Please help with the matlab code explaining how in Locality sensitive hashing(LSH), hash tables are stored and manipulated for search

Please demonstrate with Matlab Code., how hashtables are stored and searched for to find ANNF(Approximate Nearest Neighbor fields) in LSH

Answer 1

[Hari]

Hi Merlyn,

Here is an sample example for the same:

Generate Data and Hash Functions:

Create a sample dataset and define hash functions. These hash functions will map similar data points to the same bucket.

data = rand(100, 2); % 100 2D data points
numHashTables = 5;
numHashFunctions = 4;
hashFunctions = randn(numHashFunctions, 2, numHashTables);

Create Hash Tables:

Initialize hash tables to store indices of data points. Each table corresponds to a set of hash functions.

hashTables = cell(1, numHashTables);
for i = 1:numHashTables
    hashTables{i} = containers.Map('KeyType', 'char', 'ValueType', 'any');
end

Populate Hash Tables:

For each data point, compute the hash keys using the hash functions and store the indices in the corresponding hash table.

for i = 1:size(data, 1)
    for j = 1:numHashTables
        hashKey = sign(hashFunctions(:, :, j) * data(i, :)');
        keyStr = num2str(hashKey');
        if isKey(hashTables{j}, keyStr)
            hashTables{j}(keyStr) = [hashTables{j}(keyStr), i];
        else
            hashTables{j}(keyStr) = i;
        end
    end
end

Search for Approximate Nearest Neighbors:

To find ANNF, compute the hash keys for the query point and retrieve potential neighbors from the hash tables.

queryPoint = [0.5, 0.5];
candidateIndices = [];
for j = 1:numHashTables
    hashKey = sign(hashFunctions(:, :, j) * queryPoint');
    keyStr = num2str(hashKey');
    if isKey(hashTables{j}, keyStr)
        candidateIndices = [candidateIndices, hashTables{j}(keyStr)];
    end
end
candidateIndices = unique(candidateIndices);

Evaluate Neighbors:

Compute distances from the query point to the candidates and select the nearest ones.

distances = vecnorm(data(candidateIndices, :) - queryPoint, 2, 2);
[~, sortedIndices] = sort(distances);
nearestNeighbors = candidateIndices(sortedIndices(1:5)); % Top 5 neighbors

Refer to the documentation of "containers.Map" function to know more about the properties supported: https://www.mathworks.com/help/matlab/ref/containers.map.html

Hope this helps!

[Walter Roberson]

    hashTables{i} = containers.Map('KeyType', 'char', 'ValueType', 'any');

These days, consideration should be given to using a dictionary() instead of contrainers.Map()