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Cosine Similarity – comprehending the mathematics and exactly how it really works with python codes

Cosine Similarity – comprehending the mathematics and exactly how it really works with python codes

1. Introduction

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a widely used approach to fit comparable papers is dependant on counting the number that is maximum of terms involving the papers.

But this approach has a flaw that is inherent. That is, given that size regarding the document increases, the amount of typical terms have a tendency to increase regardless of if the papers speak about various subjects.

The cosine similarity helps over come this fundamental flaw into the ‘count-the-common-words’ or Euclidean distance approach.

2. What’s Cosine Similarity and just why will it be beneficial?

Cosine similarity is a metric utilized to ascertain exactly just just how comparable the papers are aside from their size.

Mathematically, it steps the cosine of this angle between two vectors projected in a multi-dimensional area. The two vectors I am talking about are arrays containing the word counts of two documents in this context.

As a similarity metric, so how exactly does cosine similarity vary from the true quantity of typical terms?

Whenever plotted on a multi-dimensional room, where each dimension corresponds up to a word into the document, the cosine similarity catches the orientation (the angle) of this papers and never the magnitude. If you would like the magnitude, calculate the Euclidean distance rather.

The cosine similarity is beneficial because regardless of if the 2 comparable papers are far aside because of the Euclidean distance because regarding the size (like, the phrase ‘cricket’ appeared 50 times within one document and 10 times an additional) they might nevertheless have a smaller angle among them. Smaller the angle, greater the similarity.

3. Cosine Similarity Example

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Let us assume you have got 3 papers predicated on a few celebrity cricket players – Sachin Tendulkar and Dhoni. Two for the papers (A) and (B) come from the wikipedia pages on the particular players and also the 3rd document (C) is an inferior snippet from Dhoni’s wikipedia page. (more…)