Robust M-Estimation Based Bayesian Cluster Enumeration for Real Elliptically Symmetric Distributions

Robustly determining the optimal number of clusters in a data set is an essential factor in a wide range of applications. Cluster enumeration becomes challenging when the true underlying structure in the observed data is corrupted by heavy-tailed noise and outliers. Recently, Bayesian cluster enumeration criteria have been derived by formulating cluster enumeration as maximization of the posterior probability of candidate models. This article generalizes robust Bayesian cluster enumeration so that it can be used with any arbitrary Real Elliptically Symmetric (RES) distributed mixture model. Our framework also covers the case of M-estimators that allow for mixture models, which are decoupled from a specific probability distribution. Examples of Huber's and Tukey's M-estimators are discussed. We derive a robust criterion for data sets with finite sample size, and also provide an asymptotic approximation to reduce the computational cost at large sample sizes. The algorithms are applied to simulated and real-world data sets, including radar-based person identification, and show a significant robustness improvement in comparison to existing methods

Bayesian Cluster Enumeration Criterion for Unsupervised Learning

We derive a new Bayesian Information Criterion (BIC) by formulating the problem of estimating the number of clusters in an observed data set as maximization of the posterior probability of the candidate models. Given that some mild assumptions are satisfied, we provide a general BIC expression for a broad class of data distributions. This serves as a starting point when deriving the BIC for specific distributions. Along this line, we provide a closed-form BIC expression for multivariate Gaussian distributed variables. We show that incorporating the data structure of the clustering problem into the derivation of the BIC results in an expression whose penalty term is different from that of the original BIC. We propose a two-step cluster enumeration algorithm. First, a model-based unsupervised learning algorithm partitions the data according to a given set of candidate models. Subsequently, the number of clusters is determined as the one associated with the model for which the proposed BIC is maximal. The performance of the proposed two-step algorithm is tested using synthetic and real data sets.Comment: 14 pages, 7 figure

Robust and Distributed Cluster Enumeration and Object Labeling

This dissertation contributes to the area of cluster analysis by providing principled methods to determine the number of data clusters and cluster memberships, even in the presence of outliers. The main theoretical contributions are summarized in two theorems on Bayesian cluster enumeration based on modeling the data as a family of Gaussian and t distributions. Real-world applicability is demonstrated by considering advanced signal processing applications, such as distributed camera networks and radar-based person identification. In particular, a new cluster enumeration criterion, which is applicable to a broad class of data distributions, is derived by utilizing Bayes' theorem and asymptotic approximations. This serves as a starting point when deriving cluster enumeration criteria for specific data distributions. Along this line, a Bayesian cluster enumeration criterion is derived by modeling the data as a family of multivariate Gaussian distributions. In real-world applications, the observed data is often subject to heavy tailed noise and outliers which obscure the true underlying structure of the data. Consequently, estimating the number of data clusters becomes challenging. To this end, a robust cluster enumeration criterion is derived by modeling the data as a family of multivariate t distributions. The family of t distributions is flexible by variation of its degree of freedom parameter (ν) and it contains, as special cases, the heavy tailed Cauchy for ν = 1, and the Gaussian distribution for ν → ∞. Given that ν is sufficiently small, the robust criterion accounts for outliers by giving them less weight in the objective function. A further contribution of this dissertation lies in refining the penalty terms of both the robust and Gaussian criterion for the finite sample regime. The derived cluster enumeration criteria require a clustering algorithm that partitions the data according to the number of clusters specified by each candidate model and provides an estimate of cluster parameters. Hence, a model-based unsupervised learning method is applied to partition the data prior to the calculation of an enumeration criterion, resulting in a two-step algorithm. The proposed algorithm provides a unified framework for the estimation of the number of clusters and cluster memberships. The developed algorithms are applied to two advanced signal processing use cases. Specifically, the cluster enumeration criteria are extended to a distributed sensor network setting by proposing two distributed and adaptive Bayesian cluster enumeration algorithms. The proposed algorithms are applied to a camera network use case, where the task is to estimate the number of pedestrians based on streaming-in data collected by multiple cameras filming a non-stationary scene from different viewpoints. A further research focus of this dissertation is the cluster membership assignment of individual data points and their associated cluster labels given that the number of clusters is either prespecified by the user or estimated by one of the methods described earlier. Solving this task is required in a broad range of applications, such as distributed sensor networks and radar-based person identification. For this purpose, an adaptive joint object labeling and tracking algorithm is proposed and applied to a real data use case of pedestrian labeling in a calibration-free multi-object multi-camera setup with low video resolution and frequent object occlusions. The proposed algorithm is well suited for ad hoc networks, as it requires neither registration of camera views nor a fusion center. Finally, a joint cluster enumeration and labeling algorithm is proposed to deal with the combined problem of estimating the number of clusters and cluster memberships at the same time. The proposed algorithm is applied to person labeling in a real data application of radar-based person identification without prior information on the number of individuals. It achieves comparable performance to a supervised approach that requires knowledge of the number of persons and a considerable amount of training data with known cluster labels. The proposed unsupervised method is advantageous in the considered application of smart assisted living, as it extracts the missing information from the data. Based on these examples, and, also considering the comparably low computational cost, we conjuncture that the proposed methods provide a useful set of robust cluster analysis tools for data science with many potential application areas, not only in the area of engineering

Detection of Gait Asymmetry Using Indoor Doppler Radar

Doppler radar systems enable unobtrusive and privacy-preserving long-term monitoring of human motions indoors. In particular, a person's gait can provide important information about their state of health. Utilizing micro-Doppler signatures, we show that radar is capable of detecting small differences between the step motions of the two legs, which results in asymmetric gait. Image-based and physical features are extracted from the radar return signals of several individuals, including four persons with different diagnosed gait disorders. It is shown that gait asymmetry is correctly detected with high probability, irrespective of the underlying pathology, for at least one motion direction.Comment: 6 pages, 5 figures, 4 tables; accepted at the IEEE Radar Conference 2019, Boston, MA, US

Contributions to Robust Graph Clustering: Spectral Analysis and Algorithms

This dissertation details the design of fast, and parameter free, graph clustering methods to robustly determine set cluster assignments. It provides spectral analysis as well as algorithms that adapt the obtained theoretical results to the implementation of robust graph clustering techniques. Sparsity is of importance in graph clustering and a first contribution of the thesis is the definition of a sparse graph model consistent with the graph clustering objectives. This model is based on an advantageous property, arising from a block diagonal representation, of a matrix that promotes the density of connections within clusters and sparsity between them. Spectral analysis of the sparse graph model including the eigen-decomposition of the Laplacian matrix is conducted. The analysis of the Laplacian matrix is simplified by defining a vector that carries all the relevant information that is contained in the Laplacian matrix. The obtained spectral properties of sparse graphs are adapted to sparsity-aware clustering based on two methods that formulate the determination of the sparsity level as approximations to spectral properties of the sparse graph models. A second contribution of this thesis is to analyze the effects of outliers on graph clustering and to propose algorithms that address robustness and the level of sparsity jointly. The basis for this contribution is to specify fundamental outlier types that occur in the cases of extreme sparsity and the mathematical analysis of their effects on sparse graphs to develop graph clustering algorithms that are robust against the investigated outlier effects. Based on the obtained results, two different robust and sparsity-aware affinity matrix construction methods are proposed. Motivated by the outliers’ effects on eigenvectors, a robust Fiedler vector estimation and a robust spectral clustering methods are proposed. Finally, an outlier detection algorithm that is built upon the vertex degree is proposed and applied to gait analysis. The results of this thesis demonstrate the importance of jointly addressing robustness and the level of sparsity for graph clustering algorithms. Additionally, simplified Laplacian matrix analysis provides promising results to design graph construction methods that may be computed efficiently through the optimization in a vector space instead of the usually used matrix space

Activity Analysis; Finding Explanations for Sets of Events

Automatic activity recognition is the computational process of analysing visual input and reasoning about detections to understand the performed events. In all but the simplest scenarios, an activity involves multiple interleaved events, some related and others independent. The activity in a car park or at a playground would typically include many events. This research assumes the possible events and any constraints between the events can be defined for the given scene. Analysing the activity should thus recognise a complete and consistent set of events; this is referred to as a global explanation of the activity. By seeking a global explanation that satisfies the activity’s constraints, infeasible interpretations can be avoided, and ambiguous observations may be resolved. An activity’s events and any natural constraints are defined using a grammar formalism. Attribute Multiset Grammars (AMG) are chosen because they allow defining hierarchies, as well as attribute rules and constraints. When used for recognition, detectors are employed to gather a set of detections. Parsing the set of detections by the AMG provides a global explanation. To find the best parse tree given a set of detections, a Bayesian network models the probability distribution over the space of possible parse trees. Heuristic and exhaustive search techniques are proposed to find the maximum a posteriori global explanation. The framework is tested for two activities: the activity in a bicycle rack, and around a building entrance. The first case study involves people locking bicycles onto a bicycle rack and picking them up later. The best global explanation for all detections gathered during the day resolves local ambiguities from occlusion or clutter. Intensive testing on 5 full days proved global analysis achieves higher recognition rates. The second case study tracks people and any objects they are carrying as they enter and exit a building entrance. A complete sequence of the person entering and exiting multiple times is recovered by the global explanation

Air Force Institute of Technology Research Report 2013

This report summarizes the research activities of the Air Force Institute of Technology’s Graduate School of Engineering and Management. It describes research interests and faculty expertise; lists student theses/dissertations; identifies research sponsors and contributions; and outlines the procedures for contacting the school. Included in the report are: faculty publications, conference presentations, consultations, and funded research projects. Research was conducted in the areas of Aeronautical and Astronautical Engineering, Electrical Engineering and Electro-Optics, Computer Engineering and Computer Science, Systems Engineering and Management, Operational Sciences, Mathematics, Statistics and Engineering Physics

New Methods to Improve Large-Scale Microscopy Image Analysis with Prior Knowledge and Uncertainty

Multidimensional imaging techniques provide powerful ways to examine various kinds of scientific questions. The routinely produced datasets in the terabyte-range, however, can hardly be analyzed manually and require an extensive use of automated image analysis. The present thesis introduces a new concept for the estimation and propagation of uncertainty involved in image analysis operators and new segmentation algorithms that are suitable for terabyte-scale analyses of 3D+t microscopy images.Comment: 218 pages, 58 figures, PhD thesis, Department of Mechanical Engineering, Karlsruhe Institute of Technology, published online with KITopen (License: CC BY-SA 3.0, http://dx.doi.org/10.5445/IR/1000057821

New Methods to Improve Large-Scale Microscopy Image Analysis with Prior Knowledge and Uncertainty

Multidimensional imaging techniques provide powerful ways to examine various kinds of scientific questions. The routinely produced data sets in the terabyte-range, however, can hardly be analyzed manually and require an extensive use of automated image analysis. The present work introduces a new concept for the estimation and propagation of uncertainty involved in image analysis operators and new segmentation algorithms that are suitable for terabyte-scale analyses of 3D+t microscopy images