Simultaneous Learning of Nonlinear Manifold and Dynamical Models for High-dimensional Time Series

The goal of this work is to learn a parsimonious and informative representation for high-dimensional time series. Conceptually, this comprises two distinct yet tightly coupled tasks: learning a low-dimensional manifold and modeling the dynamical process. These two tasks have a complementary relationship as the temporal constraints provide valuable neighborhood information for dimensionality reduction and conversely, the low-dimensional space allows dynamics to be learnt efficiently. Solving these two tasks simultaneously allows important information to be exchanged mutually. If nonlinear models are required to capture the rich complexity of time series, then the learning problem becomes harder as the nonlinearities in both tasks are coupled. The proposed solution approximates the nonlinear manifold and dynamics using piecewise linear models. The interactions among the linear models are captured in a graphical model. By exploiting the model structure, efficient inference and learning algorithms are obtained without oversimplifying the model of the underlying dynamical process. Evaluation of the proposed framework with competing approaches is conducted in three sets of experiments: dimensionality reduction and reconstruction using synthetic time series, video synthesis using a dynamic texture database, and human motion synthesis, classification and tracking on a benchmark data set. In all experiments, the proposed approach provides superior performance.

Simultaneous Learning of Non-Linear Manifold and Dynamical Models for High-Dimensional Time Series

The goal of this work is to learn a parsimonious and informative representation for high-dimensional time series. Conceptually, this comprises two distinct yet tightly coupled tasks: learning a low-dimensional manifold and modeling the dynamical process. These two tasks have a complementary relationship as the temporal constraints provide valuable neighborhood information for dimensionality reduction and conversely, the low-dimensional space allows dynamics to be learnt efficiently. Solving these two tasks simultaneously allows important information to be exchanged mutually. If nonlinear models are required to capture the rich complexity of time series, then the learning problem becomes harder as the nonlinearities in both tasks are coupled. The proposed solution approximates the nonlinear manifold and dynamics using piecewise linear models. The interactions among the linear models are captured in a graphical model. The model structure setup and parameter learning are done using a variational Bayesian approach, which enables automatic Bayesian model structure selection, hence solving the problem of over-fitting. By exploiting the model structure, efficient inference and learning algorithms are obtained without oversimplifying the model of the underlying dynamical process. Evaluation of the proposed framework with competing approaches is conducted in three sets of experiments: dimensionality reduction and reconstruction using synthetic time series, video synthesis using a dynamic texture database, and human motion synthesis, classification and tracking on a benchmark data set. In all experiments, the proposed approach provides superior performance.

Vector Associative Maps: Unsupervised Real-time Error-based Learning and Control of Movement Trajectories

This article describes neural network models for adaptive control of arm movement trajectories during visually guided reaching and, more generally, a framework for unsupervised real-time error-based learning. The models clarify how a child, or untrained robot, can learn to reach for objects that it sees. Piaget has provided basic insights with his concept of a circular reaction: As an infant makes internally generated movements of its hand, the eyes automatically follow this motion. A transformation is learned between the visual representation of hand position and the motor representation of hand position. Learning of this transformation eventually enables the child to accurately reach for visually detected targets. Grossberg and Kuperstein have shown how the eye movement system can use visual error signals to correct movement parameters via cerebellar learning. Here it is shown how endogenously generated arm movements lead to adaptive tuning of arm control parameters. These movements also activate the target position representations that are used to learn the visuo-motor transformation that controls visually guided reaching. The AVITE model presented here is an adaptive neural circuit based on the Vector Integration to Endpoint (VITE) model for arm and speech trajectory generation of Bullock and Grossberg. In the VITE model, a Target Position Command (TPC) represents the location of the desired target. The Present Position Command (PPC) encodes the present hand-arm configuration. The Difference Vector (DV) population continuously.computes the difference between the PPC and the TPC. A speed-controlling GO signal multiplies DV output. The PPC integrates the (DV)·(GO) product and generates an outflow command to the arm. Integration at the PPC continues at a rate dependent on GO signal size until the DV reaches zero, at which time the PPC equals the TPC. The AVITE model explains how self-consistent TPC and PPC coordinates are autonomously generated and learned. Learning of AVITE parameters is regulated by activation of a self-regulating Endogenous Random Generator (ERG) of training vectors. Each vector is integrated at the PPC, giving rise to a movement command. The generation of each vector induces a complementary postural phase during which ERG output stops and learning occurs. Then a new vector is generated and the cycle is repeated. This cyclic, biphasic behavior is controlled by a specialized gated dipole circuit. ERG output autonomously stops in such a way that, across trials, a broad sample of workspace target positions is generated. When the ERG shuts off, a modulator gate opens, copying the PPC into the TPC. Learning of a transformation from TPC to PPC occurs using the DV as an error signal that is zeroed due to learning. This learning scheme is called a Vector Associative Map, or VAM. The VAM model is a general-purpose device for autonomous real-time error-based learning and performance of associative maps. The DV stage serves the dual function of reading out new TPCs during performance and reading in new adaptive weights during learning, without a disruption of real-time operation. YAMs thus provide an on-line unsupervised alternative to the off-line properties of supervised error-correction learning algorithms. YAMs and VAM cascades for learning motor-to-motor and spatial-to-motor maps are described. YAM models and Adaptive Resonance Theory (ART) models exhibit complementary matching, learning, and performance properties that together provide a foundation for designing a total sensory-cognitive and cognitive-motor autonomous system.

Texture Segregation By Visual Cortex: Perceptual Grouping, Attention, and Learning

A neural model is proposed of how laminar interactions in the visual cortex may learn and recognize object texture and form boundaries. The model brings together five interacting processes: region-based texture classification, contour-based boundary grouping, surface filling-in, spatial attention, and object attention. The model shows how form boundaries can determine regions in which surface filling-in occurs; how surface filling-in interacts with spatial attention to generate a form-fitting distribution of spatial attention, or attentional shroud; how the strongest shroud can inhibit weaker shrouds; and how the winning shroud regulates learning of texture categories, and thus the allocation of object attention. The model can discriminate abutted textures with blurred boundaries and is sensitive to texture boundary attributes like discontinuities in orientation and texture flow curvature as well as to relative orientations of texture elements. The model quantitatively fits a large set of human psychophysical data on orientation-based textures. Object boundar output of the model is compared to computer vision algorithms using a set of human segmented photographic images. The model classifies textures and suppresses noise using a multiple scale oriented filterbank and a distributed Adaptive Resonance Theory (dART) classifier. The matched signal between the bottom-up texture inputs and top-down learned texture categories is utilized by oriented competitive and cooperative grouping processes to generate texture boundaries that control surface filling-in and spatial attention. Topdown modulatory attentional feedback from boundary and surface representations to early filtering stages results in enhanced texture boundaries and more efficient learning of texture within attended surface regions. Surface-based attention also provides a self-supervising training signal for learning new textures. Importance of the surface-based attentional feedback in texture learning and classification is tested using a set of textured images from the Brodatz micro-texture album. Benchmark studies vary from 95.1% to 98.6% with attention, and from 90.6% to 93.2% without attention.

ARTMAP: Supervised Real-Time Learning and Classification of Nonstationary Data by a Self-Organizing Neural Network

This article introduces a new neural network architecture, called ARTMAP, that autonomously learns to classify arbitrarily many, arbitrarily ordered vectors into recognition categories based on predictive success. This supervised learning system is built up from a pair of Adaptive Resonance Theory modules (ARTa and ARTb) that are capable of self-organizing stable recognition categories in response to arbitrary sequences of input patterns. During training trials, the ARTa module receives a stream {a^(p)} of input patterns, and ARTb receives a stream {b^(p)} of input patterns, where b^(p) is the correct prediction given a^(p). These ART modules are linked by an associative learning network and an internal controller that ensures autonomous system operation in real time. During test trials, the remaining patterns a^(p) are presented without b^(p), and their predictions at ARTb are compared with b^(p). Tested on a benchmark machine learning database in both on-line and off-line simulations, the ARTMAP system learns orders of magnitude more quickly, efficiently, and accurately than alternative algorithms, and achieves 100% accuracy after training on less than half the input patterns in the database. It achieves these properties by using an internal controller that conjointly maximizes predictive generalization and minimizes predictive error by linking predictive success to category size on a trial-by-trial basis, using only local operations. This computation increases the vigilance parameter ρa of ARTa by the minimal amount needed to correct a predictive error at ARTb· Parameter ρa calibrates the minimum confidence that ARTa must have in a category, or hypothesis, activated by an input a^(p) in order for ARTa to accept that category, rather than search for a better one through an automatically controlled process of hypothesis testing. Parameter ρa is compared with the degree of match between a^(p) and the top-down learned expectation, or prototype, that is read-out subsequent to activation of an ARTa category. Search occurs if the degree of match is less than ρa. ARTMAP is hereby a type of self-organizing expert system that calibrates the selectivity of its hypotheses based upon predictive success. As a result, rare but important events can be quickly and sharply distinguished even if they are similar to frequent events with different consequences. Between input trials ρa relaxes to a baseline vigilance pa When ρa is large, the system runs in a conservative mode, wherein predictions are made only if the system is confident of the outcome. Very few false-alarm errors then occur at any stage of learning, yet the system reaches asymptote with no loss of speed. Because ARTMAP learning is self stabilizing, it can continue learning one or more databases, without degrading its corpus of memories, until its full memory capacity is utilized.