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I'm implementing an algorithm for doing dimensionality reduction: I'm going from a high dimennsional space (images) to a L dimensional space (where L is the number of classes). On this space I'm applying a classifier. In order to test my algorithm, I'm applying it on the MNIST dataset. The two different classifier I'm using are Gaussian classifier and K nearnest neighbours.

By Gaussian Classifier I'm using this, where I have K different multivariate gaussian: one for each class label l_k. The learning part of the Gaussian Classifier is learning the shape of the gaussian (mean and covariance matrix) on the training set, and then it label a point $x$ in the test set according to the maximum probability: $$ P(l_k|x) = \frac{p(x|l_k)p(l_k)}{\sum_{i=1}^K{p(x|l_i)}}$$

Surprisingly, in all the experiment I did so far, have seen the kNN outperform Gaussian classifier! By better performance I simply mean the ratio of correctly classified sample vs mis-classified ones.

def evaluate_me(y_pred, test_labels):
    r=0
    w=0
    for i in range(len(test_labels)):
        if y_pred[i] == test_labels[i]:
            r+=1
        else:
            w+=1
    print("Tested ", len(test_labels), " digits")
    print("Correct: ", r, "wrong: ", w, "error rate: ", float(w)*100/(r+w), "%")
    print("Got correctly ", float(r)*100/(r+w), "%")
    return

print("Trasforming training set")
Y_train = dim_red.transform(X=x_train)

print("Transforming test test")
Y_test= dim_red.transform(X=x_test)

print("Done")

knn_test_labels = classify_knn(Y_train, Y_test, train_labels)
gc_test_labels = classify_gaussian(Y_train, Y_test, train_labels)

print("kNN evaluation")
evaluate_me(knn_test_labels, test_labels)
print("Gaussian evaluation")
evaluate_me(gc_test_labels, test_labels)

Do you have any explanation for this? To me it's sounds strange, since I expect the GC to use more information on the dataset than the plain KNN, since it takes care of different variance on the multiple dimenisons, and the a prori probability of each class.

In particular, can you think of a dataset that perform better with KNN than GC

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  • $\begingroup$ What constitutes better performance? How are classifiers used for dimensionality reduction. What are the results from your code? $\endgroup$ May 19, 2017 at 14:54
  • $\begingroup$ Could you elaborate on the Gaussian classifier? Is this a mixture of gaussians? If yes, please elaborate on how it classifies. For example KNN classifies in accordance to the closest centroid. $\endgroup$
    – Alex R.
    May 19, 2017 at 17:22

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