A Neural Model of Multidigit Numerical Representation and Comparison

The Extended Spatial Number Network (ESpaN) is a neural model that simulates processing of high-level numerical stimuli such as multi-digit numbers. The ESpaN model targets the explanation of human psychophysical data, such as error rates and reaction times, about multi-digit (base 10) numerical stimuli, and describes how such a competence can develop through learning. The model suggests how the brain represents and processes an open-ended set of numbers and their regularities, such as the place-value structure, with finite resources in the brain. The model does that by showing how a multi-digit spatial number map forms through interactions with learned semantic categories that symbolize separate digits, as well as place markers like "tens," "hundreds," "thousands," etc. When number-stimuli are presented to the network, they trigger learning of associations between specific semantic categories and corresponding spatial locations of the spatial number map that together build a multi-digit spatial representation. Training of the network is aimed at portraying the process of development of human numerical competence during the first years of a child's life. The earlier SpaN model proposed a spatial number map, which both human and animal possess in their Where cortical processing stream, that can explain many data about analog numerical representation and comparison. The ESpaN model shows how learned cognitive categories in the What cortical processing stream can extend numerical competence to multi-digit numbers with a place-value structure. The ESpaN model hereby suggests how cortical cognitive and spatial processes can utilize a learned What-and-Where interstream interaction to control the development of multidigit numerical abilities.National Science Foundation (IRI-97-20333); Defense Advanced Research Projects Agency and the Office of Naval Research (NOOOI4-95-I-0409

A Neural Model of How the Brain Represents and Compares Multi-Digit Numbers: Spatial and Categorical Processes

Both animals and humans are capable of representing and comparing numerical quantities, but only humans seem to have evolved multi-digit place-value number systems. This article develops a neural model, called the Spatial Number Network, or SpaN model, which predicts how these shared numerical capabilities are computed using a spatial representation of number quantities in the Where cortical processing stream, notably the Inferior Parietal Cortex. Multi-digit numerical representations that obey a place-value principle are proposed to arise through learned interactions between categorical language representations in the What cortical processing stream and the Where spatial representation. It is proposed that learned semantic categories that symbolize separate digits, as well as place markers like "tens," "hundreds," "thousands," etc., are associated through learning with the corresponding spatial locations of the Where representation, leading to a place-value number system as an emergent property of What-Where information fusion. The model quantitatively simulates error rates in quantification and numerical comparison tasks, and reaction times for number priming and numerical assessment and comparison tasks. In the Where cortical process, it is proposed that transient responses to inputs are integrated before they activate an ordered spatial map that selectively responds to the number of events in a sequence. Neural mechanisms are defined which give rise to an ordered spatial numerical map ordering and Weber law characteristics as emergent properties. The dynamics of numerical comparison are encoded in activity pattern changes within this spatial map. Such changes cause a "directional comparison wave" whose properties mimic data about numerical comparison. These model mechanisms are variants of neural mechanisms that have elsewhere been used to explain data about motion perception, attention shifts, and target tracking. Thus, the present model suggests how numerical representations may have emerged as specializations of more primitive mechanisms in the cortical Where processing stream. The model's What-Where interactions can explain human psychophysical data, such as error rates and reaction times, about multi-digit (base 10) numerical stimuli, and describe how such a competence can develop through learning. The SpaN model and its explanatory range arc compared with other models of numerical representation.Defense Advanced Research Projects Agency and the Office of Naval Research (N00014-95-1-0409); National Science Foundation (IRI-97-20333

Robust 3D Action Recognition through Sampling Local Appearances and Global Distributions

3D action recognition has broad applications in human-computer interaction and intelligent surveillance. However, recognizing similar actions remains challenging since previous literature fails to capture motion and shape cues effectively from noisy depth data. In this paper, we propose a novel two-layer Bag-of-Visual-Words (BoVW) model, which suppresses the noise disturbances and jointly encodes both motion and shape cues. First, background clutter is removed by a background modeling method that is designed for depth data. Then, motion and shape cues are jointly used to generate robust and distinctive spatial-temporal interest points (STIPs): motion-based STIPs and shape-based STIPs. In the first layer of our model, a multi-scale 3D local steering kernel (M3DLSK) descriptor is proposed to describe local appearances of cuboids around motion-based STIPs. In the second layer, a spatial-temporal vector (STV) descriptor is proposed to describe the spatial-temporal distributions of shape-based STIPs. Using the Bag-of-Visual-Words (BoVW) model, motion and shape cues are combined to form a fused action representation. Our model performs favorably compared with common STIP detection and description methods. Thorough experiments verify that our model is effective in distinguishing similar actions and robust to background clutter, partial occlusions and pepper noise

Topological Equivalence and Similarity in Multi-Representation Geographic Databases

Geographic databases contain collections of spatial data representing the variety of views for the real world at a specific time. Depending on the resolution or scale of the spatial data, spatial objects may have different spatial dimensions, and they may be represented by point, linear, or polygonal features, or combination of them. The diversity of data that are collected over the same area, often from different sources, imposes a question of how to integrate and to keep them consistent in order to provide correct answers for spatial queries. This thesis is concerned with the development of a tool to check topological equivalence and similarity for spatial objects in multi-representation databases. The main question is what are the components of a model to identify topological consistency, based on a set of possible transitions for the different types of spatial representations. This work develops a new formalism to model consistently spatial objects and spatial relations between several objects, each represented at multiple levels of detail. It focuses on the topological consistency constraints that must hold among the different representation of objects, but it is not concerned about generalization operations of how to derive one representation level from another. The result of this thesis is a?computational tool to evaluate topological equivalence and similarity across multiple representations. This thesis proposes to organize a spatial scene -a set of spatial objects and their embeddings in space- directly as a relation-based model that uses a hierarchical graph representation. The focus of the relation-based model is on relevant object representations. Only the highest-dimensional object representations are explicitly stored, while their parts are not represented in the graph

Multi-set canonical correlation analysis for 3D abnormal gait behaviour recognition based on virtual sample generation

Small sample dataset and two-dimensional (2D) approach are challenges to vision-based abnormal gait behaviour recognition (AGBR). The lack of three-dimensional (3D) structure of the human body causes 2D based methods to be limited in abnormal gait virtual sample generation (VSG). In this paper, 3D AGBR based on VSG and multi-set canonical correlation analysis (3D-AGRBMCCA) is proposed. First, the unstructured point cloud data of gait are obtained by using a structured light sensor. A 3D parametric body model is then deformed to fit the point cloud data, both in shape and posture. The features of point cloud data are then converted to a high-level structured representation of the body. The parametric body model is used for VSG based on the estimated body pose and shape data. Symmetry virtual samples, pose-perturbation virtual samples and various body-shape virtual samples with multi-views are generated to extend the training samples. The spatial-temporal features of the abnormal gait behaviour from different views, body pose and shape parameters are then extracted by convolutional neural network based Long Short-Term Memory model network. These are projected onto a uniform pattern space using deep learning based multi-set canonical correlation analysis. Experiments on four publicly available datasets show the proposed system performs well under various conditions

Multi-Scale Representation Learning for Spatial Feature Distributions using Grid Cells

Unsupervised text encoding models have recently fueled substantial progress in NLP. The key idea is to use neural networks to convert words in texts to vector space representations based on word positions in a sentence and their contexts, which are suitable for end-to-end training of downstream tasks. We see a strikingly similar situation in spatial analysis, which focuses on incorporating both absolute positions and spatial contexts of geographic objects such as POIs into models. A general-purpose representation model for space is valuable for a multitude of tasks. However, no such general model exists to date beyond simply applying discretization or feed-forward nets to coordinates, and little effort has been put into jointly modeling distributions with vastly different characteristics, which commonly emerges from GIS data. Meanwhile, Nobel Prize-winning Neuroscience research shows that grid cells in mammals provide a multi-scale periodic representation that functions as a metric for location encoding and is critical for recognizing places and for path-integration. Therefore, we propose a representation learning model called Space2Vec to encode the absolute positions and spatial relationships of places. We conduct experiments on two real-world geographic data for two different tasks: 1) predicting types of POIs given their positions and context, 2) image classification leveraging their geo-locations. Results show that because of its multi-scale representations, Space2Vec outperforms well-established ML approaches such as RBF kernels, multi-layer feed-forward nets, and tile embedding approaches for location modeling and image classification tasks. Detailed analysis shows that all baselines can at most well handle distribution at one scale but show poor performances in other scales. In contrast, Space2Vec's multi-scale representation can handle distributions at different scales.Comment: 15 pages; Accepted to ICLR 2020 as a spotlight pape

Modeling and simulation of phase-transitions in multicomponent aluminum alloy casting

The casting process of aluminum products involves the spatial distribution of alloying elements. It is essential that these elements are uniformly distributed in order to guarantee reliable and consistent products. This requires a good understanding of the main physical mechanisms that affect the solidification, in particular the thermodynamic description and its coupling to the transport processes of heat and mass that take place. The continuum modeling is reviewed and methods for handling the thermodynamics component of multi-element alloys are proposed. Savings in data-storage and computing costs on the order of 100 or more appear possible, when a combination of data-reduction and data-representation methods is used. To test the new approach a simplified model was proposed and shown to qualitatively capture the evolving solidification front