# Transform-Invariant Non-Parametric Clustering of Covariance Matrices and its Application to Unsupervised Joint Segmentation and Action Discovery

arXiv: https://arxiv.org/abs/1710.10060 · HTML: https://mlsanity.com/paper/1710.10060/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Oct 2017.

## Built on by (most cited first, 1 of 1)

- [Generalizing Robot Imitation Learning with Invariant Hidden Semi-Markov Models](https://mlsanity.com/paper/1811.07489/) (2018)

## Abstract (arXiv)

In this work, we tackle the problem of transform-invariant unsupervised learning in the space of Covariance matrices and applications thereof. We begin by introducing the Spectral Polytope Covariance Matrix (SPCM) Similarity function; a similarity function for Covariance matrices, invariant to any type of transformation. We then derive the SPCM-CRP mixture model, a transform-invariant non-parametric clustering approach for Covariance matrices that leverages the proposed similarity function, spectral embedding and the distance-dependent Chinese Restaurant Process (dd-CRP) (Blei and Frazier, 2011). The scalability and applicability of these two contributions is extensively validated on real-world Covariance matrix datasets from diverse research fields. Finally, we couple the SPCM-CRP mixture model with the Bayesian non-parametric Indian Buffet Process (IBP) - Hidden Markov Model (HMM) (Fox et al., 2009), to jointly segment and discover transform-invariant action primitives from complex sequential data. Resulting in a topic-modeling inspired hierarchical model for unsupervised time-series data analysis which we call ICSC-HMM (IBP Coupled SPCM-CRP Hidden Markov Model). The ICSC-HMM is validated on kinesthetic demonstrations of uni-manual and bi-manual cooking tasks; achieving unsupervised human-level decomposition of complex sequential tasks.