Inferring Latent States and Refining Force Estimates via Hierarchical Dirichlet Process Modeling in Single Particle Tracking Experiments

Optical microscopy provides rich spatio-temporal information characterizing in vivo molecular motion. However, effective forces and other parameters used to summarize molecular motion change over time in live cells due to latent state changes, e.g., changes induced by dynamic micro-environments, photobleaching, and other heterogeneity inherent in biological processes. This study focuses on techniques for analyzing Single Particle Tracking (SPT) data experiencing abrupt state changes. We demonstrate the approach on GFP tagged chromatids experiencing metaphase in yeast cells and probe the effective forces resulting from dynamic interactions that reflect the sum of a number of physical phenomena. State changes are induced by factors such as microtubule dynamics exerting force through the centromere, thermal polymer fluctuations, etc. Simulations are used to demonstrate the relevance of the approach in more general SPT data analyses. Refined force estimates are obtained by adopting and modifying a nonparametric Bayesian modeling technique, the Hierarchical Dirichlet Process Switching Linear Dynamical System (HDP-SLDS), for SPT applications. The HDP-SLDS method shows promise in systematically identifying dynamical regime changes induced by unobserved state changes when the number of underlying states is unknown in advance (a common problem in SPT applications). We expand on the relevance of the HDP-SLDS approach, review the relevant background of Hierarchical Dirichlet Processes, show how to map discrete time HDP-SLDS models to classic SPT models, and discuss limitations of the approach. In addition, we demonstrate new computational techniques for tuning hyperparameters and for checking the statistical consistency of model assumptions directly against individual experimental trajectories; the techniques circumvent the need for "ground-truth" and subjective information.Comment: 25 pages, 6 figures. Differs only typographically from PLoS One publication available freely as an open-access article at http://journals.plos.org/plosone/article?id=10.1371/journal.pone.013763

Managerial Segmentation of Service Offerings in Work Commuting, MTI Report WP 12-02

Methodology to efficiently segment markets for public transportation offerings has been introduced and exemplified in an application to an urban travel corridor in which high tech companies predominate. The principal objective has been to introduce and apply multivariate methodology to efficiently identify segments of work commuters and their demographic identifiers. A set of attributes in terms of which service offerings could be defined was derived from background studies and focus groups of work commuters in the county. Adaptive choice conjoint analysis was used to derive the importance weights of these attributes in available service offering to these commuters. A two-stage clustering procedure was then used to explore the grouping of individual’s subsets into homogeneous sub-groups of the sample. These subsets are commonly a basis for differentiation in service offerings that can increase total ridership in public transportation while approximating cost neutrality in service delivery. Recursive partitioning identified interactions between demographic predictors that significantly contributed to the discrimination of segments in demographics. Implementation of the results is discussed

SEGMENTATION, RECOGNITION, AND ALIGNMENT OF COLLABORATIVE GROUP MOTION

Modeling and recognition of human motion in videos has broad applications in behavioral biometrics, content-based visual data analysis, security and surveillance, as well as designing interactive environments. Significant progress has been made in the past two decades by way of new models, methods, and implementations. In this dissertation, we focus our attention on a relatively less investigated sub-area called collaborative group motion analysis. Collaborative group motions are those that typically involve multiple objects, wherein the motion patterns of individual objects may vary significantly in both space and time, but the collective motion pattern of the ensemble allows characterization in terms of geometry and statistics. Therefore, the motions or activities of an individual object constitute local information. A framework to synthesize all local information into a holistic view, and to explicitly characterize interactions among objects, involves large scale global reasoning, and is of significant complexity. In this dissertation, we first review relevant previous contributions on human motion/activity modeling and recognition, and then propose several approaches to answer a sequence of traditional vision questions including 1) which of the motion elements among all are the ones relevant to a group motion pattern of interest (Segmentation); 2) what is the underlying motion pattern (Recognition); and 3) how two motion ensembles are similar and how we can 'optimally' transform one to match the other (Alignment). Our primary practical scenario is American football play, where the corresponding problems are 1) who are offensive players; 2) what are the offensive strategy they are using; and 3) whether two plays are using the same strategy and how we can remove the spatio-temporal misalignment between them due to internal or external factors. The proposed approaches discard traditional modeling paradigm but explore either concise descriptors, hierarchies, stochastic mechanism, or compact generative model to achieve both effectiveness and efficiency. In particular, the intrinsic geometry of the spaces of the involved features/descriptors/quantities is exploited and statistical tools are established on these nonlinear manifolds. These initial attempts have identified new challenging problems in complex motion analysis, as well as in more general tasks in video dynamics. The insights gained from nonlinear geometric modeling and analysis in this dissertation may hopefully be useful toward a broader class of computer vision applications

Recurrent Pixel Embedding for Instance Grouping

We introduce a differentiable, end-to-end trainable framework for solving pixel-level grouping problems such as instance segmentation consisting of two novel components. First, we regress pixels into a hyper-spherical embedding space so that pixels from the same group have high cosine similarity while those from different groups have similarity below a specified margin. We analyze the choice of embedding dimension and margin, relating them to theoretical results on the problem of distributing points uniformly on the sphere. Second, to group instances, we utilize a variant of mean-shift clustering, implemented as a recurrent neural network parameterized by kernel bandwidth. This recurrent grouping module is differentiable, enjoys convergent dynamics and probabilistic interpretability. Backpropagating the group-weighted loss through this module allows learning to focus on only correcting embedding errors that won't be resolved during subsequent clustering. Our framework, while conceptually simple and theoretically abundant, is also practically effective and computationally efficient. We demonstrate substantial improvements over state-of-the-art instance segmentation for object proposal generation, as well as demonstrating the benefits of grouping loss for classification tasks such as boundary detection and semantic segmentation

Heterogeneous Trajectory Forecasting via Risk and Scene Graph Learning

Heterogeneous trajectory forecasting is critical for intelligent transportation systems, while it is challenging because of the difficulty for modeling the complex interaction relations among the heterogeneous road agents as well as their agent-environment constraint. In this work, we propose a risk and scene graph learning method for trajectory forecasting of heterogeneous road agents, which consists of a Heterogeneous Risk Graph (HRG) and a Hierarchical Scene Graph (HSG) from the aspects of agent category and their movable semantic regions. HRG groups each kind of road agents and calculates their interaction adjacency matrix based on an effective collision risk metric. HSG of driving scene is modeled by inferring the relationship between road agents and road semantic layout aligned by the road scene grammar. Based on this formulation, we can obtain an effective trajectory forecasting in driving situations, and superior performance to other state-of-the-art approaches is demonstrated by exhaustive experiments on the nuScenes, ApolloScape, and Argoverse datasets.Comment: Submitted to IEEE Transactions on Intelligent Transportation Systems, 202