Neighbourhood preserving quantisation for LSH

Abstract

We introduce a scheme for optimally allocating multiple bits per hyperplane for Locality Sensitive Hashing (LSH). Existing approaches binarise LSH projections by thresholding at zero yielding a single bit per dimension. We demonstrate that this is a sub-optimal bit allocation approach that can easily destroy the neighbourhood structure in the original feature space. Our proposed method, dubbed Neighbourhood Preserving Quantization (NPQ), assigns multiple bits per hyperplane based upon adaptively learned thresholds. NPQ exploits a pairwise affinity matrix to discretise each dimension such that nearest neighbours in the original feature space fall within the same quantisation thresholds and are therefore assigned identical bits. NPQ is not only applicable to LSH, but can also be applied to any low-dimensional projection scheme. Despite using half the number of hyperplanes, NPQ is shown to improve LSH-based retrieval accuracy by up to 65% compared to the state-of-the-art.

Learning to Project and Binarise for Hashing Based Approximate Nearest Neighbour Search

“…In the most closely related past research authors have generally focused on either learning the hashing hyperplanes [1,4,6] or the quantisation thresholds [2,3,7,8] based on the distribution of the data. Seminal approaches for datadependent hyperplane learning either solving an eigenvalue problem to generate a set of orthogonal hyperplanes, for example using Principal Components Analysis (PCA) [9], or frame a custom objective functions that uses pairwise labels to appropriately position the hyperplanes within the feature space [1].…”

“…This approach is commonly known as Single Bit Quantisation (SBQ). Recently there has been significant interest in improving on SBQ by learning one or more thresholds to quantise projections [2,3,8,7]. These quantisation models use either an unsupervised objective such as k-means or squared error minimisation to learn a good set of thresholds for each projected dimension [7,8], or propose a semi-supervised objective that takes into consideration the neighbourhood structure between the data-points in the input feature space [2,3].…”

“…We couple the graph regularised projection model (GRH) of [1] and the semi-supervised quantisation model (NPQ) of [2]. The hyperplanes are learnt using GRH and the projections quantised using NPQ.…”

“…Having learnt the projections of our data-points in steps 1-3, we then quantise the learnt projections using NPQ [2]:…”

“…Equation (9) is directly maximised using Evolutionary Algorithms [2], and encourages a clustering of the projected dimension that respects the constraints in S. …”