Enhance cosine similarity compution

[omarmahamid]

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name: Feature request
about: Suggest an idea for this project

cosine similarity is in this way:

instead of computing 3 dot times O(3N) we can enhance it the factor of linear time by 3 to be O(N)

I did a JMH benchmark:

package com.microsoft.semantickernel.data;

import com.microsoft.semantickernel.data.vectorsearch.VectorOperations;
import org.openjdk.jmh.annotations.Benchmark;
import org.openjdk.jmh.annotations.BenchmarkMode;
import org.openjdk.jmh.annotations.Fork;
import org.openjdk.jmh.annotations.Level;
import org.openjdk.jmh.annotations.Measurement;
import org.openjdk.jmh.annotations.Mode;
import org.openjdk.jmh.annotations.OutputTimeUnit;
import org.openjdk.jmh.annotations.Scope;
import org.openjdk.jmh.annotations.Setup;
import org.openjdk.jmh.annotations.State;
import org.openjdk.jmh.annotations.Warmup;
import org.openjdk.jmh.runner.Runner;
import org.openjdk.jmh.runner.RunnerException;
import org.openjdk.jmh.runner.options.CommandLineOptionException;
import org.openjdk.jmh.runner.options.CommandLineOptions;
import org.openjdk.jmh.runner.options.Options;
import org.openjdk.jmh.runner.options.OptionsBuilder;
import java.util.ArrayList;
import java.util.List;
import java.util.Random;
import java.util.concurrent.TimeUnit;


@State(Scope.Benchmark)
@BenchmarkMode(Mode.AverageTime)
@OutputTimeUnit(TimeUnit.NANOSECONDS)
@Fork(1)
@Warmup(iterations = 5)
@Measurement(iterations = 2)
public class VectorOperationsBenchmark {

    List<Float> vector1;
    List<Float> vector2;

    @Setup(Level.Trial)
    public void setUp(){
        Random rand = new Random();
        vector1 = new ArrayList<>();
        vector2 = new ArrayList<>();

        for (int i = 0; i < 100; i++) {
            vector1.add(rand.nextFloat());
            vector2.add(rand.nextFloat());
        }
    }


    @Benchmark
    public void benchmarkVectorOperations() {
        VectorOperations.cosineSimilarity(vector1, vector2);
    }


    @Benchmark
    public void benchmarkVectorOperationsOptimized() {
        VectorOperations.optimizeCosineSimilarity(vector1, vector2);
    }

    public static void main(String[] args) throws RunnerException, CommandLineOptionException {
        Options opt = new OptionsBuilder()
            .parent(new CommandLineOptions(args))
            .timeUnit(TimeUnit.NANOSECONDS)
            .include(VectorOperationsBenchmark.class.getSimpleName())
            .build();

        new Runner(opt).run();
    }

}

and the result is:

Benchmark                                                     Mode  Cnt    Score   Error  Units
VectorOperationsBenchmark.benchmarkVectorOperations           avgt    2  202.292          ns/op
VectorOperationsBenchmark.benchmarkVectorOperationsOptimized  avgt    2   96.457          ns/op

it's a major performance for huge vectors.

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