Created
February 20, 2015 08:13
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| import re | |
| import scipy.io | |
| import scipy.linalg | |
| import scipy.sparse.linalg; | |
| import numpy | |
| import matplotlib.pyplot | |
| def relative_residual(U, z): | |
| m, n = U.shape | |
| return numpy.linalg.norm((numpy.eye(m) - U.dot(U.T)).dot(z)) / numpy.linalg.norm(z) | |
| training_digits = scipy.io.loadmat('training_digits.mat')['azip'] | |
| correct_training_digits = scipy.io.loadmat('correct_training_digits.mat')['dzip'] | |
| test_digits = scipy.io.loadmat('test_digits.mat')['testzip'] | |
| correct_test_digits = scipy.io.loadmat('correct_test_digits.mat')['dtest'][0] | |
| correct_training_digits_indicies = [[] for i in range(0,10)] | |
| for digit in range(0,10): | |
| for idx, val in enumerate(numpy.nditer(correct_training_digits)): | |
| if digit == int(val): | |
| correct_training_digits_indicies[int(val)].append(idx) | |
| training_set = [None] * 10 | |
| for digit in range(0,10): | |
| training_set[digit] = training_digits[:,correct_training_digits_indicies[digit]] | |
| singular_values = [numpy.zeros((256,1)) for i in range(0,10)] | |
| matplotlib.pyplot.figure(1) | |
| for digit in range(0,10): | |
| s = scipy.linalg.svdvals(training_set[digit]) | |
| for i in range(0,s.shape[0]): | |
| singular_values[digit][i] = s[i] | |
| matplotlib.pyplot.plot(range(0,256), singular_values[digit]) | |
| matplotlib.pyplot.axis([1, 256, 0, 240]) | |
| matplotlib.pyplot.hold(True) | |
| matplotlib.pyplot.hold(False) | |
| correct_predictions = numpy.zeros((10,16)) | |
| for rank in range(5,21): | |
| U = [None] * 10 | |
| s = [None] * 10 | |
| Vh = [None] * 10 | |
| for digit in range(0,10): | |
| U[digit], s[digit], Vh[digit] = scipy.sparse.linalg.svds(training_set[digit], k=rank) | |
| for i in range(0,test_digits.shape[1]): | |
| residuals = numpy.zeros(10) | |
| z = test_digits[:,i] | |
| for digit in range(0,10): | |
| residuals[digit] = relative_residual(U[digit], z) | |
| predicted_digit = numpy.argmin(residuals) | |
| if correct_test_digits[i] == predicted_digit: | |
| correct_predictions[predicted_digit][rank-5] += 1 | |
| matplotlib.pyplot.figure(2) | |
| accuracy_k = numpy.zeros((16,)) | |
| for rank in range(5,21): | |
| accuracy_k[rank-5] = numpy.sum(correct_predictions[:,rank-5]) / test_digits.shape[1] | |
| matplotlib.pyplot.plot(range(5,21), accuracy_k) | |
| matplotlib.pyplot.figure(3) | |
| accuracy_digit = numpy.zeros((10,)) | |
| for digit in range(0,10): | |
| num_digits = numpy.where(correct_test_digits == digit)[0].__len__() | |
| accuracy_digit[digit] = numpy.sum(correct_predictions[digit,:]) / (16*num_digits) | |
| matplotlib.pyplot.plot(range(0,10), accuracy_digit) | |
| matplotlib.pyplot.show() |
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