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 betweendocuments in two clusters. Formally, for two cluster C; and C, let C= C;U Cj, n = C, we define1sim(C,, C) =E s(x, y)Σn.(n- 1) x.y € C, x =yWhere s(x,is the cosine similarity betweeny)andy.Given a list of clusters C. C2, .... Cm assume that their pairwise similarities are saved in a two dimensional array**",of sizem2. Given three clusters C, C;, and Cr show that there is a way to compute sim(C;U C;, C) in constant time. Note that we ignore the dimensionality in time complexity.

Hierarchical agglomerative clustering HAC is Bottom-up hierarchical clustering, which is frequently…

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 C, let C=C,U C,, n = |C|, we define sim(C, C) =G-D'E s(x, v) n (n-1 x.y € C, x*y Where s(x. v) is the cosine similarity between x and y. Given a list of clusters C. Ca. . Coy assume that their pairwise similarities are saved in a two dimensional array of size m2. Given three clusters C. C., and Cu show that there is a way to compute sim(C.UC. CL) in constant time. Note that we ignore the dimensionality in time complexity.

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 C, let C=C,U C,, n = |C|, we define sim(C, C) =G-D'E s(x, v) n (n-1 x.y € C, x*y Where s(x. v) is the cosine similarity between x and y. Given a list of clusters C. Ca. . Coy assume that their pairwise similarities are saved in a two dimensional array of size m2. Given three clusters C. C., and Cu show that there is a way to compute sim(C.UC. CL) in constant time. Note that we ignore the dimensionality in time complexity.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

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 C, let C= C;U Cj, n = C, we define
1
sim(C,, C) =
E s(x, y)
Σ
n.(n- 1) x.y € C, x =y
Where s(x,
is the cosine similarity between
y)
and
y.
Given a list of clusters C. C2, .... Cm assume that their pairwise similarities are saved in a two dimensional array
**",
of size
m
2. Given three clusters C, C;, and Cr show that there is a way to compute sim(C;U C;, C) in constant time. Note that we ignore the dimensionality in time complexity.

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