에서 어떤 가중치(w) 값을 사용하느냐에 따라 정확도가 달라진 다는 것을 배웠다. +그렇다면 어떻게 최적의 가중치 값을 찾아야 하는지 알아야 하는데 이를 위해서 사용하는 정량화 방법이 loss function이다. +loss fuction은 어느 가중치 값이 얼마나 "안 좋은지"를 알려주는 지표이다. +그리고 이 안 좋은 가중치를 좋은 가중치로 바꿔나가는 과정을 optimization이라고 한다. +f(x, W) = Wx + b +이 식에서 x는 이미지, W는 가중치, b는 편향값이다. +이 식에서 loss를 구하는 방법은 각 카테고리 (고양이 자동차 개구리 등)별로 loss를 각각 구해서 그걸 모두 더한 후 평균을 내는 것이다. +강의 자료에서 제시된 고양이 자동차 개구리 이미지를 통해 loss를 구한 값들은 다음과 같다. + +- SVM loss (= hinge loss) +sj는 정답이 아닌 클래스의 score이고 syi는 정답 클래스의 score 값이다. +만약, syi > sj + safety margin(강의자료에서는 1)이면 loss = 0이고, +syi < sj + safety margin 이면 loss = sj - syi + safety margin이다. +SVM loss = SUM(j != y_i) { max (0, sj-syi+1) } +강의 자료의 고양이 자동차 개구리의 케이스로 계산한 SVM loss = 5.27이다. +고양이 자동차의 경우는 loss 값이 작지만 개구리에서 12.9의 loss 값이 나온다. + +Q1. 그런데 이 때 자동차의 score 값을 조금 변경해서 loss 값을 계산해도 loss 값이 크게 변동하지 않는 것을 볼 수 있다. +따라서, SVM hinge loss는 데이터에 민감하지 않다는 특성이 있음을 알 수 있다. +Q2. 그럼 최소 최댓값은 어떻게 될까? +loss의 최소값은 0이다. 그리고 최대값은 무한대이다. +Q3. 만약 W가 매우 작아져서 score가 0에 근사해지면 어떻게 되나? +계산해보면, 클래스 3개니까 (2+2+2)/3 = 2가 나오고 만일 클래스가 9개라면 (9+9+9+~+9)/10 = 9가 나올 것이다. +따라서 그럴 경우 loss = 클래스 갯수 -1이 된다. 이 계산은 디버그 용으로 사용한다. +0으로 해주었을 때 loss가 클래수 갯수 -1의 값으로 나오는지 검사하는 것이다. +이걸 sanity check라고 부른다. +Q4. 지금까지 계산하면서 정답 클래스 값을 제외하고 계산했는데 그 이유는? +정답 클래스 값을 포함해서 계산하게 되면 모든 경우에서 loss 값이 +1 증가하게 된다. +그러나 우리는 loss 값이 0에 근사하게 되길 바라기 때문에 정답 클래스 값을 제외하는 것이다. +Q5. 만약 sum 대신 평균을 이용하면 어떻게 되나? +계산해보면 딱히 상관은 없다. 단지 평균을 사용했기 때문에 scale만 작아질 뿐이다. +다만, loss가 0에 가까워지도록 하길 바라기 때문에 scale을 크게 해서 변화를 관찰하는 것이 좋은 방법일 수 있다! +Q6. 그럼 max 값에 제곱승을 해서 계산하면? +제곱승을 해서 계산하게 되면 nonlinear한 결과가 나오고, 답이 달라지게 된다. +이렇게 계산하는 방식을 squared hinge loss라고 하는데 때에 따라서는 이 방식이 잘 먹힐 때도 있다. +그래서 "아주 좋다"와 "아주 나쁘다"를 따질 때 유용한 방식이다. (그러나 잘 사용하지는 않음) + +그런데 이렇게 구하는 W 값은 과연 유일한 걸까? -> 아님 +각각의 score 값을 2배 혹은 3배 증가시켜도 똑같은 loss 값이 나올 수 있다. 따라서 W는 여러 개가 나올 수 있다. +유일하지 않는 W값이 문제가 되는 이유는 +-> 우리는 새로운 값에 대해서 예측을 하기 위해 model을 만들기 때문에 test set에 더 관심이 많고 따라서 정확도도 test set을 통해서 추출한다. +그런데 지금까지 구한 W값은 train set에 맞춰서 나온 것들이기 때문에 최적값도 train set에 맞춰져서 나오게 된다. +그래서 그 최적값은 test set에는 맞지 않을 수도 있다는 문제가 있다. +-> overfitting의 문제가 생길 수도 있다는 것이다. + +따라서 test set에도 맞을 수 있는 W값을 찾아야 하는데 이를 위해 사용하는 방식이 regularization이다. +L(W) = 1/N * SUM^N_(i=1) { Li(f(xi, W), yi) } + lamda R(W) +이 식에서 왼쪽의 항은 data loss이고 오른쪽의 항은 regularization이다. +data loss는 train set의 입장에서, regularazation은 test set의 입장에 있기 때문에 +이 식에 따르면, 매 loss 값을 계산할 때 마다 train에만 맞는 것을 학습하려고 하면 regularization에서 패널티를 부여하게 된다. +이 과정을 통해서 test set에도 맞는 W 값을 찾아나갈 수 있다. + +* 여기서 lamda R(W)가 무엇이길래 패널티를 부여하는 것일까? +일단 다항식이 너무 깊어지게 되면 복잡한 계산을 하게 되기 때문에 이를 방지하는 효과가 있다. +그리고 L1 regularization, L2 regularization이 있는데 +전자는 실제로 차수 값이 0이 되도록하고, 후자는 전체 차수의 값이 0에 가깝도록 유도한다. +따라서 L1은 원하는 특성이 제거될 수 있기 때문에 L2가 모든 것을 고려한다는 점에서 비교우위를 가지게 된다. +그리고 lamda 값은 규제의 강도 값이고, 높으면 모델이 단순해지며 underfitting / 낮으면 모델이 복잡해지며 overfitting이 된다는 문제가 있다. + +위와 같은 특성들 때문에 L1은 가중치 값 중 0이 있는 경우를, L2는 전체적으로 0에 가깝게 퍼진 가중치 값을 선호한다. + +어쨋든 우리의 목적에 더 부합하는 것은 L2 regularization이기 때문에 이를 더 많이 사용하고 이는 dropout, batch normalization에서도 많이 사용한다. + +- softmax classifier (=cross entropy) +모든 스코어에 exp를 취하고 그걸 모두 더한 뒤 원하는 클래스의 점수에 exp를 취해서 나눈다. +이렇게 계산한 것은 확률 값으로 도출되며, 이 때 원하는 정답 클래스에 -log를 취해 loss를 구하게 된다. +softmax는 multinomial logistic regression이다. (logistic regression = sigmoid function) +위와 같은 정의에 따라 위의 계산 방식에서 exp를 취해주는 것이다. +그리고 우리는 얼마나 "안" 좋은지를 판단하고자 하는데 +x축을 확률, y축을 loss라고 했을 때, -log의 함수가 확률이 1에 가까워질 수록 0에 가까워지기 때문에 -log를 취해 최종 loss를 구하게 되는 것이다. + +Q1. 이런 방식을 취했을 때 min, max는? +이론적으로 최소는 0, 최대는 무한대이다. (feat. -log graph) +Q2. 만약 score가 0에 가까워지면? +-log(1/클래스 갯수)가 되고 이 또한 디버깅 용으로 사용하며, sanity check라고 불린다. + +강의자료에서는 예시 자료를 통해 svm과 softmax를 비교하고 있다. +1. max값을 취해서 loss를 구하는 것과 exp를 취해서 확률 값으로 loss를 구하는 것의 차이가 있다. +2. 만약 data point를 흔들어 주게 되면? +SVM의 경우에는 딱히 영향이 없었고 둔감하다는 결론이 나왔으나, +cross-entropy loss의 경우에는 조금만 데이터가 바뀌어도 확률에 영향이 있었고 매우 민감하다는 결론이 나온다. + ++) Full loss라는 것은 언제가 regularization을 추가한다. + +위와 같은 방식들을 통해서 얻은 결론은 "어떤 W값이 얼마나 안좋은지"이다. +그렇다면 좋은 W값은? -> Optimization을 통해 구할 수 있다. +optimization은 쉽게 말하면 산 골짜기의 가장 깊은 곳으로 내려가는 것과 같으며 이 과정이 곧 loss가 0에 가까워지도록 하는 것이다. +몇 가지 방법이 소개되고 있는데 그 중에서 Random search는 사용하지 말아야 한다. (연산 오래 걸릴 수 있음.) +보통은 Follow the slope (gradient descent)경사 하강법을 사용한다. + +1-dimension, the derivative of a function +d f(x) / d x = lim_(h->0) { ( f(x+h) - f(x) ) / h } (* 만약 다차원이면 편미분 형태의 식) +이렇게 수식으로 하나하나 계산해서 사용하는 방법 -> numerical 방법 (수치적 방법) +이 방식은 모든 가중치 W 값에 조금씩 변화를 줘가면서 loss 값의 변화를 관찰하는 것인데 이렇게 하면 너무 연산이 오래 걸린다. +단지 W가 변화할 때의 loss 값을 알고 싶을 뿐이라면? +미분을 이용한 analytic gradient(해석적 방법)을 사용한다. 이 방식을 사용하면 일일이 계산할 필요없이 딱! 원하는 값이 나오게 된다. +요약하자면, +numerical gradient: 정확하지 않고 느리지만 간편한 연산 방식 (오류가 덜 나는 편) +analytic gradient: 정확하고 빠르지만 복잡한 연산 방식 (오류가 날 가능성이 있음) +이다. 보통은 해석적 방법을 더 많이 사용하지만 디버깅을 할 때는 수치적 방법을 사용하기도 한다. 이를 gradient check라고 한다. + +위와 같이 gradient 계산한 것들은 앞에 -가 붙으면 음의 기울기이기 때문에 +방향으로 이동하고 +앞에 +가 붙으면 - 방향으로 이동하면서 그래프에서 가장 낮은 지점으로 이동한다. +여기서 한 번 이동할 때 이동하는 거리를 step size (=learning rate)라고 부른다. 이 값도 적절한 값을 찾아서 적용시키는 것이 중요하다. +그래서 임의의 w 위치에서 가운데 빨간색 지점으로 가는 것, 즉 기울기가 0에 가까운 지점으로 가는 것이 목표이다. + ++) 지금까지 계산한 방식들은 N을 한 번에 올려서 계산했는데, 만약 N이 굉장히 큰 값이라면 매우 비효율적인 결과가 나올 것이다. +그래서 이 N을 나눠서 계산하는 stochastic gradient descent (SGD)를 많이 사용한다. +mini batch를 두어서 데이터 갯수를 잘라 사용하는 것인데 보통 2의 제곱수 만큼 잘라서 사용한다. +(256개를 가지고 W를 업데이트하고 그 다음 256개를 가지고 W를 업데이트하는 것을 반복하는 식이다.) + +그냥 이미지를 그대로 넣어버리는 식으로 사용하는 것은 성능이 그닥 좋지 않았다. (이전 강의록의 말 머리가 2개 있는 식이라던가..) +그래서 CNN이 연구 되기 전까지는 이미지의 특징을 뽑아내고 이 특징을 합쳐서 linear regression에 넣는 방식을 사용해왔다. +이전에 linear classification으로 해결할 수 없는 것들의 예시를 보여주었었는데 이 때 극좌표계로 변환함으로써 직선으로 구분 가능한 형태로 바뀌는 경우가 있었다. +이미지를 활용할 때는 이렇게 하지 않지만 여기서 동기 부여를 받아 특징을 추출하는 방식으로 이어지게 된 것이다. +특징 추출의 한 가지 방법이 바로 color histogram이다. 컬러 hue 값이 있는데 여기에 어떤 컬러가 많이 나오는지 count 해서 특징을 추출하는 것이다. +2번 째 방법은 HoG(Historam of Oriented Gradients)이다. 방향 값을 히스토 그램으로 표현하는 것이다. +전체 이미지 내에서 어느 방향으로의 각도가 많은지 히스토그램으로 나타내 특징을 추출하는 것이다. +3번 째 방법은 bag of words이다. 자연어 처리에서 많이 사용하는 방법인데 +먼저 이미지를 여러 개로 잘라낸 뒤, 비지도 학습과 같이 클러스터링을 돌려 각도, 색 등의 특징을 추출한다. +이 후 새로운 이미지가 들어오면 이 이미지를 잘라내서 클러스터와 비교해 어떤 특징이 있는지 비교한다. + +그러나 CNN 연구 방식이 도입된 후 특징을 미리 뽑아내는 것이 아니라 입력된 이미지에서 스스로 특징을 추출하도록 하여 사용하고 있다. + (-> 다음 강의: neural network & backpropagation) \ No newline at end of file From aea28fdc1dda4735f39c96e62898ef25ca3a7460 Mon Sep 17 00:00:00 2001 From: MSY99 Date: Mon, 28 Mar 2022 23:06:07 +0900 Subject: [PATCH 10/20] =?UTF-8?q?CV=5FWeek4=5F=EC=98=88=EC=8A=B5=EA=B3=BC?= =?UTF-8?q?=EC=A0=9C=5F=EB=AF=BC=EC=86=8C=EC=97=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 예습과제 --- "Week4_\354\230\210\354\212\265.txt" | 56 ++++++++++++++++++++++++++++ 1 file changed, 56 insertions(+) create mode 100644 "Week4_\354\230\210\354\212\265.txt" diff --git "a/Week4_\354\230\210\354\212\265.txt" "b/Week4_\354\230\210\354\212\265.txt" new file mode 100644 index 0000000..9d04114 --- /dev/null +++ "b/Week4_\354\230\210\354\212\265.txt" @@ -0,0 +1,56 @@ +정리하자면, Gradient Descent을 이용해 손실 함수가 최소화되는 가중치 w를 수정해나간다. +여기서 계산방식의 효율이 높은 analytic gradient 방식으로 chain rule을 이용한다. +이 계산 방식을 3가지의 예제를 통해 익힐 것이며, 여기서 쓰이는게 바로 Back propagation(오차 역전파)이다. +결과값에서 거꾸로 거슬러서 가중치 w를 계산해주는 방식이다. + +(*주의) +오차역전파는 가중치를 계산하는 방식으로 생각하고, 경사 하강법은 가중치를 업데이트하는 방식으로 생각하면 된다. +그래서 이번 4장은 업데이트가 아닌 가중치를 계산하는 방법만 다룬다. + +AlexNet이나 Neural Turing Machine을 보면 input에서 loss function를 도출할 때까지의 노드가 굉장히 많다. +이런 방대한 모델의 가중치 계산을 일일이 하게 되면 오래 걸리지만, Back propagtion을 이용하면 chain rule을 통해 반복 계산으로 전부 구할 수 있다. + +강의 예시 (작성하려다가 gitbhub에 Latex 적용 어떻게 하는지 몰라서 스킵합니다.) +간단한 함수 하나를 설정하고 이 함수 모델에 따라 반대로 거슬러 올라가면서 가중치를 계산해준다. (=Back propagation) +최종 값은 df/df = 1이다. +(중략) +chain rule을 이용해서 합성 함수의 미분을 풀어낸다. 이 때 global gradient * local gradient로 표현한다. +이런 식으로 계산 과정을 통해서 합성 함수의 미분을 풀어내는 과정을 보여준다. + +간단한 함수를 다룬 뒤에는 sigmoid 함수에 back propagation을 적용하는 것을 보여준다. + +예시 함수들에 back propagation을 적용하는 것들을 적기에는 text로 작성하는 것이 너무 시간이 오래 걸리고 latex와 이미지 첨부가 안 돼서 스킵. + +어쨋든 이런 식으로 계산한 것들을 보면 사실 sigmoid 함수를 이용해 일반화가 가능하다는 것을 알 수 있다. +위 과정들에서 chain rule을 통해 구해온 것들은 사실 sigmoid gate를 통해 한 번에 계산이 가능하고 일반화된 공식이 있다. + +add gate: gradient distributor (현재의 가중치를 다음 단계로 뿌려줌) +max gate: gradient router (큰 값에 가중치를 부여) +mul gate: gradient switcher (서로의 값을 바꿔줌) +이렇게 gate들을 일반화 시킬 수 있다. + +이미지 데이터를 다루고자 할 때는 모든 픽셀 값들을 1차원 array로 재배치 하기 때문에 차원이 굉장이 높다. class도 여러 개인 이미지 데이터의 가중치는 매우 높은 차원의 행렬 데이터일 것이기 때문에 이 때는 Jacobian matrix(행렬의 미분 연산)을 이용한다. +그렇게 하면 diagonal의 특성에 따라 대각 행렬만 계산하면 돼서 연산이 좀 간단해진다. + +다음 예시로는 L2 regularization function f를 다룬다. +여기서 f(x, W)의 x는 n차원, W는 n*n 차원이다. 이 예씨는 2장에서의 linear regression의 예시ㅣ로 접해본 구성이다. 클래스가 3개라서 w의 차원이 x차원보다 많다. +L2의 최종값은 0.116이 나오고, 출력 노드의 미분값은 1이다. L2 노드 이전의 [0.22, 0.26]은 W, x의 행렬 연산 결과값이다. +f(q)로 함수를 지정하면 f(q) = sum {q^2}이고, 이는 2q로 미분되므로 가중치는 *2를 해주어 [0.44, 0.52]이다. +mul gate에서는 서로가 서로의 계수이므로 값을 교환하는 방식으로 일반화 가능했었다. 따라서 [0.2, 0.4] * [0.44, 0.52]를 서로 행렬 계산해서 2*2 행렬로 만들어 준다. (W가 2*2 행렬임) +이후 결과값은 [[0.2*0.44, 0.4*0.44], [0.2*0.52, 0.4*0.52]]의 값이 나온다. +x에는 local gradient를 w값으로 하여 계산하고, Wx에서 x1에 들어가는 w값이 0.1, -0.3임을 고려해 transpose를 해준다. +이러면 최종 결과 값은 (01*0.44) + (-0.3*0.52) = -0.112, (0.5*0.44) + (0.8*0.52) = 0.636이다. + +위와 같은 방식으로 backpropagation을 수행한다는 것을 배웠다. + +Neural Network를 구성할 때 이제 단순한 Linear regression만 하는 것이 아니라 hidden layor를 추가해 모델을 구축한다. +hidden layor를 input node와 output node 사이에 100개를 추가한 것은 2-layor NN이라고 부른다. (헷갈릴 것 같다....) +이를 통해 NN과 같은 모델은 각각 하나의 클래스에 하나의 분류기로만 이용해서 그 특징에만 부합한 클래스를 부여했던 것이 hidden layor를 포함함으로써 한 개의 클래스에도 여러 개의 분류기가 생겨 다양한 특징을 잡아 분류할 수 있게 되었다는 발전이 있다! +이런 방식으로 2-layor, 3-layor NN을 만들 때, 함수는 max 함수를 이용하게 된다. <-- 여기서 함수는 활성화 함수를 말하는데 이전에는 sigmoid를 많이 사용했으나 이제는 relu를 더 많이 사용한다. +(이런 식의 NN 구조가 인체의 신경망이랑 비슷하지 않느냐 근데 헷갈리지는 말라는 이야기) + +활성화 함수들 (Activation function)의 종류가 다양하다. sigmoid, tanh, ReLu, Leaky ReLu, Maxout, ELU 함수들의 그래프를 소개했다. +NN 모델의 구조를 간단하게 보여주는데 여러 개의 노드들이 있는 layor를 거쳐 값이 도출되는 과정을 설명한다. 이런 방식을 Fully Connected (FC)라고 한다. + +4강은 Back propagation으로 W를 계산하는 방법을 배우고 NN 모델 맛보기를 했다. +다음 강의에서는 CNN의 구조를 살펴본다. \ No newline at end of file From 20364afa083d3a03b677bf0a976242ce45bb0c73 Mon Sep 17 00:00:00 2001 From: MSY99 Date: Mon, 28 Mar 2022 23:13:17 +0900 Subject: [PATCH 11/20] =?UTF-8?q?CV=5FWeek4=5F=EC=98=88=EC=8A=B5=EA=B3=BC?= =?UTF-8?q?=EC=A0=9C=5F=EB=AF=BC=EC=86=8C=EC=97=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit PR이 안 돼서 계속 다시 시도하는 중 --- "Week4_\354\230\210\354\212\265.txt" | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git "a/Week4_\354\230\210\354\212\265.txt" "b/Week4_\354\230\210\354\212\265.txt" index 9d04114..6c32cdc 100644 --- "a/Week4_\354\230\210\354\212\265.txt" +++ "b/Week4_\354\230\210\354\212\265.txt" @@ -53,4 +53,4 @@ hidden layor를 input node와 output node 사이에 100개를 추가한 것은 2 NN 모델의 구조를 간단하게 보여주는데 여러 개의 노드들이 있는 layor를 거쳐 값이 도출되는 과정을 설명한다. 이런 방식을 Fully Connected (FC)라고 한다. 4강은 Back propagation으로 W를 계산하는 방법을 배우고 NN 모델 맛보기를 했다. -다음 강의에서는 CNN의 구조를 살펴본다. \ No newline at end of file +다음 5강에서는 CNN의 구조를 살펴본다. \ No newline at end of file From 2ddc047af8f94869a10cd696872df6e35ae92ca5 Mon Sep 17 00:00:00 2001 From: Hwa_i <76520221+FleurHwai@users.noreply.github.com> Date: Mon, 4 Apr 2022 00:18:23 +0900 Subject: [PATCH 12/20] Update README.md --- README.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/README.md b/README.md index 4a1056b..aeca000 100644 --- a/README.md +++ b/README.md @@ -15,10 +15,10 @@ |4|22/03/29|cs231n 4주차|cs224n 4강|4장 관련 필사| |5|22/04/05|cs231n 5주차|cs224n 5강|파이썬 머신러닝 완벽가이드 5장| |6|22/04/12|cs231n 6주차|cs224n 6강|5장 관련 필사| -|7|22/04/19|cs231n 7주차|cs224n 7강|파이썬 머신러닝 완벽가이드 6장| -|8|22/05/03|cs231n 8주차|cs224n 8강|6장 관련 필사| -|9|22/05/10|cs231n 9주차|cs224n 9강|파이썬 머신러닝 완벽가이드 7장| -|10|22/05/17|cs231n 10주차|cs224n 10강|7장 관련 필사| +|7|22/04/19|cs231n 7주차|cs224n 7강|파이썬 머신러닝 완벽가이드 7장| +|8|22/05/03|cs231n 8주차|cs224n 8강|7장 관련 필사| +|9|22/05/10|cs231n 9주차|cs224n 9강|파이썬 머신러닝 완벽가이드 6장| +|10|22/05/17|cs231n 10주차|cs224n 10강|6장 관련 필사| |11|22/05/24|cs231n 11주차|cs224n 11강|파이썬 머신러닝 완벽가이드 9장| |12|22/05/31|cs231n 12주차|cs224n 12강|9장 관련 필사| |13|22/06/07|cs231n 13주차|cs224n 13강|캐글 필사 1| From 4b0c9ff078539acb09fd36941933fec3db48119d Mon Sep 17 00:00:00 2001 From: MSY99 Date: Mon, 11 Apr 2022 16:58:15 +0900 Subject: [PATCH 13/20] =?UTF-8?q?CV=5FWeek6=5F=EC=98=88=EC=8A=B5=EA=B3=BC?= =?UTF-8?q?=EC=A0=9C=5F=EB=AF=BC=EC=86=8C=EC=97=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 예습과제 --- ...0\354\212\265\352\263\274\354\240\234.txt" | 145 ++++++++++++++++++ 1 file changed, 145 insertions(+) create mode 100644 "Week6 \354\230\210\354\212\265\352\263\274\354\240\234.txt" diff --git "a/Week6 \354\230\210\354\212\265\352\263\274\354\240\234.txt" "b/Week6 \354\230\210\354\212\265\352\263\274\354\240\234.txt" new file mode 100644 index 0000000..b94f1a4 --- /dev/null +++ "b/Week6 \354\230\210\354\212\265\352\263\274\354\240\234.txt" @@ -0,0 +1,145 @@ +Activation functions +딥러닝에 있어서 비선형성을 가해주는 중요한 역할 +몇 가지 활성화 함수들의 예시이 있는데 그중에서 시그모이드 함수는 그동안 많이 다뤘다. +그런데 이 함수는 비선형성을 갖추고 있음에도 최종 output을 낼 때만 이용한다. +그 이유는 +1. 기울기 gradient 값을 없애버린다. (vanishing gradient) +Neural Network는 backpropagation이라는 기법 때문에 강력한 모델을 만들 수 있었다. +하지만 sigmoid 함수를 사용하면 backprop에 문제가 생긴다. +sigmoid 함수에서 x=-10 일때는 거의 0이고, x=0일 때 기울기가 거의 최대일 때도 0.25 정도이다. +back prop 과정이 이전의 기울기 값에 계속해서 local gradient를 곱해주는 식인데, global gradient가 거의 0이니 결국 모두 0에 수렴해서 기울기 값이 소실되어버리는 것이다. +결과적으로 w가 update되지 못한다는 것이다. + +2. Zero-center의 문제도 있다. +시그모이드 함수를 보면 output 값이 항상 양수이다. 0을 중심으로 값이 분포하고 있지 않고 +Neural Network는 층을 계속해서 쌓았기 때문에 이전 노드의 output 값이 다음의 입력 값이 된다. +시그모이드를 활성화 함수로 이용하면 계속해서 양수의 값만 input 된다는 것이다. +또 입력값이 항상 양수이면 gradient에서 문제가 생기기도 한다. +back prop 과정에서 시그모이드 함수이므로 dl/df * df/dwi로 w의 기울기를 구할 때 체인 룰을 구한다. +df/dwi는 x_i이고 여기서 입력값은 항상 양수이므로 dl/df의 부호를 따라가게 된다. +전부 양수이거나 전부 음수가 되는 것이다. +그래서 위 슬라이드 오른쪽 그래프를 보면 w1을 x축, w2를 y축인 2차원이라고 보았을 때, update가 초기 가중치 0에서 강의록 그림처럼 파란색 화살표가 best w라 하자. +빨간색 화살표처럼 지그재그로 가중치가 update 되기 때문에 비효율적이라는 문제가 있다. 입력값이 양수이기 때문에 생기는 문제이다. + +3. exp() is a bit compute expensive 연산이 무겁다고 한다. + +위의 1~3 문제로 인해 시그모이드 함수는 activation 함수로는 이용하지 않는다. + +다음은 하이퍼볼릭 탄젠트 함수이다. +시그모이드 함수와 유사하지만 zero centered 문제를 해소했지만 마찬가지로 기울기 소실 문제가 해결되지 못 해 활성화 함수로는 적합하지 않습니다. + +ReLU 함수는 양의 방향에서 입력값 x를 그대로 배출하기 때문에 기울기가 살아있다. f(x) = max(0, x) 식을 사용하는 이 함수는 기울기 소실 문제를 어느 정도 해결했다. +따라서 양의 영역에서는 가중치 w의 update가 가능해진다. +exp 연산도 사라져서 계산적으로도 효율적이다. +그래서 ReLU 함수는 2012 AlexNet에서 쓰이기 시작하면서 CNN과 큰 규모의 데이터에 매우 잘 작동했다. +하지만 음의 영역에서는 기울기가 모두 0이 되고 zero - centered 문제가 남아있어 입력 값의 음의 부분은 전부 0이 되기 때문에 vanishing gradient, zero centered 문제로 효율성 문제도 생긴다. + +그 문제를 해결한 것이 dead ReLU이다. +w initialization에서 dead ReLU에 빠져버리면 업데이트가 안 될 수도 있고 learning rate를 크게 설정할 경우, w가 너무 크게 비약해서 학습이 안 되는 상황이 발생하는 단점이 있다. + +이렇게 ReLU를 활성화 함수로 한 모델을 훈련 도중에 network의 일부가 freeze 되는데 이는 10~20% 정도가 dead ReLU에 빠진 것이라 한다. 이는 문제이긴 하지만 train은 잘 된다고 한다. +즉, 시그모이드 함수에 비해 기울기 소실 문제가 적으면서 학습이 되고 큰 문제가 있지 않아 상용화된 것이라 생각하면 된다. + +그래도 어쨋든 문제가 없는 건 아니라서.. ReLU 함수에 약간의 bias를 주어서 시작하려는 시도가 있다. +(처음부터 dead ReLU로 빠뜨리지 않게 하려는 시도인 듯) +좀더 active의 가능성을 높여주는 것이다. 위에서 말했듯이 initialization은 중요하기 때문이다. (효과가 미미해 안 하는 사람도 있다.) + +Leaky ReLU는 렐루 함수의 효율성과 함께 dead ReLU의 단점을 보완한 것이다. +음의 영역에서도 경미한 기울기를 주어 vanishing gradient를 해결한 것이다. + +PReLU도 있다. Leaky는 음의 영역의 기울기가 있다면 PReLU는 파라미터로 알파 X를 만들어서 융통성 있게 해결한 것이다. + +ELU 함수도 있는데 _| 모양의 함수를 모두 LU 함수라고 한다. +ELU는 0에서의 미분 불가점을 미분 가능하게 smoothing 시켰다. +이 함수가 Leaky ReLU와 비교했을 때 노이즈에 대해서 더 강건하다고 하는데 이는 zero mean에서 함수가 스무스하기 때문에 생긴 특징이다. +따라서 zero mean의 결과값들을 출력하는데 장점이 있다. 하지만 여전히 음의 영역에서 기울기 값 소실이 있고 exp 연산으로 인한 효율성 저하도 있다. +ReLU < ELU < Leaky ReLU 정도 이다. +보통은 각각의 장단점을 보고 경험에 따라 사용할 함수를 결정한다고 한다. +(그리고 다 한 번씩 사용해보면서 성능이 가장 좋은 것을 선택해서 쓰면 된다고 하는데 sigmoid는 그냥 쓰지 말라고 한다.) + +Maxout Neuron은 파라미터를 더 두어서 각각 출력 갑시 다른 함수 2개 중에 max 값을 취하는 함수이다. +maxout은 기울기 소실은 없지만 연산량이 2배라는 비효율성이 있다. + +데이터 전처리 내용도 다룬다. +zero centering / normalize가 전처리 방식 중 하나로 나온다. +데이터들의 중앙값이 0에 가깝도록 배치한 뒤 각각의 들쑥날쑥한 feature들을 어떤 범위 내로 모아주었다. + +하지만 이미지 데이터에서는 zero centering만 한다. 어차피 이미지 데이터들은 픽셀 값이 전부 같은 범위이기 때문이다. (0~255) + +zero centering을 하는 이유는 입력값이 전부 양수이면 w가 전부 음수나 양수가 되어서 업데이트가 일방향으로만 일어나기 때문에 비효율적이기 때문이다. +zero mean으로는 그 문제를 해결할 수 없고 오직 첫 layer에서 zero centering이 되고 그 이후에 네트워크가 깊어짐녀 깊어질수록 활성화 함수로 값이 양수만 나와서 첫 layer 정도에만 의미가 있다고 한다. + +전처리로 PCA나 whitening 기법들을 생각해볼 수 있다. 하지만 이미지 데이터에서는 zero mean 정도만 학 다른 복잡한 기법은 안 쓴다고 한다. +왜냐면 이미지 데이터를 저차원의 새로운 피쳐들로 이루어서 학습을 진행하는 것이 아니라 convolutional layer에서 오리지널의 이미지 데이터를 필터 등으로 공간적인 구조로 바라봐야 함을 알기 때문이라고 합니다. + +train set과 test set을 전처리할 때는 동일한 mean을 이용해 zero mean을 해준다. +여기서 mean값을 이미지의 전체 데이터로 할지, 아니면 각각 독립된 채널마다의 mean으로 이용할지 선택할 수 있는데, 이는 큰 차이는 나지 않는다고 한다. + +VGGNet은 알렉스 넷보다 이후에 나온 것인데 각각의 채널별로 mean값을 두어 zero mean을 했다고 한다. + + +Weight Initialization +Neural Net에서 weight를 전부 0으로 맞추면 뉴런들은 전부 똑같은 것을 수행하게 됩니다. +w가 전부 0이기 때문에 입력값에서부터 모든 뉴런이 계속 똑같은 값을 내놓는다는 것이고, 활성화 함수가 작동하지 않으니, layer가 의미 없어지는 상황이라고 생각하면 된다. + +그래서 이를 해결하기 위한 방식으로는 +1. 맨 처음 w에 아주 작은 랜덤의 값을 부여하는 것이다. 정규 분포로부터 가져온 작은 편차들의 값들을 랜덤으로 w initialization 해주는 것이다. 하지만 이 방법도 Neural Net이 깊어지면 문제가 발생한다. +w initialization에서 임의의 작은 값들을 랜덤하게 주니 1보다 작은 w값들이 layer가 깊어질수록 계속해서 곱해지니까, 0으로 수렴해버린 것이다. +값이 너무 작아져서 collapse 되어 버린 것이다. + +-> 이런 상황에서의 w의 gradient는 입력값, 출력값들이 애초에 0에 수렴할 정도로 작은 값들이니 gradient마저도 엄청나게 작아지게 된다. 그래서 update도 잘 이루어지지 않는다. +그래서 항상 활성화 함수에 대해서 foward pass와 backward에서의 gradient의 흐름을 잘 파악하고 생각해야한다고 강조한다. + +가중치를 0.01이 아니라 1을 곱해서 0으로 수렴하지 않도록 한 결과가 있다. 그랬더니 출력값들이 1과 -1로만 가버려서 explode 해버린다. +tanh 함수에서 1과 -1 값들을 전부 기울기아 0이 되는 saturated 지점이었는데 기울기가 전부 0이 되어 update가 마찬가지로 되지 않는다. +그래서 강의에서는 initialization이 w를 작게 하면 collapse가 되고, 너무 크게 하면 saturate되기 때문에 매우 어려운 것이라고 한다. +(initialization이 잘된 예시로 2010년의 Xavier initialization) +(*입력 값들의 수가 적으면 우리는 큰 값의 w가 필요하다. 그래서 더 적은 수로 나누어 스케일링 해주고, 반대로 입력값들의 수가 많으면 우리는 작은 값은 w가 필요해서 큰 수로 나누어 스케일링을 하는 것이다.) + +하지만 이 방식은 비선형 함수인 ReLU를 이용하면, 다시금 문제가 발생한다. zero-mean 함수였던 tanh와는 다르게 ReLU는 음수 부분은 전부 0이 되기 때문에 강의록과 같은 그래프가 나타난다. +활성화 함수를 지나면서 편차가 강제로 절반이 된다. layer가 깊어질수록 std가 0에 가까워지는 것이 보인다. 출력값들이 0이 많다면 w의 update는 잘 이루어지지 않을 것이다. +여기서 np.sqrt(fan_in/2)로 수정해 2로 더 나누어주면 (뉴런의 절반이 죽기 때문에) 그래프의 상황이 더 나아지는 것을 볼 수 있고 마지막 layer에도 출력값이 살아있다. +이렇게 작은 차이에도 weight의 값들에 대해서 주의를 기울이면, 큰 차이가 난다는 것을 강조한다. + +Batch normalization +우리가 원하는 가우시안의 범위 내에서 activation 값들을 뽑고 싶은 idea에서 기인한 방식이다. +현재 batch에서의 평균과 분산을 이용해서 훈련 처음부터 batch normalization을 취해 주어 모든 층에서 정규 분포를 따르게끔 하는 것이다. +각 뉴런에서 평균과 분산을 구하는 function을 이용해서 batch마다 normalization을 해주는 것인데 이는 미분 가능한 함수라서 back prop에도 문제가 없다. +이걸 이용하면 굳이 weight init을 안 해도 된다고 한다. 이는 기본적으로 training과정에서 gradient vanishing의 문제를 일어나지 않도록 한다. + +batch normalization은 각 층의 input distribution을 평균 0, 표준편차 1로 만드는 것이다. +network 각 층의 activation마다 input distribution이 달라지만 internal covariance shift이 달라지는 문제를 해결하기 위해 사용된다. +보통 batch 별로 데이터를 train 시키는데, 이때 N*D의 batch input이 들어오면 이것을 normalize한다. +이는 일반적으로 activation layer 전에 사용되어 잘 분포되도록 한 후, activation을 진행할 수 있도록 한다. BN 목적이 네트워크 연산 결과가 원하는 방향의 분포대로 나오는 것이기 때문에 activation function이 적용되 분포가 달라지기 전에 적용하는 것이다. + +그런데 BN을 사용할 때 과연 unit gaussian이 적합한지에 대해서 판단하여야 한다. +BN이 적절한지에 대한 판단을 학습에 의ㅣ하여 조절할 수 있다고 한다. 처음 normalize를 진행하고 이후 감마 값과 같은 하이퍼 파라미터 값들을 조정하여 batch norm을 할지 않 할지 선택하는 것이다. +감마 값은 normalizing scale를 조절해주고 베타 값은 shift를 조절해주는 파라미터 값이다. +이 값들을 학습을 통해 조절함으로서 normalize 정도를 조절할 수 있다. + +먼저 mean과 variance를 구하고 normalize를 한다. +그리고 scale, shift를 얼마나 할지 학습을 통해 값을 정하게 된다. + +BN을 하게 되면 dropout를 사용하지 않아도 된다고 한다. BN의 논문 저자는 dropout을 대체할 수 있다고 하였으나 실제적으로 둘 다 모두 사용했을 때 성능이 좋은 경우도 있고 의견이 다양하게 존재하는 것이다. + +Babysitting the Learning Process +이 과정은 +1. 먼저 전처리 과정을 진행해준다. 이미지의 경우 zero - centered를 사용한다. +2. 사용할 neural architecture를 정해준다. +3. sanity check를 통해 loss가 적절하게 나오는지 확인한다. +4. 규제 값을 올렸을 때 loss가 증가하였고, network가 잘 동작하는지 확인할 수 있다. +5. 그리고 먼저 작은 데이터셋을 이용해서 훈련을 시켜본다. +6. data 수가 작기 때문에 overfitting이 발생하고, train acc가 100% 나오는 것을 확인할 수 있다.. + overfitting이 나온다는 것은 모델이 제대로 동작하고 있다는 의미로 받아드려고 된다. +7. 이제 적절한 hyper parameter 값들을 설정해줄 것이다. 강의록에 따라 lr를 정하면 loss가 매우 조금씩 바뀌는 것을 확인할 수 있었다. +하지만 train acc가 조금씩 높아지는 것을 보면 느리지만 train이 되는 것을 확인할 수 있다. +8. 다시 lr로 설정하니 cost 값이 Nan이 되는 것을 확인할 수 있다. 이것은 값이 너무 커서 튕겨 나간것이라 할 수 있다. +9. 또 lr를 수정해도 inf로 튕겨져 나가는 것을 확인할 수 있고 몇 번의 실험을 통해 1e-3~1e-5 값이 적절한 값이라는 것을 추측할 수 있다. + +Hyperparameter Optimization +처음에는 범위를 크게 잡았다가 좁은 범위로 좁혀나가는 방법을 사용한다. + +이렇게 hyperparameter를 찾기 위한 방법으로 Grid Search와 Random Search가 있는데 Grid Search는 일정한 간격을 가지고 있어, 제일 best case를 찾지 못할 수도 있다. +그래서 Random Search 방법을 더 많이 사용한다고 한다. +이렇게 적절한 hyperparameter를 찾음으로서 좋은 train이 이루어지는 환경을 설정할 수 있다. +hyperparamter에는 network architecture, lr, decay, regularization 등이 있다고 한다 \ No newline at end of file From 527ff717add1273e6b251b81664047e5f6c883a2 Mon Sep 17 00:00:00 2001 From: MSY99 Date: Mon, 11 Apr 2022 17:06:14 +0900 Subject: [PATCH 14/20] =?UTF-8?q?CV=5FWeek6=5F=EC=98=88=EC=8A=B5=EA=B3=BC?= =?UTF-8?q?=EC=A0=9C=5F=EB=AF=BC=EC=86=8C=EC=97=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit pr!! --- "Week6 \354\230\210\354\212\265\352\263\274\354\240\234.txt" | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git "a/Week6 \354\230\210\354\212\265\352\263\274\354\240\234.txt" "b/Week6 \354\230\210\354\212\265\352\263\274\354\240\234.txt" index b94f1a4..74373d3 100644 --- "a/Week6 \354\230\210\354\212\265\352\263\274\354\240\234.txt" +++ "b/Week6 \354\230\210\354\212\265\352\263\274\354\240\234.txt" @@ -142,4 +142,4 @@ Hyperparameter Optimization 이렇게 hyperparameter를 찾기 위한 방법으로 Grid Search와 Random Search가 있는데 Grid Search는 일정한 간격을 가지고 있어, 제일 best case를 찾지 못할 수도 있다. 그래서 Random Search 방법을 더 많이 사용한다고 한다. 이렇게 적절한 hyperparameter를 찾음으로서 좋은 train이 이루어지는 환경을 설정할 수 있다. -hyperparamter에는 network architecture, lr, decay, regularization 등이 있다고 한다 \ No newline at end of file +hyperparamter에는 network architecture, lr, decay, regularization 등이 있다고 한다. \ No newline at end of file From 144162194dc197d5c7db493de1e6cf1693ed9189 Mon Sep 17 00:00:00 2001 From: MSY99 <101084413+MSY99@users.noreply.github.com> Date: Tue, 3 May 2022 20:42:50 +0900 Subject: [PATCH 15/20] =?UTF-8?q?CV=5FWeek8=5F=EC=98=88=EC=8A=B5=EA=B3=BC?= =?UTF-8?q?=EC=A0=9C=5F=EB=AF=BC=EC=86=8C=EC=97=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit pdf 파일로 제출합니다. 사진이 있어야할 것 같아서 노션에서 작업하고 pdf 변환했어요. --- ...0\354\212\265\352\263\274\354\240\234.pdf" | Bin 0 -> 1960421 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 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zc}9R(px&1kIIQ=wKv7B=O>GQ;;qjU)W~7{bqTY@Z8MMAUPlIBqw*$F|Sf-%$6xJ7@ z@z~ygM(B{pP@HnJ7pXb$y-0Z1PK%d316+n6_KCs9bR zKywAG8;Uk72i&OjrQx@;hMB|D028Z;r1aA_Vzd+c>eh3^G&l9o&A4ZHTQ#8S^ zOs+5Nt5%MJQkyeJbAlcp*Zj z9AuVQ1{}u`>&tN>k<)NI;qN65VmC2oQ6PB(2S~I7tH%1rNgQD_z!@ofiPT9>W^jHW zfyEHMiId4(iihBc*8|wau@O9uz+?IG6r?|B-FO;;1wn(rK+r_8FGmx;6S5{EZt)yX ztR>G$%AJI2Is^fo@UZ|W2*1JeB1iOv&xI3k4k8JhOz614GbFzv8M|RuGRX&s zl;9U2A~EM5#BKq)lI=uNrV?bHm^USHLNth=#2SeJcCnmc(*hA!l@NvX01{6^cOjc3 zd@-OD@_8&p_&*WSNzAXvQ$+j~A?e356_tz}^9#m6&;*LWjo`(J+yYEXIg(dRUtoEO zI4uICBgPOp!v8@}!mo)kl$r4up!S5EWtoV1ph85vgp`obQ;8xlCsZgPc%yM8z-rhR zOEgR52MQd-x(0~^5knzFVQeZvAS8Su1Rp|v5)TT4=LZOh7#9o#%MTDNA!mTe7&A!{ ztP$2VNfdt2S0Z9J2#}Bq6k#zIl4MYEJUaTwD9O;GMjL4ApQ4a}0p zI6yH~tj~(6lI;M5AzcGyrf?ht8iDPB#tC?h0G;Dl0quzThD?)j6=;CkF~2;4r=cCB z__!Uo1LU6-H$<#CEfTdVa80zb3sPOqP^Kni527Mu1zwiu3mjuTfb@mX4Y-~G`+J#| zp~#5l!hm5CG`MmU%L>ZvI1hvBhDi7g=*kk$V;Mqz42f5v5F`;c2+L6?t?)AlZ8Z;N) z_~7Tsq3yzmic!gpR>I+}Y663-iPn-h-5MpqS2{Z!t01XP1cnp{_mJ0_jC$OzT zZG`Z<5CMqy6_7e&Oa}!#C}iSsm7+dD;|Se_S0Y4QfU*FglVH&pH$uV+Ld9c%W#YL& zm7ma4rObfm$AfdnHp4@W4C^i+9KwfzrV;U%hjk Date: Mon, 23 May 2022 23:16:19 +0900 Subject: [PATCH 17/20] =?UTF-8?q?CV=5FWeek11=5F=EC=98=88=EC=8A=B5=EA=B3=BC?= =?UTF-8?q?=EC=A0=9C=5F=EB=AF=BC=EC=86=8C=EC=97=B0?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit ㅇㅇ --- ...0\210\354\212\265\352\263\274\354\240\234" | 93 +++++++++++++++++++ 1 file changed, 93 insertions(+) create mode 100644 "Week11 \354\230\210\354\212\265\352\263\274\354\240\234" diff --git "a/Week11 \354\230\210\354\212\265\352\263\274\354\240\234" "b/Week11 \354\230\210\354\212\265\352\263\274\354\240\234" new file mode 100644 index 0000000..06a61e3 --- /dev/null +++ "b/Week11 \354\230\210\354\212\265\352\263\274\354\240\234" @@ -0,0 +1,93 @@ +### Image Segmentation + +semantic Segmentation: 이미지의 픽셀들이 어떤 클래스에 속하는지 예측하는 과정 +Classification처럼 미리 클래스의 수와 종류를 정해 놓아야 한다. 단, 개별 객체가 구분되지 않는다는 단점이 있다. + +이를 구현하기 위한 방법으로는 + +1. Sliding Window → Patch를 만들고 전체 영역을 모두 돌면서 한 픽셀이 어느 카테고리에 들어가는지 찾는 방법 +계산량이 너무 많다는 단점이 있음 +2. Fully Convolutional Network → 입력의 Spatial Size를 유지해야한다는 특징이 있다. 모든 픽셀에 대해 카테고리 Score를 계산해야 하기 때문에 계산량이 많다. +3. 2번에서 FC Layer 대신 Spatial resolution을 다시 키우는 방법이 제안 +이 과정에서 Upsampling이라는 과정을 거친다. + +### Upsampling + +간단히 말하자면 Downsampling의 역과정이라고 생각하면 된다. 이미지의 사이즈를 늘리게 되면 빈 공간이 생겨날텐데, 이런 빈 공간을 채우는 Issue가 발생. + +이를 해결하는 방법으로는 + +1. Unpooling +단순히 0으로 채우거나 인접한 값을 복사하여 채운다. +2. Max Unpooling +대부분의 네트워크가 downsampling 과정을 거칠 때 Maxpooling 가정을 거치는데 네트워크가 주로 대칭적인 특징을 가지고 있어 그 위치로 Upsampling을 하는 과정이다. +3. Transpose Convolution +Convolution 연산을 행렬로 생각하고 내적의 과정으로 이해할 수 있다. + +입력값을 가중치라고 생각하고, 필터의 값을 곱해서 output에 채워넣는다. 만약 겹치는 부분이 있을 경우 그 구간에 있는 값들을 모두 더해주면 된다. +Deconvolution / Upconvolution / Fractionally strided convolution / Backward strided convolution + +### Instance Segmentation + +Semantic Segmentation은 개별 객체를 구분할 수 없다는 단점이 있었다. 이 단점을 보완하기 위해 나온 방법이 Instance Segmentation이다. + +각각의 픽셀 별로 카테고리 score를 매기는 방식이 아니라 각각 픽셀 별로 Object가 있는지 없는지를 판단한다. +Instance Segmentation과 Object Detection을 결합하여 만들어진 대표적인 알고리즘 = Mask R-CNN이다. + +Classification + Localization + +Classification과 Localization은 이미지에서 하나의 물체에 대해 그 물체가 어떤 것에 속하고, 그 물체가 어디에 위치해 있는지 찾아내는 Task이다. + +보통 Image Classification을 위한 네트워크는 최종적으로 하나의 FC 층이 존재하지만 이 Task는 2개의 FC 층을 이용하여 Bounding Box와 Classification을 찾는다. +따라서 학습을 시킬 때 2개의 Loss function을 이용한다. Multi task Loss이기 때문에 네트워크 가중치들의 각각의 미분값을 사용하므로 Loss function의 단위가 달라도 gradient 계산이 가능하다. + +Object Detection + +한 장의 이미지에서 다수의 물체를 찾고 그 물체가 어디 있는지 알아내는 Task이다. Classification + Localization과 달리 이미지 마다 객체의 수가 달라져 이를 미리 예측할 수 없다. 즉, 더 어려운 Task이다. + +2-stage Detector / 1-stage Detector 두 가지가 있다. +이를 나누는 기준은 Classification과 Localization을 단계별로 할 경우: 2-stage, 이를 한 번에 진행할 경우 1-stage이다. + +R-CNN + +- Selective Search Algorithm: 딥 러닝을 사용하지 않고 Rule based로 된 알고리즘으로 물체가 있는 영역을 찾는데 효과적인 알고리즘이다. + +Region Proposals은 딥러닝을 쓰지않고 찾는 방법 중 가장 성능이 좋은 알고리즘이다. +간단히 설명하면 물체의 스케일이나 위치를 모두 고려해 모든 후보군을 처음에 샅샅이 조사한 다음, Greedy Algorithm을 이용해서 여러 영역에서 비슷한 부분을 합치는 식으로 영역을 통합하는 방법이다. → Region of Interest = RoI를 추출 +→ RoI를 CNN에 training 시키기 위해 input size를 맞춰줌 +→ CNN을 통과한 다음 SVM을 통해서 Classification 과정을 거침. +→ Linear Regression을 통해서 Bounding BoX도 Loss 값을 계산 +→ 2개의 Loss가 최소가 되는 방향으로 training + +- 계산량이 많다. +- Memory가 많이 든다. +- 학습 과정이 느리다 +- Test time이 느리다. +- 학습되지 않는 Region Proposal이 존재한다. + +Fast R-CNN + +계산 비용이 많이 드는 이유 → 각각의 RoI 영역에서 CNN 과정을 다 진행시켜서 + +⇒ Fast R-CNN에서는 Input Image에 대해 한 번의 CNN 과정을 거친다. +→ Feature Map에서 Region Proposal을 찾아낸다. +→ RoI의 영역에 모두 다른 Issue가 발생 +* 일반적인 방법으로 Pooling을 통해 Input size를 맞춰야하는데 RoI가 달라서 문제가 생긴다. +→ RoI pooling이라는 새로운 기법을 이용하여 Feature map의 size를 통일 +→ FC 층을 통해서 Classification에 대한 Loss 값을 계산 +→ 마찬가지로 Bounding Box에 대한 Loss 값 계산 + +Faster R-CNN + +Feature map을 만드는 CNN과 그 이후 classification + localization하는데 사용하는 CNN을 공유해서 사용한다는 아이디어에서 출발한다. + +*RPN classify object / not object (binary classification)RPN regress box coordinatesFinal classification score (object classes)Final box coordinates* + +이렇게 4개의 Loss function이 필요하다. + +RPN은 Region Proposal Network를 의미한다. +Faster R-CNN에서는 총 9개의 anchor box를 사용한다. + +Anchor box란 물체의 모양이 어더게 생겼는지 모르니 서로 다른 비율의 Bounding box를 만들고, 모두 시도를 해서 최적의 Bounding box를 찾기 위해 사용하는 것 + +물체가 있을 확률 = IoU → 내가 예측한 Bounding Box의 크기과 실제 GT의 값을 비교해보는 것 From b15616b7fd7f3eba6c281420f724ce2791110546 Mon Sep 17 00:00:00 2001 From: MSY99 <101084413+MSY99@users.noreply.github.com> Date: Tue, 21 Jun 2022 00:58:43 +0900 Subject: [PATCH 18/20] =?UTF-8?q?CV=5FWeek15=5F=EC=98=88=EC=8A=B5=EA=B3=BC?= 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