R. C. Lacher

Back-propagation learning in expert networks

Expert networks are event-driven, acyclic networks of neural objects derived from expert systems. The neural objects process information through a nonlinear combining function that is different from, and more complex than, typical neural network node processors. The authors develop back-propagation learning for acyclic, event-driven networks in general and derive a specific algorithm for learning in EMYCIN-derived expert networks. The algorithm combines back-propagation learning with other features of expert networks, including calculation of gradients of the nonlinear combining functions and the hypercube nature of the knowledge space. It offers automation of the knowledge acquisition task for certainty factors, often the most difficult part of knowledge extraction. Results of testing the learning algorithm with a medium-scale (97-node) expert network are presented.

Cell-like spaces

In this note we give a characterization of those compacta which can be embedded in manifolds as cellular sets (the cell-like spaces). There are three conditions equivalent to cell likeness for a finitedimensional compactum X. One of these is that X have the Cechhomotopy-type of a point, as defined by Borsuk in [1]. Another is a technical condition which implies that McMillans cellularity criterion [5] holds, not just for compact absolute retracts but for arbitrary cell-like spaces. It follows that most of the theorems of [5] hold for cell-like subsets of manifolds. DEFINITION. A subset X of the n-manifold N is said to be cellular in N if there exists a sequence Ql, Q2, * * * of topological n-cells in N, with XCQi+,CInt Qi for each i, such that x=n 1 Qi. Clearly cellularity is a property of the embedding of X in N. However, there is the corresponding intrinsic topological property, as follows: DEFINITION. A space X is cell-like if there is an embedding f of X into some manifold N such that f(X) is cellular in N. Cellularity was first defined by Brown in [3]. Since then, the idea has been important in the study of manifolds, and hence the problem of recognizing cellular sets has also been important. By far the best recognition criterion was given by McMillan in [5]. There he proved that, if X is a compact absolute retract in the interior of the combinatorial n-manifold N, n > 5, then X is cellular in N provided that the inclusion XCN has property (*) below.

Hybrid learning in expert networks

Expert networks are defined as the embodiment of an experts rule-based knowledge in an acyclic feedforward network. A transformation process is used to create an expert network from an expert system to enable training of the certainty factors of the expert systems rules from data. Certainty factors in the expert system correspond to connection weights in the network. The training algorithm presented begins with only the basic architecture of the network and uses a reinforcement learning process to arrive at an improved knowledge state and a back-propagation segment to complete convergence to correct values. Results of a case study illustrate the practicality of the proposed design and of the hybrid learning algorithm used.<<ETX>>

Extracting rules by destructive learning

A method is presented for extracting general rules from a trained artificial neural network (ANN), which is trained by destructive learning. The method presented here takes advantage of the pruned network which contains more exact knowledge regarding the problem. The method consists of three phases: training, pruning, and rule-extracting. The training phase is concerned with ANN learning, using a general backpropagation (BP) algorithm. In the pruning phase, redundant hidden units and links are deleted trained network, and then, the link weights remaining in the network are re-trained to obtain near-saturated outputs from hidden units. The rule-extracting algorithm uses the pruned network to extract rules. After applying the proposed method to the MONKs problems testbed, we found 6, 27, and 20 rules which could classify all 432 testing data with 100, 100, and 98.1% accuracy for each MONKs problem, respectively. In addition, the proposed method outperformed most other machine learning methods with which it was compared.<<ETX>>

Network complexity and learning efficiency of constructive learning algorithms

Connectionist constructive learning dynamically constructs a network to balance the complexity of the network topology with the complexity of the function specified by the training data. In order to evaluate the quality of a constructive learning algorithm, not only the learning efficiency of the algorithm need to be measured, but also the topological complexity of the constructed network has to be examined. This paper discusses both the learning speeds and the network sizes of constructive learning algorithms. As the backprop requires more nodes than necessary for the network to converge, it is used as a reference to measure the complexity of constructive networks. Experiments using two constructive algorithms, cascade correlation and stack, indicates that the network built by constructive learning algorithms can have less complexity than the network required by the backprop algorithm.<<ETX>>

A model for the asymptotic behavior of loop entanglement in a constrained liquid region

A constrained liquid region in a semicrystalline polymer has been modeled by random walk in the slab defined by two parallel planes a distance M units apart in space. Loops (walks beginning and ending on the same plane) play the role of strands of polymer that exit and reenter the same crystal while ties (walks that go from plane to opposite plane) play the role of strands that connect two crystals. A simulation has been designed to investigate the extent to which entanglement of loops may contribute to material properties. Results of the simulation indicate that several measures of entanglement (calculated from the matrix of linking numbers of a left loop with a complete distribution of right loops) approach positive constant values or increase without bound as M increases (while the effect of ties is known to be inversely proportional to M). A model of the simulation, in which random loops are replaced by loops with predictable geometry, yields asymptotic estimates of one such entanglement measure. The ...

Hierarchical Architectures for Reasoning

This chapter has a threefold purpose: (1) to introduce a general framework for parallel/distributed computation, the computational network; (2) to expose in detail a symbolic example of a computational network, related to expert systems, called an expert network; and (3) to describe and investigate how an expert network can be realized as a neural network possessing a hierarchical symbolic/sub-symbolic architectural organization.

A disjoint disks property for 3-manifolds

Abstract We show that the map separation property (MSP), a concept due to H.W. Lambert and R.B. Sher, is an appropriate analogue of J.W. Cannon’s disjoint disks property (DDP) for the class C of compact generalized 3-manifolds with zero-dimensional singular set, modulo the Poincare conjecture. Our main result is that the Poincare conjecture (in dimension three) is equivalent to the conjecture that every Xϵ C with the MSP is a topological 3-manifold.

Embeddings with mapping cylinder neighborhoods

Musr a submanifold Mm C N” having a mapping cylinder neighborhood be locally flat? This question has been answered in dimensions n ~4 and its relation with the infamous double suspension problem is well-known in dimensions n 2 5. (More detail and references appear in 8 1 below.) Perhaps the main result of this paper is that such manifolds are indeed locally flat provided they are freely embedded (i.e. that for each E > 0 there exists a map A : Mm x L”-m-’ --f (N” -Mm) such that h(x x Ln-m-l) is within E of x and links Mm homologically; here L”-m-’ is any simply connected manifold if n m 13 and is the sphere Sn-m-’ if n m 5 2); if n m = 2 we need the additional assumption that M”-* is locally flat at some point. A corollary is that freely embedded PL submanifolds are locally flat. The concepts of mapping cylinder neighborhood and freeness can be combined to obtain that of a strongly free submanifold Mm C N”: Instead of a mapping cylinder neighborhood, we require that there exist a map A of the mapping cylinder Z, into N” (where 7: Mm x L”-*-‘+ Mm is projection on the first factor) such that AIM” = identity and A(Z,, -Mm) C (N” -Mm), and A(6’(x)) links Mm. Another of our results is that strongly free submanifolds are locally flat (n # 4, with the flat spot proviso when n m = 2). These results each have local form. The method of proof in each case is to deduce that M” is locally homotopically unknotted in N”. In the course of the proof, criteria for commutativity of T,( U”), and others for the vanishing of 7~q( U”), 2 s q Ik, are developed for open orientable manifolds U” ; these criteria are perhaps of independent interest. For commutativity of T,( U”) we require that for any compact connected set C in U” there exist a compact connected orientable manifold K” with abelian fundamental group and a degree one map (K”, 8K”) --) (U”, U” C) which induces an injection H,(K”) + H1( U”). For vanishing of T~( U”)(2 5 q 5 k) we require that for any C there exist a compact connected orientable K” with TV = 0 (25 q 5 k) and a degree one map (K”, 8K”) + (U”, U” C) which induces an isomorphism T,(K”) + P,( U”). Conventions. Our notation is that of [23] with the. following exceptions. In all cases our homology is taken with integer coefficients and the coefficient group is suppressed from the notation. Our notation for the mapping cylinder Z.+ of a map 4: X + Y is as follows: Z, is the quotient space of XX [O, l] U Y X 2 in which points (x, 1) and (4(x), 2) are identified; X is identified with the image of X x 0 in Z+ ; and Y is identified with the image of Y x 2 in Z,. We use Z, to denote the image of X x [0, t] in 5. If M is a manifold we denote by aM the set of boundary points of M and set g = M JM.

Human shape recognition using the method of moments and artificial neural networks

The research described in the paper explores the feasibility of an automated adaptive system capable of recognizing that a moving object in a sequence of two-dimensional images is a human or, at the very least has a human shape. To address this problem a method employing the method of standard moments, and artificial neural networks has been designed and implemented The results of the method implementation and testing indicate the validity of the system design and the techniques used. The automated human recognition system developed recognizes left and right human profiles with a success rate of 87.5% and 92.5% respectively. The system is also successful in distinguishing images of human profiles from images of tailgating persons, crouching persons, objects, persons with objects and plain image noise.