arXiv subjects

Jeff Calder

Publications and source records attributed to Jeff Calder.

58 records · Page 4Linked to original sources

arXiv2014

Pareto-depth for Multiple-query Image Retrieval

Most content-based image retrieval systems consider either one single query, or multiple queries that include the same object or represent the same semantic information. In this paper we consider the content-based image retrieval problem for multiple query images corresponding to different image semantics. We propose a novel multiple-query information retrieval algorithm that combines the Pareto front method (PFM) with efficient manifold ranking (EMR). We show that our proposed algorithm outperforms state of the art multiple-query retrieval algorithms on real-world image databases. We attribute this performance improvement to concavity properties of the Pareto fronts, and prove a theoretical result that characterizes the asymptotic concavity of the fronts.

cs.IR↗

arXiv2013

A Hamilton-Jacobi equation for the continuum limit of non-dominated sorting

We show that non-dominated sorting of a sequence of i.i.d. random variables in Euclidean space has a continuum limit that corresponds to solving a Hamilton-Jacobi equation involving the probability density function of the random variables. Non-dominated sorting is a fundamental problem in multi-objective optimization, and is equivalent to finding the canonical antichain partition and to problems involving the longest chain among Euclidean points. As an application of this result, we show that non-dominated sorting is asymptotically stable under random perturbations in the data. We give a numerical scheme for computing the viscosity solution of this Hamilton-Jacobi equation and present some numerical simulations for various density functions.

math.AP↗

arXiv2013

A PDE-based approach to non-dominated sorting

Non-dominated sorting is a fundamental combinatorial problem in multiobjective optimization, and is equivalent to the longest chain problem in combinatorics and random growth models for crystals in materials science. In a previous work, we showed that non-dominated sorting has a continuum limit that corresponds to solving a Hamilton-Jacobi equation. In this work we present and analyze a fast numerical scheme for this Hamilton-Jacobi equation, and show how it can be used to design a fast algorithm for approximate non-dominated sorting.

math.NA↗

arXiv2013

Multi-criteria Anomaly Detection using Pareto Depth Analysis

We consider the problem of identifying patterns in a data set that exhibit anomalous behavior, often referred to as anomaly detection. In most anomaly detection algorithms, the dissimilarity between data samples is calculated by a single criterion, such as Euclidean distance. However, in many cases there may not exist a single dissimilarity measure that captures all possible anomalous patterns. In such a case, multiple criteria can be defined, and one can test for anomalies by scalarizing the multiple criteria using a linear combination of them. If the importance of the different criteria are not known in advance, the algorithm may need to be executed multiple times with different choices of weights in the linear combination. In this paper, we introduce a novel non-parametric multi-criteria anomaly detection method using Pareto depth analysis (PDA). PDA uses the concept of Pareto optimality to detect anomalies under multiple criteria without having to run an algorithm multiple times with different choices of weights. The proposed PDA approach scales linearly in the number of criteria and is provably better than linear combinations of the criteria.

cs.LG↗