The Sensorimotor Approach in CoSy: The Example of Dimensionality Reduction

This chapter presents an algorithm implementing a basic requirement for any interface between sensory data and cognitive functions: dimensionality reduction. The algorithm extends the classical framework of dimensionality reduction to the case where sensory data are acquired through an embodied agent, by grounding the metric that is at the basis of the dimensionality reduction in the sensorimotor abilities of the agent. The final objective (which was not realized because of time constraints) within CoSy was to build on this to provide a demonstration of some basic unsupervised learning of interactions with space and objects, as would be required in an explorer-type scenario.

[1]  David S. Broomhead,et al.  A New Approach to Dimensionality Reduction: Theory and Algorithms , 2000, SIAM J. Appl. Math..

[2]  Claude-Pierre Jeannerod,et al.  On the complexity of polynomial matrix computations , 2003, ISSAC '03.

[3]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[4]  Benjamin Kuipers,et al.  The Spatial Semantic Hierarchy , 2000, Artif. Intell..

[5]  J. Friedman Exploratory Projection Pursuit , 1987 .

[6]  Joel W. Burdick,et al.  Trajectory generation for kinematic legged robots , 1997, Proceedings of International Conference on Robotics and Automation.

[7]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[8]  Professor Dr. Dr. h.c. Hermann Haken,et al.  Synergetic Computers and Cognition , 1991, Springer Series in Synergetics.

[9]  Michael E. Tipping,et al.  Probabilistic Principal Component Analysis , 1999 .

[10]  Michel Verleysen,et al.  Nonlinear dimensionality reduction of data manifolds with essential loops , 2005, Neurocomputing.

[11]  Nanda Kambhatla,et al.  Dimension Reduction by Local Principal Component Analysis , 1997, Neural Computation.

[12]  J. Kruskal Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis , 1964 .

[13]  J. Kevin O'Regan,et al.  Perception of the Structure of the Physical World Using Unknown Multimodal Sensors and Effectors , 2003, NIPS.

[14]  Richard Montgomery,et al.  Optimal Control of Deformable Bodies and Its Relation to Gauge Theory , 1991 .

[15]  Mikhail Belkin,et al.  Laplacian Eigenmaps for Dimensionality Reduction and Data Representation , 2003, Neural Computation.

[16]  J. Findlay,et al.  Active Vision: The Psychology of Looking and Seeing , 2003 .

[17]  Tucker R. Balch,et al.  Symmetry in Markov Decision Processes and its Implications for Single Agent and Multiagent Learning , 2001, ICML.

[18]  Raymond Reiter,et al.  Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems , 2001 .

[19]  A. Isidori Nonlinear Control Systems , 1985 .

[20]  D. Chalmers The conscious mind: in search of a fundamental theory , 1996 .

[21]  Robert Pless,et al.  Isomap and Nonparametric Models of Image Deformation , 2005, 2005 Seventh IEEE Workshops on Applications of Computer Vision (WACV/MOTION'05) - Volume 1.

[22]  G. Reinsel,et al.  Multivariate Reduced-Rank Regression: Theory and Applications , 1998 .

[23]  Guillermo Sapiro,et al.  Differential Invariant Signatures and Flows in Computer Vision: A Symmetry Group Approach , 1994, Geometry-Driven Diffusion in Computer Vision.

[24]  René Thom,et al.  Structural stability and morphogenesis , 1977, Pattern Recognit..

[25]  Robert Pless Differential Structure in non-Linear Image Embedding Functions , 2004, 2004 Conference on Computer Vision and Pattern Recognition Workshop.

[26]  A. Noë,et al.  A sensorimotor account of vision and visual consciousness. , 2001, The Behavioral and brain sciences.

[27]  Johannes Schumacher,et al.  An Introduction to Hybrid Dynamical Systems, Springer Lecture Notes in Control and Information Sciences 251 , 1999 .

[28]  P. Thomas Fletcher,et al.  Statistics of shape via principal geodesic analysis on Lie groups , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[29]  Sanjoy Dasgupta,et al.  A Generalization of Principal Components Analysis to the Exponential Family , 2001, NIPS.

[30]  Michel Verleysen,et al.  Curvilinear Distance Analysis versus Isomap , 2002, ESANN.

[31]  John W. Sammon,et al.  A Nonlinear Mapping for Data Structure Analysis , 1969, IEEE Transactions on Computers.

[32]  P. Michor,et al.  Natural operations in differential geometry , 1993 .

[33]  Jeanny Hérault,et al.  CCA : "Curvilinear component analysis" , 1995 .

[34]  Bernhard Schölkopf,et al.  Nonlinear Component Analysis as a Kernel Eigenvalue Problem , 1998, Neural Computation.

[35]  Bernd Fritzke,et al.  A Growing Neural Gas Network Learns Topologies , 1994, NIPS.

[36]  Olaf Sporns,et al.  Mapping Information Flow in Sensorimotor Networks , 2006, PLoS Comput. Biol..

[37]  Hyun Seung Yang,et al.  Non-uniform image compression using a biologically motivated selective attention model , 2005, Neurocomputing.

[38]  J. Piaget,et al.  The Origins of Intelligence in Children , 1971 .

[39]  J. Gibson The Senses Considered As Perceptual Systems , 1967 .

[40]  Thomas Martinetz,et al.  'Neural-gas' network for vector quantization and its application to time-series prediction , 1993, IEEE Trans. Neural Networks.

[41]  John W. Tukey,et al.  A Projection Pursuit Algorithm for Exploratory Data Analysis , 1974, IEEE Transactions on Computers.

[42]  Mukund Balasubramanian,et al.  The Isomap Algorithm and Topological Stability , 2002, Science.

[43]  Leslie Pack Kaelbling,et al.  Planning and Acting in Partially Observable Stochastic Domains , 1998, Artif. Intell..

[44]  R. Bajcsy Active perception , 1988 .

[45]  J. Crutchfield Information and Its Metric , 1990 .

[46]  Stefan Schaal,et al.  Local dimensionality reduction for locally weighted learning , 1997, Proceedings 1997 IEEE International Symposium on Computational Intelligence in Robotics and Automation CIRA'97. 'Towards New Computational Principles for Robotics and Automation'.

[47]  Ben J. A. Kröse,et al.  Coordinating Principal Component Analyzers , 2002, ICANN.

[48]  A. Sloman,et al.  Note: This Paper Was Originally Published (on Pages 380—401) in Physical and Biological Processing of Images Image Interpretation: the Way Ahead? A.1. Introduction , 1982 .

[49]  Rajesh P. N. Rao,et al.  Learning Lie Groups for Invariant Visual Perception , 1998, NIPS.

[50]  Jerrold E. Marsden,et al.  Symmetries in Motion: Geometric Foundations of Motion Control , 1998 .

[51]  Benjamin Kuipers,et al.  Consciousness: Drinking from the Firehose of Experience , 2005, AAAI.

[52]  Benjamin Kuipers,et al.  Map Learning with Uninterpreted Sensors and Effectors , 1995, Artif. Intell..

[53]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[54]  Dana H. Ballard,et al.  Animate Vision , 1991, Artif. Intell..

[55]  Joel W. Burdick,et al.  Propulsion and control of deformable bodies in an ideal fluid , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[56]  Richard M. Murray,et al.  Geometric phases and robotic locomotion , 1995, J. Field Robotics.

[57]  H. Poincaré La science et l'hypothèse , 1968 .

[58]  C. Koch,et al.  A framework for consciousness , 2003, Nature Neuroscience.

[59]  F. Wilczek,et al.  Geometry of self-propulsion at low Reynolds number , 1989, Journal of Fluid Mechanics.

[60]  H. Helmholtz The Facts in Perception , 1977 .

[61]  Pierre-Louis Bazin,et al.  Structure from Motion: Theoretical Foundations of a Novel Approach Using Custom Built Invariants , 2002, ArXiv.

[62]  J Kevin O'Regan,et al.  Color naming, unique hues, and hue cancellation predicted from singularities in reflection properties. , 2006, Visual neuroscience.

[63]  Gert Smolka,et al.  Attributive Concept Descriptions with Complements , 1991, Artif. Intell..

[64]  Michael I. Jordan,et al.  Distance Metric Learning with Application to Clustering with Side-Information , 2002, NIPS.

[65]  Geraint Rees,et al.  Neural correlates of consciousness in humans , 2002, Nature Reviews Neuroscience.

[66]  S Zeki,et al.  The autonomy of the visual systems and the modularity of conscious vision. , 1998, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[67]  R. Shepard The analysis of proximities: Multidimensional scaling with an unknown distance function. II , 1962 .

[68]  Thomas Voegtlin,et al.  Recursive principal components analysis , 2005, Neural Networks.

[69]  Aaron Sloman,et al.  The Altricial-Precocial Spectrum for Robots , 2005, IJCAI.

[70]  Joshua B. Tenenbaum,et al.  Global Versus Local Methods in Nonlinear Dimensionality Reduction , 2002, NIPS.

[71]  Joydeep Ghosh,et al.  A Unified Model for Probabilistic Principal Surfaces , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[72]  W. Torgerson Multidimensional scaling: I. Theory and method , 1952 .

[73]  E. Aronson,et al.  Theory and method , 1985 .

[74]  Reza Shadmehr,et al.  Learning of action through adaptive combination of motor primitives , 2000, Nature.

[75]  Ales Leonardis,et al.  Incremental PCA for on-line visual learning and recognition , 2002, Object recognition supported by user interaction for service robots.

[76]  Samuel Kaski,et al.  Improved learning of Riemannian metrics for exploratory analysis [Neural Networks 17 (8–9) 1087–1100] , 2005 .

[77]  William Bialek,et al.  Optimal Manifold Representation of Data: An Information Theoretic Approach , 2003, NIPS.

[78]  Nicolas Le Roux,et al.  Spectral Dimensionality Reduction , 2006, Feature Extraction.