Dirichlet Process Gaussian Mixture Models Research Articles

Density-adaptive registration of pointclouds based on Dirichlet Process Gaussian Mixture Models

We propose an algorithm for rigid registration of pre- and intra-operative patient anatomy, represented as pointclouds, during minimally invasive surgery. This capability is essential for development of augmented reality systems for guiding such interventions. Key challenges in this context are differences in the point density in the pre- and intra-operative pointclouds, and potentially low spatial overlap between the two. Solutions, correspondingly, must be robust to both of these phenomena. We formulated a pointclouds registration approach which considers the pointclouds after rigid transformation to be observations of a global non-parametric probabilistic model named Dirichlet Process Gaussian Mixture Model. The registration problem is solved by minimizing the Kullback-Leibler divergence in a variational Bayesian inference framework. By this means, all unknown parameters are recursively inferred, including, importantly, the optimal number of mixture model components, which ensures the model complexity efficiently matches that of the observed data. By presenting the pointclouds as KDTrees, both the data and model are expanded in a coarse-to-fine style. The scanning weight of each point is estimated by its neighborhood, imparting the algorithm with robustness to point density variations. Experiments on several datasets with different levels of noise, outliers and pointcloud overlap show that our method has a comparable accuracy, but higher efficiency than existing Gaussian Mixture Model methods, whose performance is sensitive to the number of model components.

(H)DPGMM: a hierarchy of Dirichlet process Gaussian mixture models for the inference of the black hole mass function

ABSTRACT We introduce (H)DPGMM, a hierarchical Bayesian non-parametric method based on the Dirichlet process Gaussian mixture model, designed to infer data-driven population properties of astrophysical objects without being committal to any specific physical model. We investigate the efficacy of our model on simulated data sets and demonstrate its capability to reconstruct correctly a variety of population models without the need of fine-tuning of the algorithm. We apply our method to the problem of inferring the black hole mass function given a set of gravitational wave observations from LIGO and Virgo, and find that the (H)DPGMM infers a binary black hole mass function that is consistent with previous estimates without the requirement of a theoretically motivated parametric model. Although the number of systems observed is still too small for a robust inference, (H)DPGMM confirms the presence of at least two distinct modes in the observed merging black hole mass function, hence suggesting in a model-independent fashion the presence of at least two classes of binary black hole systems.

A Dirichlet Process Based Type-1 and Type-2 Fuzzy Modeling for Systematic Confidence Bands Prediction

This paper presents a new methodology for fuzzy logic systems modeling based on the Dirichlet process Gaussian mixture models (DPGMM). The proposed method simultaneously allows for the systematic elicitation of confidence bands as well as the automatic determination of model complexity. This work is new since existing fuzzy model elicitation techniques use ad hoc methods for confidence band estimations, which do not meet the stringent requirements of today's challenging environments where data are sparse, incomplete, and characterized by noise as well as uncertainties. The proposed approach involves an integration of fuzzy and Bayesian topologies and allows for the generation of confidence bands based on both the random and linguistic uncertainties embedded in the data. Additionally, the proposed method provides a “right-first time approach” to fuzzy modeling as it does not require an iterative model complexity determination. In order to see how the proposed framework performs across a variety of challenging data modeling problems, the proposed approach was tested on a nonlinear synthetic dataset as well as two real multidimensional datasets generated by the authors from materials science and bladder cancer studies. Results show that the proposed approach consistently provides better generalization performances than other well-known soft computing modeling frameworks—in some cases, improvements of up to 20% in modeling accuracy were achieved. The proposed method also provides the capability to handle uncertainties via the generation of systematic confidence intervals for informing on model reliability. These results are significant since the generic methodologies developed in this paper should help material scientists as well as clinicians, for example, assess the risks involved in making informed decisions based on model predictions.

Gaussian mixture models as automated particle classifiers for fast neutron detectors

AbstractPulse shape discrimination (PSD) is the task of classifying electronic pulse shapes for different particle types such as gamma rays and fast neutrons interacting in scintillators and read out by photo sensitive detectors. This field has been limited in its adoption of techniques found in the statistical learning community. Methods initially employed in the 1960s for analog electronic circuitry persist in the current PSD literature describing operations performed on digitized pulses, which are amenable to statistical rigor. Despite vast amounts of data collected at low energy levels, traditional PSD methods are unable to discriminate particles below a certain threshold. In this work, Gaussian mixture models (GMMs) are used as a clustering technique for fast neutron detection in the absence of labeled data. GMMs yield improvements spanning the energy spectrum in a desirably efficient, unsupervised fashion. An extension, the Dirichlet Process GMM, provides further flexibility and classification improvement.

Automatic Depression Analysis Using Dynamic Facial Appearance Descriptor and Dirichlet Process Fisher Encoding

Depression causes mood disorders with noticeable problems in day-to-day activities. Current methods of assessing depression depend almost entirely on clinical interviews or questionnaires. They lack systematic and efficient ways of incorporating behavioral observations that are strong indicators of a psychological disorder. To help clinicians effectively and efficiently diagnose depression severity, automated systems, using objective and quantifiable data for depression assessment, are being developed. This paper presents a framework toward estimating a clinical depression-specific score, namely the Beck Depression Inventory–II (BDI-II) score, based on the analysis of facial expressions features. To extract facial dynamic features, we propose a novel dynamic feature descriptor denoted as median robust local binary patterns from three orthogonal planes (MRLBP-TOP), which can capture both the microstructure and macrostructure of facial appearance and dynamics. To aggregate the MRLBP-TOP over an image sequence, we propose a variant to the Fisher vector (FV) encoding scheme, denoted as the Dirichlet process FV (DPFV). DPFV adopts Dirichlet process Gaussian mixture models (DPGMM) to automatically learn the number of GMM mixtures and model parameters. Experimental results on the AVEC2013 and AVEC2014 depression databases have demonstrated the effectiveness of the proposed method.

Dirichlet Process Gaussian Mixture Models for Real-Time Monitoring and Their Application to Chemical Mechanical Planarization

The goal of this work is to use sensor data for online detection and identification of process anomalies (faults). In pursuit of this goal, we propose Dirichlet process Gaussian mixture (DPGM) models. The proposed DPGM models have two novel outcomes: 1) DP-based statistical process control (SPC) chart for anomaly detection and 2) unsupervised recurrent hierarchical DP clustering model for identification of specific process anomalies. The presented DPGM models are validated using numerical simulation studies as well as wireless vibration signals acquired from an experimental semiconductor chemical mechanical planarization (CMP) test bed. Through these numerically simulated and experimental sensor data, we test the hypotheses that DPGM models have significantly lower detection delays compared with SPC charts in terms of the average run length (ARL1) and higher defect identification accuracies (F-score) than popular clustering techniques, such as mean shift. For instance, the DP-based SPC chart detects pad wear anomaly in CMP within 50 ms, as opposed to over 140 ms with conventional control charts. Likewise, DPGM models are able to classify different anomalies in CMP.

Batch Discovery of Recurring Rare Classes toward Identifying Anomalous Samples.

We present a clustering algorithm for discovering rare yet significant recurring classes across a batch of samples in the presence of random effects. We model each sample data by an infinite mixture of Dirichlet-process Gaussian-mixture models (DPMs) with each DPM representing the noisy realization of its corresponding class distribution in a given sample. We introduce dependencies across multiple samples by placing a global Dirichlet process prior over individual DPMs. This hierarchical prior introduces a sharing mechanism across samples and allows for identifying local realizations of classes across samples. We use collapsed Gibbs sampler for inference to recover local DPMs and identify their class associations. We demonstrate the utility of the proposed algorithm, processing a flow cytometry data set containing two extremely rare cell populations, and report results that significantly outperform competing techniques. The source code of the proposed algorithm is available on the web via the link: http://cs.iupui.edu/~dundar/aspire.htm.

Background Subtraction with DirichletProcess Mixture Models.

Video analysis often begins with background subtraction. This problem is often approached in two steps-a background model followed by a regularisation scheme. A model of the background allows it to be distinguished on a per-pixel basis from the foreground, whilst the regularisation combines information from adjacent pixels. We present a new method based on Dirichlet process Gaussian mixture models, which are used to estimate per-pixel background distributions. It is followed by probabilistic regularisation. Using a non-parametric Bayesian method allows per-pixel mode counts to be automatically inferred, avoiding over-/under- fitting. We also develop novel model learning algorithms for continuous update of the model in a principled fashion as the scene changes. These key advantages enable us to outperform the state-of-the-art alternatives on four benchmarks.

Dirichlet process Gaussian mixture models: choice of the base distribution

In the Bayesian mixture modeling framework it is possible to infer the necessary number of components to model the data and therefore it is unnecessary to explicitly restrict the number of components. Nonparametric mixture models sidestep the problem of finding the "correct" number of mixture components by assuming infinitely many components. In this paper Dirichlet process mixture (DPM) models are cast as infinite mixture models and inference using Markov chain Monte Carlo is described. The specification of the priors on the model parameters is often guided by mathematical and practical convenience. The primary goal of this paper is to compare the choice of conjugate and non-conjugate base distributions on a particular class of DPM models which is widely used in applications, the Dirichlet process Gaussian mixture model (DPGMM). We compare computational efficiency and modeling performance of DPGMM defined using a conjugate and a conditionally conjugate base distribution. We show that better density models can result from using a wider class of priors with no or only a modest increase in computational effort.

Dirichlet process Gaussian mixture models

In the Bayesian mixture modeling framework it is possible to infer the necessary number of components to model the data and therefore it is unnecessary to explicitly restrict the number of componen...