Persistent Homology of Attractors For Action Recognition

In this paper, we propose a novel framework for dynamical analysis of human actions from 3D motion capture data using topological data analysis. We model human actions using the topological features of the attractor of the dynamical system. We reconstruct the phase-space of time series corresponding to actions using time-delay embedding, and compute the persistent homology of the phase-space reconstruction. In order to better represent the topological properties of the phase-space, we incorporate the temporal adjacency information when computing the homology groups. The persistence of these homology groups encoded using persistence diagrams are used as features for the actions. Our experiments with action recognition using these features demonstrate that the proposed approach outperforms other baseline methods.Comment: 5 pages, Under review in International Conference on Image Processin

Shape Parameter Estimation

Performance of machine learning approaches depends strongly on the choice of misfit penalty, and correct choice of penalty parameters, such as the threshold of the Huber function. These parameters are typically chosen using expert knowledge, cross-validation, or black-box optimization, which are time consuming for large-scale applications. We present a principled, data-driven approach to simultaneously learn the model pa- rameters and the misfit penalty parameters. We discuss theoretical properties of these joint inference problems, and develop algorithms for their solution. We show synthetic examples of automatic parameter tuning for piecewise linear-quadratic (PLQ) penalties, and use the approach to develop a self-tuning robust PCA formulation for background separation.Comment: 20 pages, 10 figure

Crowd Counting with Decomposed Uncertainty

Research in neural networks in the field of computer vision has achieved remarkable accuracy for point estimation. However, the uncertainty in the estimation is rarely addressed. Uncertainty quantification accompanied by point estimation can lead to a more informed decision, and even improve the prediction quality. In this work, we focus on uncertainty estimation in the domain of crowd counting. With increasing occurrences of heavily crowded events such as political rallies, protests, concerts, etc., automated crowd analysis is becoming an increasingly crucial task. The stakes can be very high in many of these real-world applications. We propose a scalable neural network framework with quantification of decomposed uncertainty using a bootstrap ensemble. We demonstrate that the proposed uncertainty quantification method provides additional insight to the crowd counting problem and is simple to implement. We also show that our proposed method exhibits the state of the art performances in many benchmark crowd counting datasets.Comment: Accepted in AAAI 2020 (Main Technical Track

Synthesis and characterization of polymer-supported calix[4]arenes and bifunctional ion-exchange resins for selective metal ion complexation

Bifunctional ion-exchange resins and polymer-supported calix[4]arenes have been synthesized and characterized. The ion-selectivity of these polymers was evaluated. Phosphonic acid polymers were synthesized from polystyrene beads at varying levels of crosslinking and studied for their ability to complex Eu(III) and Fe(III) from varying acid concentrations. The percent complexed decreased with increasing crosslinking and acid concentrations regardless of the type of support used. However, by introducing a hydrophilic sulfonic acid ligand into the polymer matrix, rapid kinetics was obtained even with a highly crosslinked gel from high ionic strength solutions due to increased accessibility. The principle of bifunctionality is thus proposed as an alternative to macroporosity for enhanced complexation kinetics. Complexation of metal ions through a mechanism of inter- and intra-ligand cooperation for enhanced ionic selectivities was evaluated. The diphosphonic acid resin, due to the possibility of intra-ligand cooperation of the phosphoryl groups, had high affinities for all metal ions studied especially in less acidic solutions. The dicarboxylic acid resin was ineffective at the pH studied due to protonation of the carbonyl oxygen. The complexation behavior of the phosphonoacetic acid resin was comparable to the monophosphoric acid resin, leading to the belief initially that cooperation of the phosphoryl-carbonyl groups was not possible by intra-ligand cooperation. However, the ability of a β-ketophosphonate resin to complex high amounts of Cd(II) from a 0.10 N HNO3 solution showed that they can in fact cooperate by an intra-ligand mechanism for enhanced affinities. Hydrogen bonding of the carboxylic acid proton to the phosphoryl oxygens was proposed as the reason for poor affinities displayed by the phosphonoacetic acid resin. Calix[4]arene and phosphorylated calbc[4]arene were successfully immobilized onto crosslinked polystyrene supports. The former was able to complex Cs(I) from a 1 N NaOH solution in amounts greater than 96% while the latter was effective in complexing transition metal ions fi om acidic solutions. The effective cooperation of the ligating groups arranged around the cavity was responsible for the high selectivities displayed by these resins