Utilizing Locality-Sensitive Hashing (LSH) for Market Basket Analysis

Market Basket Analysis is a powerful technique used in retail and e-commerce to uncover associations between products frequently purchased together. By analyzing transactional data, businesses can identify patterns and make informed decisions to improve sales strategies, product placements, and customer experiences.

Introduction to Market Basket Analysis

Market Basket Analysis operates on the principle of examining transactional data to uncover associations between products. The fundamental metric used in this analysis is "support," which measures the frequency of occurrence of item combinations in transactions. Common metrics derived from support include "confidence" and "lift," which provide insights into the strength and significance of associations between products.

The Apriori algorithm is a fundamental technique in data mining for discovering frequent itemsets and deriving association rules from transactional data. It works by iteratively generating candidate itemsets, counting their support, and identifying frequent itemsets above a specified threshold.
Despite its usefulness, the Apriori algorithm has limitations:

1. Computational Complexity: It can be computationally expensive, especially for large datasets, due to multiple passes over the data and generation of numerous candidate itemsets.

2. Memory Usage: The algorithm requires significant memory to store candidate itemsets and support counts, which can be challenging for systems with limited resources.

3. Inefficient for Sparse Data: In datasets with high sparsity, the algorithm may produce many low-support itemsets, leading to inefficient pruning and reduced effectiveness.

4. Apriori Property Limitation: Premature pruning based on the Apriori property may miss potentially interesting association rules if infrequent itemsets are pruned too aggressively.

For scenarios where the Apriori algorithm's limitations are prohibitive, consider exploring alternative approaches such as Locality-Sensitive Hashing (LSH) for scalable and efficient market basket analysis.

Introduction to Locality-Sensitive Hashing (LSH)

Locality-Sensitive Hashing (LSH) is a technique used in data mining and similarity search to efficiently approximate similarity between data points in high-dimensional spaces. It is particularly useful for applications involving large datasets where traditional similarity search methods, such as exhaustive pairwise comparisons, become computationally expensive.

The core idea behind LSH is to hash data points into buckets in such a way that similar data points are more likely to be hashed into the same bucket, while dissimilar points are likely to be hashed into different buckets. By organizing data into these buckets, LSH enables approximate nearest neighbor search, where similar data points can be efficiently retrieved by querying the corresponding buckets.

LSH achieves this goal by employing hash functions that satisfy the locality-sensitive property, which means that the probability of collision (i.e., two data points being hashed into the same bucket) decreases with their similarity. LSH techniques are designed to balance the trade-off between precision (retrieving similar data points) and recall (retrieving all similar data points) based on application requirements.

One of the key advantages of LSH is its ability to scale to large datasets with high-dimensional data spaces, such as text documents, images, and genetic sequences. By partitioning the data space into hash buckets, LSH reduces the search space for similarity queries, leading to significant improvements in computational efficiency.

For this demonstration, we'll be utilizing the Groceries dataset, a commonly used benchmark dataset in Market Basket Analysis. This dataset comprises transactional records from a grocery store, with each transaction representing a customer's basket containing an assortment of items. We employ a GoLang library, github/agtabesh/lsh, for implementing Locality-Sensitive Hashing (LSH) in our analysis.

Let's go through the Go code step by step (you can find the source code here):

import (
    "context"
    "encoding/csv"
    "fmt"
    "os"
    "sort"

    "github.com/agtabesh/lsh"
    "github.com/agtabesh/lsh/types"
)

The code starts by importing necessary packages. context, csv, os, and fmt are standard Go packages. sort is used for sorting slices. github/agtabesh/lsh contains the Locality-Sensitive Hashing (LSH) implementation, and github.com/agtabesh/lsh/types contains custom types used in the LSH implementation.

datasetMap, err := readVectorsFromFile("Groceries_dataset.csv")
if err != nil {
    return err
}

The program starts by reading vectors (representing transactional data) from a CSV file named "Groceries_dataset.csv" using the readVectorsFromFile function. It handles any errors that occur during file reading and returns an error if encountered.

config := lsh.LSHConfig{
    SignatureSize: 128,
}

Next, the code defines the configuration for the Locality-Sensitive Hashing (LSH) algorithm. The SignatureSize parameter determine the size of the hash signature.

hashFamily := lsh.NewXXHASH64HashFamily(config.SignatureSize)
similarityMeasure := lsh.NewHammingSimilarity()
store := lsh.NewInMemoryStore()

The code initializes components required for LSH, including the hash family (hashFamily), similarity measure (similarityMeasure), and storage mechanism (store). In this case, XXHASH64HashFamily is used for hashing, HammingSimilarity for measuring similarity, and an in-memory store.

instance, err := lsh.NewLSH(config, hashFamily, similarityMeasure, store)
if err != nil {
    return err
}

An LSH instance is created using the previously defined configuration, hash family, similarity measure, and store.

ctx := context.Background()
for i, vector := range datasetMap {
    vectorID := types.VectorID(i)
    err := instance.Add(ctx, vectorID, vector)
    if err != nil {
        return err
    }
}

The code iterates over the dataset map obtained from the CSV file, and adds them to the LSH instance.

vector := types.Vector{"white bread": 1}
count := 100
similarVectorsID, err := instance.QueryByVector(ctx, vector, count)
if err != nil {
    return err
}

A sample vector is defined, representing a product ("white bread"), and the QueryByVector method is called to find similar vectors in the LSH instance. The number of similar vectors to retrieve is specified by the count variable.

items := make(Items)
for _, vectorID := range similarVectorsID {
    for item := range datasetMap[vectorID.String()] {
        items[item.String()]++
    }
}
n := 10
result := items.Top(n)
fmt.Println("Result:", result)

The code iterates over the IDs of similar vectors retrieved and aggregates the associated items from the dataset map, counting their occurrences. The top 10 associated items are extracted from the aggregated data, and the result is printed to the console.

You can find the source code here

Conclusion

In conclusion, Market Basket Analysis combined with Locality-Sensitive Hashing provides a scalable and efficient solution for uncovering associations between products in large transactional datasets. By leveraging this approach, businesses can gain valuable insights to optimize their sales strategies and enhance customer experiences.

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