Approximation properties of a class of artificial neural networks are established. It is shown that feedforward networks with one layer of sigmoidal nonlinearities achieve integrated squared error of order O(1/n), where n is the number of nodes. The approximated function is assumed to have a bound on the first moment of the magnitude distribution of the Fourier transform. The nonlinear parameters associated with the sigmoidal nodes, as well as the parameters of linear combination, are adjusted in the approximation. In contrast, it is shown that for series expansions with n terms, in which only the parameters of linear combination are adjusted, the integrated squared approximation error cannot be made smaller than order 1/n/sup 2/d/ uniformly for functions satisfying the same smoothness assumption, where d is the dimension of the input to the function. For the class of functions examined, the approximation rate and the parsimony of the parameterization of the networks are shown to be advantageous in high-dimensional settings. >

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Universal approximation bounds for superpositions of a sigmoidal function

http://cvssp-data.eps.surrey.ac.uk/Personal/AdrianHilton/Publications_files/survey_techrep.pdf

A survey of advances in vision-based human motion capture and analysis

In this chapter we survey the theory of two-party communication complexity. This field of theoretical computer science aims at studying the following, seemingly very simple, scenario: There are two players Alice who holds an n-bit string x and Bob who holds an n-bit string y. Their goal is to communicate in order to compute the value of some boolean function f(x, y), while exchanging a number of bits which is as small as possible. In the first part of this survey we present, mainly by giving examples, some of the results (and techniques) developed as part of this theory. We put an emphasis on proving lower bounds on the amount of communication that must be exchanged in the above scenario for certain functions f . In the second part of this survey we will exemplify the wide applicability of the results proved in the first part to other areas of computer science. While it is obvious that there are many applications of the results to problems in which communication is involved (e.g., in distributed systems), we concentrate on applications in which communication does not appear explicitly in the statement of the problems. In particular, we present results regarding the following models of computation: • Finite automata • Turing machines • Decision trees • Ordered binary decision diagrams (OBDDs) • VLSI chips • Networks of threshold gates We provide references to many other issues and applications of communication complexity which are not discussed in this survey.

Communication Complexity

Background subtraction methods are widely exploited for moving object detection in videos in many applications, such as traffic monitoring, human motion capture, and video surveillance. How to correctly and efficiently model and update the background model and how to deal with shadows are two of the most distinguishing and challenging aspects of such approaches. The article proposes a general-purpose method that combines statistical assumptions with the object-level knowledge of moving objects, apparent objects (ghosts), and shadows acquired in the processing of the previous frames. Pixels belonging to moving objects, ghosts, and shadows are processed differently in order to supply an object-based selective update. The proposed approach exploits color information for both background subtraction and shadow detection to improve object segmentation and background update. The approach proves fast, flexible, and precise in terms of both pixel accuracy and reactivity to background changes.

/pdf/detecting-moving-objects-ghosts-and-shadows-in-video-streams-1d8sq6g069.pdf

Detecting moving objects, ghosts, and shadows in video streams

Theoretical results concerning the capabilities and limitations of various neural network models are summarized, and some of their extensions are discussed. The network models considered are divided into two basic categories: static networks and dynamic networks. Unlike static networks, dynamic networks have memory. They fall into three groups: networks with feedforward dynamics, networks with output feedback, and networks with state feedback, which are emphasized in this work. Most of the networks discussed are trained using supervised learning. >

Progress in supervised neural networks

The emergence of asynchronous transfer mode (ATM) technology has generated new challenging problems for computer network designers. One of these challenges lies in the efficient management of ATM traffic so that the communication bandwidth of the network can be optimally utilized. Considerable standardization efforts in recent ATM Forum activities have been centered on the traffic management of available bit rate (ABR) service. In this paper, we examine congestion control schemes for ABR service in ATM networks. We describe a rate-based scheme that is now referred to by the ATM Forum as 'intelligent congestion control' and is currently considered as one of the most promising approaches. Moreover, we present analytical and simulation results illustrating the characteristics of the proposed scheme.

Intelligent congestion control for ABR service in ATM networks

1. Introduction. 2. Linear Threshold Element. 3. Computing Symmetric Functions. 4. Depth Efficient Arithmetic Circuits. 5. Depth-Size Tradeoffs. 6. Computing with Small Weights. 7. Rational Approximation and Optimal Size Circuits. 8. Geometric Framework and Spectral Analysis. 9. Limitations of AND-OR Circuits. 10. Lower Bounds via Communication Complexity. 11. Hopfield Network. Glossary. Bibliography. Index.

Discrete Neural Computation: A Theoretical Foundation

Linear threshold elements (LTEs) are the basic processing elements in artificial neural networks. An LTE computes a function that is a sign of a weighted sum of the input variables. The weights are arbitrary integers; actually, they can be very big integers—exponential in the number of input variables. However, in practice, it is very difficult to implement big weights. So the natural question that may be asked is whether there is an efficient way to simulate a network of LTEs with big weights by a network of LTEs with small weights. The following results are proved: (1) every LTE with big weights can be simulated by a depth-3, polynomial size network of LTEs with small weights; and (2) every depth-d, polynomial size network of LTEs with big weights can be simulated by a depth-$( 2d + 1 )$, polynomial size network of LTEs with small weights. To prove these results, tools from harmonic analysis of Boolean functions are used. The technique is quite general; it provides insights to some other problems. For e...

/pdf/on-the-power-of-threshold-circuits-with-small-weights-2qych57edq.pdf

On the Power of Threshold Circuits with Small Weights

A Bluetooth ad hoc network can be formed by interconnecting piconets into scatternets. The constraints and properties of Bluetooth scatternets present special challenges in forming an ad hoc network efficiently. We present and analyse a new randomized distributed algorithm for Bluetooth scatternet formation. We prove that our algorithm achieves O(log n) time complexity and O(n) message complexity. We show that: (1) in the scatternet formed by our algorithm, any device is a member of at most two piconets; (2) the number of piconets is close to being minimal.

/pdf/a-bluetooth-scatternet-formation-algorithm-4gc9vkia5m.pdf

A Bluetooth scatternet formation algorithm

An image processing and object tracking approach is proposed for the design of a video-based freeway traffic monitoring system. Proper estimation of the traffic speed in different lanes of a freeway allows for timely detection of possible congestions. The proposed method consists of a road modeling stage and a vehicle tracking stage. In the first stage, a three-dimensional model of the background road image is generated using several initial frames. In the tracking stage, each car in the scene is isolated and tracked over many frames, and by mapping its coordinates to the road's 3D model, an estimate of its velocity on the road is produced. The algorithm runs in real-time on a workstation. Experimental results on frame sequences taken from Santa Ana area freeways will be presented.

Kai-Yeung Siu

Papers

Intelligent congestion control for ABR service in ATM networks

Discrete Neural Computation: A Theoretical Foundation

On the Power of Threshold Circuits with Small Weights

A Bluetooth scatternet formation algorithm

Video-based freeway monitoring system using recursive vehicle tracking