Probabilistic Temporal Subspace Clustering

Subspace clustering is a common modeling paradigm used to identify constituent modes of variation in data with locally linear structure. These structures are common to many problems in computer vision, including modeling time series of complex human motion. However classical subspace clustering algorithms learn the relationships within a set of data without considering the temporal dependency and then use a separate clustering step (e.g., spectral clustering) for final segmentation. Moreover, these, frequently optimization-based, algorithms assume that all observations have complete features. In contrast in real-world applications, some features are often missing, which results in incomplete data and substantial performance degeneration of these approaches. In this paper, we propose a unified non-parametric generative framework for temporal subspace clustering to segment data drawn from a sequentially ordered union of subspaces that deals with the missing features in a principled way. The non-parametric nature of our generative model makes it possible to infer the number of subspaces and their dimension automatically from data. Experimental results on human action datasets demonstrate that the proposed model consistently outperforms other state-of-the-art subspace clustering approaches.