Answered: Compute the match-based similarity,…

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

Compute the match-based similarity, cosine similarity and the Jaccard coefficient, between the
two sets {A,B,C} and {A,C,D,E}.

Expert Solution

Step 1

Answers :-

let

M= { A,B,C} and N={A,C,D,E}

a) Match based similarity coefficient is

$X C (M, N) = \frac{|M \cap N|}{m a x (|M|, |N|)} s o h e r e, M \cap N = \{A, C\} \Rightarrow |M \cap N| = 2 m a x (|M|, |N|) = 4 X C (M, N) = \frac{2}{4} = \frac{1}{2} b) C o \sin e s i m i l a r i t y b e t w e e n t h e s e t s X a n d Y a r e c a l c u l a t e d b y t h e f o r m u l a k = \frac{|M \cap N|}{\sqrt{|M| \times |N|}} w h e r e |M| i s t h e n u m b e r o f e l e m e n t s i n M M = {A, B, C} a n d N = {A, C, D, E} w e h a v e M \cap N = \{A, C\} \Rightarrow |M \cap N| = 2 |M| = 3 a n d |N| = 4 k = \frac{2}{\sqrt{3 \times 4}} = \frac{1}{\sqrt{3}} c) F o r m u l a f o r J a c c a r d c o e f f i c i e n t i s J (M, N) = \frac{|M \cap N|}{|M \cup N|} s o h e r e M \cup N = {A, B, C, D, E} \Rightarrow |M \cup N| = 5 M \cap N = {A, C} \Rightarrow |M \cap N| = 2 J (M, N) = \frac{2}{5}$

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