A spatio-temporal extension to isomap nonlinear dimension reduction.pdf

A Spatio-temporal Extension to Isomap Nonlinear Dimension Reduction Odest Chadwicke Jenkins cjenkins@ Department of Computer Science, Brown University, Providence, RI 02912 USA Maja J Mataric? mataric@ Robotics Research Laboratory, Center for Robotics and Embedded Systems, Computer Science Department, University of Southern California, 941 W. 37th Place, Los Angeles, CA 90089 USA Abstract We present an extension of Isomap nonlin- ear dimension reduction (Tenenbaum et al., 2000) for data with both spatial and temporal relationships. Our method, ST-Isomap, aug- ments the existing Isomap framework to con- sider temporal relationships in local neigh- borhoods that can be propagated globally via a shortest-path mechanism. Two instantia- tions of ST-Isomap are presented for sequen- tially continuous and segmented data. Re- sults from applying ST-Isomap to real-world data collected from human motion perfor- mance and humanoid robot teleoperation are also presented. 1. Introduction The process of uncovering structure underlying unla- beled data is a challenging endeavor in unsupervised learning. Recently, several methods have been pro- posed to address this problem through dimension re- duction from pairwise relationships. These include global techniques (e.g., Kernel PCA (Scho?lkopf et al., 1998), Isomap (Tenenbaum et al., 2000)), local tech- niques (e.g., Locally Linear Embedding (Roweis Saul, 2000), Manifold Charting (Brand, 2002)), and spectral clustering (Ng et al., 2001). While these pair- wise methods have exhibited great potential, several issues remain largely unaddressed, such as dealing with out-of-sample points (Bengio et al., 2003) and tempo- ral dependencies within data. Motivated by analyzing human and humanoid robot Appearing in Proceedings of the 21 st International Confer- ence on Machine Learning, Banff, Canada, 2004. Copyright 2004 by the first author. motion, we propose an a extension to Isomap for data with both spatial and temporal relationships. Two