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Add Cosine Similarity Algorithm for Strings (#459)
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‎Algorithms.Tests/Strings/Similarity/CosineSimilarityTests.cs

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using System;
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using Algorithms.Strings.Similarity;
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using NUnit.Framework;
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namespace Algorithms.Tests.Strings.Similarity;
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[TestFixture]
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public class CosineSimilarityTests
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{
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[Test]
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public void Calculate_IdenticalStrings_ReturnsOne()
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{
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var str1 = "test";
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var str2 = "test";
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var result = CosineSimilarity.Calculate(str1, str2);
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Assert.That(result, Is.EqualTo(1.0).Within(1e-6), "Identical strings should have a cosine similarity of 1.");
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}
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[Test]
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public void Calculate_CompletelyDifferentStrings_ReturnsZero()
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{
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var str1 = "abc";
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var str2 = "xyz";
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var result = CosineSimilarity.Calculate(str1, str2);
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Assert.That(result, Is.EqualTo(0.0).Within(1e-6), "Completely different strings should have a cosine similarity of 0.");
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}
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[Test]
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public void Calculate_EmptyStrings_ReturnsZero()
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{
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var str1 = "";
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var str2 = "";
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var result = CosineSimilarity.Calculate(str1, str2);
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Assert.That(result, Is.EqualTo(0.0).Within(1e-6), "Empty strings should have a cosine similarity of 0.");
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}
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[Test]
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public void Calculate_OneEmptyString_ReturnsZero()
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{
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var str1 = "test";
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var str2 = "";
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var result = CosineSimilarity.Calculate(str1, str2);
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Assert.That(result, Is.EqualTo(0.0).Within(1e-6), "Empty string should have a cosine similarity of 0.");
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}
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[Test]
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public void Calculate_SameCharactersDifferentCases_ReturnsOne()
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{
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var str1 = "Test";
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var str2 = "test";
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var result = CosineSimilarity.Calculate(str1, str2);
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Assert.That(result, Is.EqualTo(1.0).Within(1e-6), "The method should be case-insensitive.");
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}
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[Test]
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public void Calculate_SpecialCharacters_ReturnsCorrectValue()
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{
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var str1 = "hello!";
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var str2 = "hello!";
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var result = CosineSimilarity.Calculate(str1, str2);
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Assert.That(result, Is.EqualTo(1.0).Within(1e-6), "Strings with special characters should have a cosine similarity of 1.");
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}
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[Test]
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public void Calculate_DifferentLengthWithCommonCharacters_ReturnsCorrectValue()
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{
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var str1 = "hello";
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var str2 = "hello world";
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var result = CosineSimilarity.Calculate(str1, str2);
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var expected = 10 / (Math.Sqrt(7) * Math.Sqrt(19)); // calculated manually
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Assert.That(result, Is.EqualTo(expected).Within(1e-6), "Strings with different lengths but some common characters should have the correct cosine similarity.");
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}
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[Test]
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public void Calculate_PartiallyMatchingStrings_ReturnsCorrectValue()
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{
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var str1 = "night";
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var str2 = "nacht";
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var result = CosineSimilarity.Calculate(str1, str2);
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// Assuming the correct calculation gives an expected value
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var expected = 3.0 / 5.0;
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Assert.That(result, Is.EqualTo(expected).Within(1e-6), "Partially matching strings should have the correct cosine similarity.");
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}
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}

‎Algorithms/Strings/Similarity/CosineSimilarity.cs

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using System;
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using System.Collections.Generic;
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namespace Algorithms.Strings.Similarity;
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public static class CosineSimilarity
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{
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/// <summary>
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/// Calculates the Cosine Similarity between two strings.
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/// Cosine Similarity is a measure of similarity between two non-zero vectors of an inner product space.
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/// It measures the cosine of the angle between the two vectors.
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/// </summary>
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/// <param name="left">The first string.</param>
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/// <param name="right">The second string.</param>
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/// <returns>
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/// A double value between 0 and 1 that represents the similarity
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/// of the two strings.
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/// </returns>
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public static double Calculate(string left, string right)
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{
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// Step 1: Get the vectors for the two strings
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// Each vector represents the frequency of each character in the string.
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var vectors = GetVectors(left.ToLowerInvariant(), right.ToLowerInvariant());
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var leftVector = vectors.leftVector;
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var rightVector = vectors.rightVector;
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// Step 2: Calculate the intersection of the two vectors
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// The intersection is the set of characters that appear in both strings.
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var intersection = GetIntersection(leftVector, rightVector);
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// Step 3: Calculate the dot product of the two vectors
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// The dot product is the sum of the products of the corresponding values of the characters in the intersection.
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var dotProduct = DotProduct(leftVector, rightVector, intersection);
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// Step 4: Calculate the square magnitude of each vector
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// The magnitude is the square root of the sum of the squares of the values in the vector.
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var mLeft = 0.0;
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foreach (var value in leftVector.Values)
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{
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mLeft += value * value;
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}
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var mRight = 0.0;
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foreach (var value in rightVector.Values)
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{
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mRight += value * value;
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}
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// Step 5: Check if either vector is zero
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// If either vector is zero (i.e., all characters are unique), the Cosine Similarity is 0.
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if (mLeft <= 0 || mRight <= 0)
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{
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return 0.0;
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}
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// Step 6: Calculate and return the Cosine Similarity
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// The Cosine Similarity is the dot product divided by the product of the magnitudes.
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return dotProduct / (Math.Sqrt(mLeft) * Math.Sqrt(mRight));
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}
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/// <summary>
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/// Calculates the vectors for the given strings.
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/// </summary>
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/// <param name="left">The first string.</param>
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/// <param name="right">The second string.</param>
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/// <returns>A tuple containing the vectors for the two strings.</returns>
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private static (Dictionary<char, int> leftVector, Dictionary<char, int> rightVector) GetVectors(string left, string right)
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{
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var leftVector = new Dictionary<char, int>();
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var rightVector = new Dictionary<char, int>();
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// Calculate the frequency of each character in the left string
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foreach (var character in left)
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{
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leftVector.TryGetValue(character, out var frequency);
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leftVector[character] = ++frequency;
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}
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// Calculate the frequency of each character in the right string
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foreach (var character in right)
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{
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rightVector.TryGetValue(character, out var frequency);
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rightVector[character] = ++frequency;
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}
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return (leftVector, rightVector);
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}
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/// <summary>
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/// Calculates the dot product between two vectors represented as dictionaries of character frequencies.
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/// The dot product is the sum of the products of the corresponding values of the characters in the intersection of the two vectors.
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/// </summary>
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/// <param name="leftVector">The vector of the left string.</param>
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/// <param name="rightVector">The vector of the right string.</param>
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/// <param name="intersection">The intersection of the two vectors, represented as a set of characters.</param>
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/// <returns>The dot product of the two vectors.</returns>
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private static double DotProduct(Dictionary<char, int> leftVector, Dictionary<char, int> rightVector, HashSet<char> intersection)
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{
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// Initialize the dot product to 0
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double dotProduct = 0;
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// Iterate over each character in the intersection of the two vectors
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foreach (var character in intersection)
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{
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// Calculate the product of the corresponding values of the characters in the left and right vectors
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dotProduct += leftVector[character] * rightVector[character];
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}
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// Return the dot product
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return dotProduct;
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}
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/// <summary>
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/// Calculates the intersection of two vectors, represented as dictionaries of character frequencies.
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/// </summary>
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/// <param name="leftVector">The vector of the left string.</param>
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/// <param name="rightVector">The vector of the right string.</param>
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/// <returns>A HashSet containing the characters that appear in both vectors.</returns>
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private static HashSet<char> GetIntersection(Dictionary<char, int> leftVector, Dictionary<char, int> rightVector)
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{
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// Initialize a HashSet to store the intersection of the two vectors.
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var intersection = new HashSet<char>();
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// Iterate over each key-value pair in the left vector.
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foreach (var kvp in leftVector)
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{
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// If the right vector contains the same key, add it to the intersection.
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if (rightVector.ContainsKey(kvp.Key))
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{
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intersection.Add(kvp.Key);
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}
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}
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return intersection;
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}
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}

‎README.md

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* [A181391 Van Eck's](./Algorithms/Sequences/VanEcksSequence.cs)
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* [String](./Algorithms/Strings)
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* [Similarity](./Algorithms/Strings/Similarity/)
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* [Cosine Similarity](./Algorithms/Strings/Similarity/CosineSimilarity.cs)
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* [Hamming Distance](./Algorithms/Strings/Similarity/HammingDistance.cs)
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* [Jaro Similarity](./Algorithms/Strings/Similarity/JaroSimilarity.cs)
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* [Jaro-Winkler Distance](./Algorithms/Strings/Similarity/JaroWinklerDistance.cs)

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