DAT210x - Programming with Python for DS

Module4- Lab4



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import math, random
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import matplotlib
import scipy.io

from mpl_toolkits.mplot3d import Axes3D



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# Look pretty...

# matplotlib.style.use('ggplot')
# plt.style.use('ggplot')

Some Boilerplate Code

For your convenience, we've included some boilerplate code here which will help you out. You aren't expected to know how to write this code on your own at this point, but it'll assist with your visualizations and loading of the .mat file. We've added some notes to the code in case you're interested in knowing what it's doing:



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def Plot2D(T, title, x, y, num_to_plot=40):
    # This method picks a bunch of random samples (images in your case)
    # to plot onto the chart:
    fig = plt.figure()
    
    ax = fig.add_subplot(111)
    ax.set_title(title)
    ax.set_xlabel('Component: {0}'.format(x))
    ax.set_ylabel('Component: {0}'.format(y))
    
    x_size = (max(T[:,x]) - min(T[:,x])) * 0.08
    y_size = (max(T[:,y]) - min(T[:,y])) * 0.08
    
    for i in range(num_to_plot):
        img_num = int(random.random() * num_images)
        x0, y0 = T[img_num,x]-x_size/2., T[img_num,y]-y_size/2.
        x1, y1 = T[img_num,x]+x_size/2., T[img_num,y]+y_size/2.
        img = df.iloc[img_num,:].reshape(num_pixels, num_pixels)
        ax.imshow(img, aspect='auto', cmap=plt.cm.gray, interpolation='nearest', zorder=100000, extent=(x0, x1, y0, y1))

    # It also plots the full scatter:
    ax.scatter(T[:,x],T[:,y], marker='.',alpha=0.7)

A .MAT file is a MATLAB file type. The faces dataset could have came in through .png images, but we'll show you how to do that in another lab. For now, you'll see how to import .mats:



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mat = scipy.io.loadmat('Datasets/face_data.mat')
df = pd.DataFrame(mat['images']).T
num_images, num_pixels = df.shape
num_pixels = int(math.sqrt(num_pixels))

# Rotate the pictures, so we don't have to crane our necks:
for i in range(num_images):
    df.loc[i,:] = df.loc[i,:].reshape(num_pixels, num_pixels).T.reshape(-1)

And Now, The Assignment

Implement PCA here. Reduce the dataframe df down to three components. Once you've done that, call Plot2D.

The format is: Plot2D(T, title, x, y, num_to_plot=40):

T Your transformed data, stored in an NDArray.
title Your chart's title
x Index of the principal component you want displayed on the x-axis; set it to 0 or 1
y Index of the principal component you want displayed on the y-axis; set it to 1 or 2



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# .. your code here ..

Implement Isomap here. Reduce the dataframe df down to three components. Once you've done that, call Plot2D using the first two components:



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# .. your code here ..

If you're up for a challenge, draw your dataframes in 3D. Even if you're not up for a challenge, just do it anyway. You might have to increase the dimensionality of your transformed dataset:



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# .. your code here ..



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plt.show()



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