k-Nearest Neighbour Classifiers: 2nd Edition (with Python examples)

Perhaps the most straightforward classifier in the arsenal or machine learning techniques is the Nearest Neighbour Classifier -- classification is achieved by identifying the nearest neighbours to a query example and using those neighbours to determine the class of the query. This approach to classification is of particular importance because issues of poor run-time performance is not such a problem these days with the computational power that is available. This paper presents an overview of techniques for Nearest Neighbour classification focusing on; mechanisms for assessing similarity (distance), computational issues in identifying nearest neighbours and mechanisms for reducing the dimension of the data. This paper is the second edition of a paper previously published as a technical report. Sections on similarity measures for time-series, retrieval speed-up and intrinsic dimensionality have been added. An Appendix is included providing access to Python code for the key methods.Comment: 22 pages, 15 figures: An updated edition of an older tutorial on kN

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

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

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

An Efficient Index for Visual Search in Appearance-based SLAM

Vector-quantization can be a computationally expensive step in visual bag-of-words (BoW) search when the vocabulary is large. A BoW-based appearance SLAM needs to tackle this problem for an efficient real-time operation. We propose an effective method to speed up the vector-quantization process in BoW-based visual SLAM. We employ a graph-based nearest neighbor search (GNNS) algorithm to this aim, and experimentally show that it can outperform the state-of-the-art. The graph-based search structure used in GNNS can efficiently be integrated into the BoW model and the SLAM framework. The graph-based index, which is a k-NN graph, is built over the vocabulary words and can be extracted from the BoW's vocabulary construction procedure, by adding one iteration to the k-means clustering, which adds small extra cost. Moreover, exploiting the fact that images acquired for appearance-based SLAM are sequential, GNNS search can be initiated judiciously which helps increase the speedup of the quantization process considerably

Dynamic load balancing in parallel KD-tree k-means

One among the most influential and popular data mining methods is the k-Means algorithm for cluster analysis. Techniques for improving the efficiency of k-Means have been largely explored in two main directions. The amount of computation can be significantly reduced by adopting geometrical constraints and an efficient data structure, notably a multidimensional binary search tree (KD-Tree). These techniques allow to reduce the number of distance computations the algorithm performs at each iteration. A second direction is parallel processing, where data and computation loads are distributed over many processing nodes. However, little work has been done to provide a parallel formulation of the efficient sequential techniques based on KD-Trees. Such approaches are expected to have an irregular distribution of computation load and can suffer from load imbalance. This issue has so far limited the adoption of these efficient k-Means variants in parallel computing environments. In this work, we provide a parallel formulation of the KD-Tree based k-Means algorithm for distributed memory systems and address its load balancing issue. Three solutions have been developed and tested. Two approaches are based on a static partitioning of the data set and a third solution incorporates a dynamic load balancing policy