arXiv subjects

Ba-Ngu Vo

Publications and source records attributed to Ba-Ngu Vo.

27 records · Page 2Linked to original sources

arXiv2017

Model-based Classification and Novelty Detection For Point Pattern Data

Point patterns are sets or multi-sets of unordered elements that can be found in numerous data sources. However, in data analysis tasks such as classification and novelty detection, appropriate statistical models for point pattern data have not received much attention. This paper proposes the modelling of point pattern data via random finite sets (RFS). In particular, we propose appropriate likelihood functions, and a maximum likelihood estimator for learning a tractable family of RFS models. In novelty detection, we propose novel ranking functions based on RFS models, which substantially improve performance.

cs.LG↗

arXiv2017

Clustering For Point Pattern Data

Clustering is one of the most common unsupervised learning tasks in machine learning and data mining. Clustering algorithms have been used in a plethora of applications across several scientific fields. However, there has been limited research in the clustering of point patterns - sets or multi-sets of unordered elements - that are found in numerous applications and data sources. In this paper, we propose two approaches for clustering point patterns. The first is a non-parametric method based on novel distances for sets. The second is a model-based approach, formulated via random finite set theory, and solved by the Expectation-Maximization algorithm. Numerical experiments show that the proposed methods perform well on both simulated and real data.

cs.LG↗

arXiv2016

A Generalized Labeled Multi-Bernoulli Filter for Maneuvering Targets

A multiple maneuvering target system can be viewed as a Jump Markov System (JMS) in the sense that the target movement can be modeled using different motion models where the transition between the motion models by a particular target follows a Markov chain probability rule. This paper describes a Generalized Labelled Multi-Bernoulli (GLMB) filter for tracking maneuvering targets whose movement can be modeled via such a JMS. The proposed filter is validated with two linear and nonlinear maneuvering target tracking examples.

stat.ME↗

arXiv2015

Void Probabilities and Cauchy-Schwarz Divergence for Generalized Labeled Multi-Bernoulli Models

The generalized labeled multi-Bernoulli (GLMB) is a family of tractable models that alleviates the limitations of the Poisson family in dynamic Bayesian inference of point processes. In this paper, we derive closed form expressions for the void probability functional and the Cauchy-Schwarz divergence for GLMBs. The proposed analytic void probability functional is a necessary and sufficient statistic that uniquely characterizes a GLMB, while the proposed analytic Cauchy-Schwarz divergence provides a tractable measure of similarity between GLMBs. We demonstrate the use of both results on a partially observed Markov decision process for GLMBs, with Cauchy-Schwarz divergence based reward, and void probability constraint.

stat.CO↗

arXiv2015

Multiple Extended Target Tracking with Labelled Random Finite Sets

Targets that generate multiple measurements at a given instant in time are commonly known as extended targets. These present a challenge for many tracking algorithms, as they violate one of the key assumptions of the standard measurement model. In this paper, a new algorithm is proposed for tracking multiple extended targets in clutter, that is capable of estimating the number of targets, as well the trajectories of their states, comprising the kinematics, measurement rates and extents. The proposed technique is based on modelling the multi-target state as a generalised labelled multi-Bernoulli (GLMB) random finite set (RFS), within which the extended targets are modelled using gamma Gaussian inverse Wishart (GGIW) distributions. A cheaper variant of the algorithm is also proposed, based on the labelled multi-Bernoulli (LMB) filter. The proposed GLMB/LMB-based algorithms are compared with an extended target version of the cardinalised probability hypothesis density (CPHD) filter, and simulation results show that the (G)LMB has improved estimation and tracking performance.

stat.CO↗

arXiv2015

Multi-Target Tracking with Time-Varying Clutter Rate and Detection Profile: Application to Time-lapse Cell Microscopy Sequences

Quantitative analysis of the dynamics of tiny cellular and sub-cellular structures, known as particles, in time-lapse cell microscopy sequences requires the development of a reliable multi-target tracking method capable of tracking numerous similar targets in the presence of high levels of noise, high target density, complex motion patterns and intricate interactions. In this paper, we propose a framework for tracking these structures based on the random finite set Bayesian filtering framework. We focus on challenging biological applications where image characteristics such as noise and background intensity change during the acquisition process. Under these conditions, detection methods usually fail to detect all particles and are often followed by missed detections and many spurious measurements with unknown and time-varying rates. To deal with this, we propose a bootstrap filter composed of an estimator and a tracker. The estimator adaptively estimates the required meta parameters for the tracker such as clutter rate and the detection probability of the targets, while the tracker estimates the state of the targets. Our results show that the proposed approach can outperform state-of-the-art particle trackers on both synthetic and real data in this regime.

cs.CV↗

arXiv2015

The Cauchy-Schwarz divergence for Poisson point processes

In this paper, we extend the notion of Cauchy-Schwarz divergence to point processes and establish that the Cauchy-Schwarz divergence between the probability densities of two Poisson point processes is half the squared $\mathbf{L^{2}}$-distance between their intensity functions. Extension of this result to mixtures of Poisson point processes and, in the case where the intensity functions are Gaussian mixtures, closed form expressions for the Cauchy-Schwarz divergence are presented. Our result also implies that the Bhattachryaa distance between the probability distributions of two Poisson point processes is equal to the square of the Hellinger distance between their intensity measures. We illustrate the result via a sensor management application where the system states are modeled as point processes.

cs.IT↗

arXiv2015

Generalized Labeled Multi-Bernoulli Approximation of Multi-Object Densities

In multi-object inference, the multi-object probability density captures the uncertainty in the number and the states of the objects as well as the statistical dependence between the objects. Exact computation of the multi-object density is generally intractable and tractable implementations usually require statistical independence assumptions between objects. In this paper we propose a tractable multi-object density approximation that can capture statistical dependence between objects. In particular, we derive a tractable Generalized Labeled Multi-Bernoulli (GLMB) density that matches the cardinality distribution and the first moment of the labeled multi-object distribution of interest. It is also shown that the proposed approximation minimizes the Kullback-Leibler divergence over a special tractable class of GLMB densities. Based on the proposed GLMB approximation we further demonstrate a tractable multi-object tracking algorithm for generic measurement models. Simulation results for a multi-object Track-Before-Detect example using radar measurements in low signal-to-noise ratio (SNR) scenarios verify the applicability of the proposed approach.

stat.OT↗

arXiv2015

A Generalized Labeled Multi-Bernoulli Filter Implementation using Gibbs Sampling

This paper proposes an efficient implementation of the generalized labeled multi-Bernoulli (GLMB) filter by combining the prediction and update into a single step. In contrast to the original approach which involves separate truncations in the prediction and update steps, the proposed implementation requires only one single truncation for each iteration, which can be performed using a standard ranked optimal assignment algorithm. Furthermore, we propose a new truncation technique based on Markov Chain Monte Carlo methods such as Gibbs sampling, which drastically reduces the complexity of the filter. The superior performance of the proposed approach is demonstrated through extensive numerical studies.

stat.CO↗