Projects and homework for the UW AMATH 582 Computational Methods For Data Analysis class
To run, first extract subdata.mat from this zip file.
Run HW1.m to process data, produce visualizations, and print results. See HW1.pdf for a detailed description of the results.
Several scripts were written to generate a spectrogram and generate a music score from an audio file. The first of these is "getSpectrogram.m" which ouputs a spectrogram matrix with time vector tg and frequency vector freq given the inputs:
[spectrogram, tg, freq] = getSpectrogram('GNR.m4a', 0.05, 10000)
which would open the GNR.m4a song and use a window width of 0.05 seconds and a maximum frequency of 10000 Hz to generate and display the spectrogram. The "reverseSpectrogram.m" script converts the spectrogram back to the audio data and frequency information:
[audio, frequency] = reverseSpectrogram(spectrogram, tg, freq)
Finally, the "getNotes.m" script creates a musical score from an input file and frequency bounds:
out = getNotes('GNR.m4a, 800, 200)
where out contains two string columns with timing and note location (i.e. C4, A#2). The "floydAnalysis.m" file contains a demo of these tools and is described in more detail in HW2.pdf.
Several scripts were written to analyze camera footage of a paint can on a spring. Three cameras were used to capture videos of 4 experimental setups that must be downloaded as matrix files. Principle component analysis was used to isolate the orthagonal directions of motion. To plot the analysis of the experiments, run HW3.m. A helper function was also used to isolate features from multiple frames of the photo called eigenBucket.m that has the following inputs and outputs
[EB] = eigenBucket(movie, numImages, skip)
where movie is a 4D matrix containing the RGB video, numImages is the total number of images to process, and skip is the sampling rate of frames to average the image. The output, EB is a grayscale image with the same dimensions as each frame in movie containing the 20 most common eigen-features of the frame combined into a single image.
This homeworked use principle components analysis and simple supervised machine-learning algorithms to read digits from images using the MNIST handwritten digits database. To get started, download and extract the four gzip archives from http://yann.lecun.com/exdb/mnist/ to your local directory. Then run mnistSVD.m to generate the basis matrices, which will be stored in the file pcaMats.mat. Finally, run the mnistClassifiers.m file to test the various classifiers and visualize data clusters.
Dynamic mode decomposition (DMD) was used to separate the foreground and background of images. Using a low-rank basis and isolating low frequency DMD modes, background subtraction was used to isolate moving features. The general function from dmdBgSub.m was used to process the images with the following arguments
[fgvid, bgvid] = edmdBgSub(filename, rank, cutoff)
where the rank variable determined the number of SVD modes to use for background reconstruction and the cutoff variable was used as an upper limit to the frequency for the background DMD modes.
A demo of this was implemented in HW5.m which processes two video files that can be downloaded here.. The grayscale foreground and background videos are written to AVI movie files.
Quantum transport through a DNA structure was monitored as a function of the contact self-energies. Looking at principle components of the transmission spectrum and applying regularization methods it was possible to determine the correlation between the self-energies of the contacts and the transmission energy levels present in the structure. Run TransmissionAnalysis.m to visualize the principle components analysis and regression methods. Run DOSPlot.m to compare the weighting of the contact self-energies to the locations of peaks in the 2D density of states plot.