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The detection and tracking of human landmarks in video streams has gained in reliability partly due to the availability of affordable RGB-D sensors. The analysis of such time-varying geometric data is playing an important role in the…

There exists a correlation between geospatial activity temporal patterns and type of land use. A novel self-supervised approach is proposed to stratify landscape based on mobility activity time series. First, the time series signal is…

Accurate quantification of complex human movements, such as gait, is essential for clinical diagnosis and rehabilitation but is often limited by traditional linear models rooted in Euclidean geometry. These frameworks frequently fail to…

Dexterous and autonomous robots should be capable of executing elaborated dynamical motions skillfully. Learning techniques may be leveraged to build models of such dynamic skills. To accomplish this, the learning model needs to encode a…

A central challenge in dynamic network analysis is to represent temporal evolution in a way that is both geometrically meaningful and statistically identifiable. One approach embeds a sequence of network snapshots as trajectories in a…

Temporal network data are increasingly available in various domains, and often represent highly complex systems with intricate structural and temporal evolutions. Due to the difficulty of processing such complex data, it may be useful to…

In nonlinear time series analysis and dynamical systems theory, Takens' embedding theorem states that the sliding window embedding of a generic observation along trajectories in a state space, recovers the region traversed by the dynamics.…

The brain is often studied from a network perspective, where functional activity is assessed using functional Magnetic Resonance Imaging (fMRI) to estimate connectivity between predefined neuronal regions. Functional connectivity can be…

The low-level sensory and motor signals in deep reinforcement learning, which exist in high-dimensional spaces such as image observations or motor torques, are inherently challenging to understand or utilize directly for downstream tasks.…

Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…

Imitation learning is an intuitive approach for teaching motion to robotic systems. Although previous studies have proposed various methods to model demonstrated movement primitives, one of the limitations of existing methods is that the…

Predicting human motion in unstructured and dynamic environments is difficult as humans naturally exhibit complex behaviors that can change drastically from one environment to the next. In order to alleviate this issue, we propose to encode…

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…

Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data…

Deep learning models have enjoyed great success for image related computer vision tasks like image classification and object detection. For video related tasks like human action recognition, however, the advancements are not as significant…

Identifying human actions in complex scenes is widely considered as a challenging research problem due to the unpredictable behaviors and variation of appearances and postures. For extracting variations in motion and postures, trajectories…

Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…

In this work we develop a novel and foundational framework for analyzing general Riemannian functional data, in particular a new development of tensor Hilbert spaces along curves on a manifold. Such spaces enable us to derive Karhunen-Loeve…

Tracking signals in dynamic environments presents difficulties in both analysis and implementation. In this work, we expand on a class of subspace tracking algorithms which utilize the Grassmann manifold -- the set of linear subspaces of a…

In this paper, we study the problem of learning compact (low-dimensional) representations for sequential data that captures its implicit spatio-temporal cues. To maximize extraction of such informative cues from the data, we set the problem…