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Machine Learning代写常见问题解答
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Machine Learning高分代写案例：CSCI 567 USC
Q1. K-means++ initialization
K-means++ generally performs much better than the vanilla K-means algorithm. The only difference is in the initialization of the centroids. According to the discussions in the lecture, implement this initialization in function get_k_means_plus_plus_center_indices. (Note that we also provide the vanilla initialization method in get_lloyd_k_means.)
Q2. K-means algorithm
Recall that for a dataset x_1, . . . , x_N ∈ R^Dx1,…,xN∈RD, the K-means distortion objective is:
In this part, you need to implement the K-means procedure that iteratively computes the new cluster centroids and assigns data points to the new clusters. The procedure stops whenever 1) the number of updates has reached the given maximum number, or 2) when the *average* K-means distortion objective J changes less than a given threshold between two iterations.
Implement this part in the fitfunction of the class KMeans. While assigning a sample to a cluster, if there is a tie (i.e. the sample is equidistant from two or more centroids), you should choose the one with the smaller index (which is what numpy.argmin does already).
After you complete the implementation, run KmeansTest.py to see the results of this on a toy dataset. You should be able to see three images generated in a folder called plots. In particular, you can see toy_dataset_predicted_labels.png and toy_dataset_real_labels.png, and compare the clusters identified by the algorithm against the real clusters. Your implementation should be able to recover the correct clusters sufficiently well. Representative images are shown below. Red dots are cluster centroids. Note that color coding of recovered clusters may not match that of correct clusters. This is due to mis-match in ordering the retrieved clusters and the correct clusters (which is fine).
Q3 Classification with K-means
Another application of clustering is to obtain a faster version of the nearest neighbor algorithm. Recall that nearest neighbor evaluates the distance of a test sample from every training point to predict its label, which can be very slow. Instead, we can compress the entire training dataset to just K centroids, where each centroid is now labeled as the majority class of the corresponding cluster. After this compression the prediction time of nearest neighbor is reduced from O(N) to just O(K) (see below for the pseudocode).
You need to complete the fit and predict function in KMeansClassifier following the comments in the code. Again, whenever you need to break a tie, pick the one with the smallest index.
Once completed, run KmeansTest.py again to evaluate the classifier on a test set (digits). For comparison, the script will also print accuracy of a logistic classifier and a vanilla nearest neighbor classifier. An example is shown below.
Q4 Image compression with K-means
In this part, we will take lossy image compression as another application of clustering. The idea is simply to treat each pixel of an image as a point, then perform K-means algorithm to cluster these points, and finally replace each pixel with its closest centroid.
What you need to implement is to compress an image with K centroids given (called code_vectors). Specifically, complete the function transform_image following the comments in the code.
After your implementation, run KmeansTest.py again. You should be able to see an image compressed_baboon.png in the plots folder. You can see that this image is slightly distorted as compared to the original baboon.tiff. The ideal result should take about 35-40 iterations and the Mean Square Error (between the two images) should be less than 0.0098. It takes about 1-2 minutes to complete normally.
