35 points Assume that we use cosine similarity as the similarity measure. In the hierarchical agglomerative clustering (

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35 Points Assume That We Use Cosine Similarity As The Similarity Measure In The Hierarchical Agglomerative Clustering 1 (111.82 KiB) Viewed 30 times

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35 Points Assume That We Use Cosine Similarity As The Similarity Measure In The Hierarchical Agglomerative Clustering 3 (114.99 KiB) Viewed 30 times

35 points Assume that we use cosine similarity as the similarity measure. In the hierarchical agglomerative clustering (HAC), we need to define a good way to measure the similarity of two clusters. One usual way is to use the group average similarity between documents in two clusters. Formally, for two cluster C, and C₁, let C = C₁UC₁, n = |C|, we define 1 sim(C₁, C) = s(x, y) QUESTION 1 Σ n.(n-1) x,y € C,x=y Where s(x, y) is the cosine similarity between x and y. Save Answer Given a list of clusters C₁, C2, Cm' assume that their pairwise similarities are saved in a two dimensional array of size m2. Given three clusters C₁, C₁, and Ck show that there is a way to compute sim(C,U C₁, Ck) in constant time. Note that we ignore the dimensionality in time complexity. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac).
QUESTION 2 30 points Save Answer For a list of m documents in d-dimensional vector space, each iteration of the means clustering has a time complexity of O(kdm), while the hierarchical agglomerative clustering (HAC) has a time complexity of O(dm2). We know that the overall performance of the K-means clustering depends on the choices of initial centroids. However, there is no such an issue for HAC. Describe a method to use HAC to help the k-means clustering, but the method shall maintain the same time complexity for the k-means clustering. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph X 0 11 99 Open Sans, s... V 10pt R Click Save and Submit to save and submit, Click Save All Answers to save all answers. X² X₂ >TT ¶< 田田图 BEN <> ☀ (1) 0 WORDS POWERED BY TINY A VAV I 1 ROC V Save All Anders S www Save and Submit
Additional Time Used: 166 hours, 49 minutes, 40 seconds. Question Completion Status: X QUESTION 3 35 points Save Answer Assume that you are working for amazon.com. You need to find some way to recommend products for an online shopper without asking for relevance feedback from any user. Provide one solution. For the toolbar, press ALT+F10 or ALT+FN+F10 (Mac). BIUS Paragraph ¶T Q A E Open Sans, s... V 10pt MX² X₂ 8 9 10 BEE 0 WORDS POWERED BY TINY A »¶¶< <> † O O Time Expired. ** I + ORE