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.

Fuzzy ARTMAP: A Neural Network Architecture for Incremental Supervised Learning of Analog Multidimensional Maps

A new neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors. The architecture, called Fuzzy ARTMAP, achieves a synthesis of fuzzy logic and Adaptive Resonance Theory (ART) neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and ART category choice, resonance, and learning. Fuzzy ARTMAP also realizes a new Minimax Learning Rule that conjointly minimizes predictive error and maximizes code compression, or generalization. This is achieved by a match tracking process that increases the ART vigilance parameter by the minimum amount needed to correct a predictive error. As a result, the system automatically learns a minimal number of recognition categories, or "hidden units", to met accuracy criteria. Category proliferation is prevented by normalizing input vectors at a preprocessing stage. A normalization procedure called complement coding leads to a symmetric theory in which the MIN operator (Λ) and the MAX operator (v) of fuzzy logic play complementary roles. Complement coding uses on-cells and off-cells to represent the input pattern, and preserves individual feature amplitudes while normalizing the total on-cell/off-cell vector. Learning is stable because all adaptive weights can only decrease in time. Decreasing weights correspond to increasing sizes of category "boxes". Smaller vigilance values lead to larger category boxes. Improved prediction is achieved by training the system several times using different orderings of the input set. This voting strategy can also be used to assign probability estimates to competing predictions given small, noisy, or incomplete training sets. Four classes of simulations illustrate Fuzzy ARTMAP performance as compared to benchmark back propagation and genetic algorithm systems. These simulations include (i) finding points inside vs. outside a circle; (ii) learning to tell two spirals apart; (iii) incremental approximation of a piecewise continuous function; and (iv) a letter recognition database. The Fuzzy ARTMAP system is also compared to Salzberg's NGE system and to Simpson's FMMC system.

Structure maps for hcp metals from first-principles calculations

The ability to predict the existence and crystal type of ordered structures of materials from their components is a major challenge of current materials research. Empirical methods use experimental data to construct structure maps and make predictions based on clustering of simple physical parameters. Their usefulness depends on the availability of reliable data over the entire parameter space. Recent development of high-throughput methods opens the possibility to enhance these empirical structure maps by ab initio calculations in regions of the parameter space where the experimental evidence is lacking or not well characterized. In this paper we construct enhanced maps for the binary alloys of hcp metals, where the experimental data leaves large regions of poorly characterized systems believed to be phase separating. In these enhanced maps, the clusters of noncompound-forming systems are much smaller than indicated by the empirical results alone. © 2010 The American Physical Society.

Specializing pedestrian maps to address the needs of people using wheelchairs: a case study in community-sustainable information systems

Gemstone Team FASTR (Finding Alternative Specialized Travel Routes)

Components of error of maps from remotely sensed images

The concept of a “true” ground-truth map is introduced, from which the inaccuracy/error of any production map may be measured. A partition of the mapped region is defined in terms of the “residual rectification” transformation. Geometric RMS-type and Geometric Distortion error criteria are defined as well as a map mis-classification error criterion (the latter for hard and fuzzy produc-tion maps). The total map error is defined to be the sum (over each set of the map partition men-tioned above) of these three error components integrated over each set of the partition.

Composite front maps for improved visibility of dynamic sea-surface features on cloudy SeaWiFS and AVHRR data

Novel techniques have been developed for increasing the value of cloud-affected sequences of Advanced Very High Resolution Radiometer (AVHRR) sea-surface temperature (SST) data and Sea-viewing Wide Field-of-view Sensor (SeaWiFS) ocean colour data for visualising dynamic physical and biological oceanic processes such as fronts, eddies and blooms. The proposed composite front map approach is to combine the location, strength and persistence of all fronts observed over several days into a single map, which allows intuitive interpretation of mesoscale structures. This method achieves a synoptic view without blurring dynamic features, an inherent problem with conventional time-averaging compositing methods. Objective validation confirms a significant improvement in feature visibility on composite maps compared to individual front maps. A further novel aspect is the automated detection of ocean colour fronts, correctly locating 96% of chlorophyll fronts in a test data set. A sizeable data set of 13,000 AVHRR and 1200 SeaWiFS scenes automatically processed using this technique is applied to the study of dynamic processes off the Iberian Peninsula such as mesoscale eddy generation, and many additional applications are identified. Front map animations provide a unique insight into the evolution of upwelling and eddies.

Estimating the Heading of a Husky Mobile Robot with a LiDAR Compass based on Direction Maps

Without an absolute position sensor (e.g., GPS), an accurate heading estimate is necessary for proper localization of an autonomous unmanned vehicle or robot. This paper introduces direction maps (DMs), which represent the directions of only dominant surfaces of the vehicle’s environment and can be created with negligible effort. Given an environment with reoccurring surface directions (e.g., walls, buildings, parked cars), lines extracted from laser scans can be matched with a DM to provide an extremely lightweight heading estimate that is shown, through experimentation, to drastically reduce the growth of heading errors. The algorithm was tested using a Husky A200 mobile robot in a warehouse environment over traverses hundreds of metres in length. When a simple a priori DM was provided, the resulting heading estimation showed virtually no error growth.

Annotated Chromosome Maps for Renal Disease

A combination of linkage analyses and association studies are currently employed to promote the identification of genetic factors contributing to inherited renal disease. We have standardized and merged complex genetic data from disparate sources, creating unique chromosomal maps to enhance genetic epidemiological investigations. This database and novel renal maps effectively summarize genomic regions of suggested linkage, association, or chromosomal abnormalities implicated in renal disease. Chromosomal regions associated with potential intermediate clinical phenotypes have been integrated, adding support for particular genomic intervals. More than 500 reports from medical databases, published scientific literature, and the World Wide Web were interrogated for relevant renal-related information. Chromosomal regions highlighted for prioritized investigation of renal complications include 3q13-26, 6q22-27, 10p11-15, 16p11-13, and 18q22. Combined genetic and physical maps are effective tools to organize genetic data for complex diseases. These renal chromosome maps provide insights into renal phenotype-genotype relationships and act as a template for future genetic investigations into complex renal diseases. New data from individual researchers and/or future publications can be readily incorporated to this resource via a user-friendly web-form accessed from the website: www.qub.ac.uk/neph-res/CORGI/index.php.

Positive dilations of piecewise monotonic Markov maps

We provide an explicit formula which gives natural extensions of piecewise monotonic Markov maps defined on an interval of the real line. These maps are exact endomorphisms and define chaotic discrete dynamical systems.