4,915 research outputs found
Indexability, concentration, and VC theory
Degrading performance of indexing schemes for exact similarity search in high
dimensions has long since been linked to histograms of distributions of
distances and other 1-Lipschitz functions getting concentrated. We discuss this
observation in the framework of the phenomenon of concentration of measure on
the structures of high dimension and the Vapnik-Chervonenkis theory of
statistical learning.Comment: 17 pages, final submission to J. Discrete Algorithms (an expanded,
improved and corrected version of the SISAP'2010 invited paper, this e-print,
v3
Evaluation of Hashing Methods Performance on Binary Feature Descriptors
In this paper we evaluate performance of data-dependent hashing methods on
binary data. The goal is to find a hashing method that can effectively produce
lower dimensional binary representation of 512-bit FREAK descriptors. A
representative sample of recent unsupervised, semi-supervised and supervised
hashing methods was experimentally evaluated on large datasets of labelled
binary FREAK feature descriptors
The supervised IBP: neighbourhood preserving infinite latent feature models
We propose a probabilistic model to infer supervised latent variables in the Hamming space from observed data. Our model allows simultaneous inference of the number of binary latent variables, and their values. The latent variables preserve neighbourhood structure of the data in a sense that objects in the same semantic concept have similar latent values, and objects in different concepts have dissimilar latent values. We formulate the supervised infinite latent variable problem based on an intuitive principle of pulling objects together if they are of the same type, and pushing them apart if they are not. We then combine this principle with a flexible Indian Buffet Process prior on the latent variables. We show that the inferred supervised latent variables can be directly used to perform a nearest neighbour search for the purpose of retrieval. We introduce a new application of dynamically extending hash codes, and show how to effectively couple the structure of the hash codes with continuously growing structure of the neighbourhood preserving infinite latent feature space
Drawbacks and Proposed Solutions for Real-time Processing on Existing State-of-the-art Locality Sensitive Hashing Techniques
Nearest-neighbor query processing is a fundamental operation for many image
retrieval applications. Often, images are stored and represented by
high-dimensional vectors that are generated by feature-extraction algorithms.
Since tree-based index structures are shown to be ineffective for high
dimensional processing due to the well-known "Curse of Dimensionality",
approximate nearest neighbor techniques are used for faster query processing.
Locality Sensitive Hashing (LSH) is a very popular and efficient approximate
nearest neighbor technique that is known for its sublinear query processing
complexity and theoretical guarantees. Nowadays, with the emergence of
technology, several diverse application domains require real-time
high-dimensional data storing and processing capacity. Existing LSH techniques
are not suitable to handle real-time data and queries. In this paper, we
discuss the challenges and drawbacks of existing LSH techniques for processing
real-time high-dimensional image data. Additionally, through experimental
analysis, we propose improvements for existing state-of-the-art LSH techniques
for efficient processing of high-dimensional image data.Comment: Accepted and Presented at the 5th International Conference on Signal
and Image Processing (SIGI-2019), Dubai, UA
Scalable approximate FRNN-OWA classification
Fuzzy Rough Nearest Neighbour classification with Ordered Weighted Averaging operators (FRNN-OWA) is an algorithm that classifies unseen instances according to their membership in the fuzzy upper and lower approximations of the decision classes. Previous research has shown that the use of OWA operators increases the robustness of this model. However, calculating membership in an approximation requires a nearest neighbour search. In practice, the query time complexity of exact nearest neighbour search algorithms in more than a handful of dimensions is near-linear, which limits the scalability of FRNN-OWA. Therefore, we propose approximate FRNN-OWA, a modified model that calculates upper and lower approximations of decision classes using the approximate nearest neighbours returned by Hierarchical Navigable Small Worlds (HNSW), a recent approximative nearest neighbour search algorithm with logarithmic query time complexity at constant near-100% accuracy. We demonstrate that approximate FRNN-OWA is sufficiently robust to match the classification accuracy of exact FRNN-OWA while scaling much more efficiently. We test four parameter configurations of HNSW, and evaluate their performance by measuring classification accuracy and construction and query times for samples of various sizes from three large datasets. We find that with two of the parameter configurations, approximate FRNN-OWA achieves near-identical accuracy to exact FRNN-OWA for most sample sizes within query times that are up to several orders of magnitude faster
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