10,944 research outputs found
Maximum Inner-Product Search using Tree Data-structures
The problem of {\em efficiently} finding the best match for a query in a
given set with respect to the Euclidean distance or the cosine similarity has
been extensively studied in literature. However, a closely related problem of
efficiently finding the best match with respect to the inner product has never
been explored in the general setting to the best of our knowledge. In this
paper we consider this general problem and contrast it with the existing
best-match algorithms. First, we propose a general branch-and-bound algorithm
using a tree data structure. Subsequently, we present a dual-tree algorithm for
the case where there are multiple queries. Finally we present a new data
structure for increasing the efficiency of the dual-tree algorithm. These
branch-and-bound algorithms involve novel bounds suited for the purpose of
best-matching with inner products. We evaluate our proposed algorithms on a
variety of data sets from various applications, and exhibit up to five orders
of magnitude improvement in query time over the naive search technique.Comment: Under submission in KDD 201
Large Scale Spectral Clustering Using Approximate Commute Time Embedding
Spectral clustering is a novel clustering method which can detect complex
shapes of data clusters. However, it requires the eigen decomposition of the
graph Laplacian matrix, which is proportion to and thus is not
suitable for large scale systems. Recently, many methods have been proposed to
accelerate the computational time of spectral clustering. These approximate
methods usually involve sampling techniques by which a lot information of the
original data may be lost. In this work, we propose a fast and accurate
spectral clustering approach using an approximate commute time embedding, which
is similar to the spectral embedding. The method does not require using any
sampling technique and computing any eigenvector at all. Instead it uses random
projection and a linear time solver to find the approximate embedding. The
experiments in several synthetic and real datasets show that the proposed
approach has better clustering quality and is faster than the state-of-the-art
approximate spectral clustering methods
Revisiting Kernelized Locality-Sensitive Hashing for Improved Large-Scale Image Retrieval
We present a simple but powerful reinterpretation of kernelized
locality-sensitive hashing (KLSH), a general and popular method developed in
the vision community for performing approximate nearest-neighbor searches in an
arbitrary reproducing kernel Hilbert space (RKHS). Our new perspective is based
on viewing the steps of the KLSH algorithm in an appropriately projected space,
and has several key theoretical and practical benefits. First, it eliminates
the problematic conceptual difficulties that are present in the existing
motivation of KLSH. Second, it yields the first formal retrieval performance
bounds for KLSH. Third, our analysis reveals two techniques for boosting the
empirical performance of KLSH. We evaluate these extensions on several
large-scale benchmark image retrieval data sets, and show that our analysis
leads to improved recall performance of at least 12%, and sometimes much
higher, over the standard KLSH method.Comment: 15 page
Scalable Image Retrieval by Sparse Product Quantization
Fast Approximate Nearest Neighbor (ANN) search technique for high-dimensional
feature indexing and retrieval is the crux of large-scale image retrieval. A
recent promising technique is Product Quantization, which attempts to index
high-dimensional image features by decomposing the feature space into a
Cartesian product of low dimensional subspaces and quantizing each of them
separately. Despite the promising results reported, their quantization approach
follows the typical hard assignment of traditional quantization methods, which
may result in large quantization errors and thus inferior search performance.
Unlike the existing approaches, in this paper, we propose a novel approach
called Sparse Product Quantization (SPQ) to encoding the high-dimensional
feature vectors into sparse representation. We optimize the sparse
representations of the feature vectors by minimizing their quantization errors,
making the resulting representation is essentially close to the original data
in practice. Experiments show that the proposed SPQ technique is not only able
to compress data, but also an effective encoding technique. We obtain
state-of-the-art results for ANN search on four public image datasets and the
promising results of content-based image retrieval further validate the
efficacy of our proposed method.Comment: 12 page
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