Question

When using Locality Sensitive Hashing (LSH) for deduplication, what is the specific consequence of choosing a hash family that fails to satisfy the locality-sensitive property?

Accepted Answer

Locality Sensitive Hashing is a technique designed to map similar data items into the same hash buckets with high probability, while mapping dissimilar items into different buckets. The locality-sensitive property requires that the probability of a collision—two items resulting in the same hash value—is significantly higher for items that are close to each other than for those that are far apart. If a hash family fails to satisfy this property, the fundamental mechanism of the algorithm breaks down. Specifically, the hash function becomes either random or blind to the similarity between items. Consequently, items that are highly similar will no longer be guaranteed to land in the same bucket, causing the deduplication process to miss actual duplicates, which results in a high false negative rate. Conversely, the hash function may map completely unrelated items into the same bucket, leading to a high false positive rate where the system incorrectly identifies distinct items as duplicates. In such a case, the algorithm loses its ability to organize data based on distance or similarity, essentially reducing the process to a random partitioning of the dataset that provides no efficiency or accuracy benefits for finding duplicates.

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When using Locality Sensitive Hashing (LSH) for deduplication, what is the specific consequence of choosing a hash family that fails to satisfy the locality-sensitive property?