Let the document be “good bad student good bad instructor” and the query be “good student”. Fill out the empty columns in the following table and then compute the cosine similarity between the document vector and the query vector. In the table, df denotes document frequency, idf denotes inverse document frequency (i.e., idft = log10N/dft), tf denotes term frequency, log tf denotes the tf weight based on log-frequency weighting as shown in slides (i.e., 1+log10tft,d for tft,d> 0 and 0 otherwise), d is the document vector, d’ is the length-normalized d, q is the query vector, and q’ is the length-normalized q. Assume N (number of documents in the corpus) = 10,000,000. documentquerytermsdfidftflog tfdd'tflog tf qq'bad1000good 10000instructor 10student 50000The idf values for bad, good, instructor and student are 4, 3, 6, 2.3 respectively.= <2, 2, 1, 1>.|= <1.3, 1.3, 1, 1>.d' = <0.56, 0.56, 0.43, 0.43>.d' = <0.43, 0.43, 0.21, 0.21>.q <0, 1, 0, 1>.q <0, 3, 0, 2.3>.q' <0, 0.79, 0, 0.61>.q' <0, 0.61, 0, 0.43>.cosine(d, q) = 0.705.cosine(d, q) = 0.353.

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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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Let the document be “good bad student good bad instructor” and the query be “good student”. Fill out the empty columns in the following table and then compute the cosine similarity between the document vector and the query vector. In the table, df denotes document frequency, idf denotes inverse document frequency (i.e., idf_t = log₁₀N/df_t), tf denotes term frequency, log tf denotes the tf weight based on log-frequency weighting as shown in slides (i.e., 1+log₁₀tf_t,d for tf_t,d> 0 and 0 otherwise), d is the document vector, d’ is the length-normalized d, q is the query vector, and q’ is the length-normalized q. Assume N (number of documents in the corpus) = 10,000,000.