Empirical evidence for ultrametric structure in multi-layer perceptron error surfaces

Combinatorial optimization problems share an interesting property with spin glass systems in that their state spaces can exhibit ultrametric structure. We use sampling methods to analyse the error surfaces of feedforward multi-layer perceptron neural networks learning encoder problems. The third order statistics of these points of attraction are examined and found to be arranged in a highly ultrametric way. This is a unique result for a finite, continuous parameter space. The implications of this result are discussed.

Color constancy and the functional significance of McCollough effects

A central problem in visual perception concerns how humans perceive stable and uniform object colors despite variable lighting conditions (i.e. color constancy). One solution is to 'discount' variations in lighting across object surfaces by encoding color contrasts, and utilize this information to 'fill in' properties of the entire object surface. Implicit in this solution is the caveat that the color contrasts defining object boundaries must be distinguished from the spurious color fringes that occur naturally along luminance-defined edges in the retinal image (i.e. optical chromatic aberration). In the present paper, we propose that the neural machinery underlying color constancy is complemented by an 'error-correction' procedure which compensates for chromatic aberration, and suggest that error-correction may be linked functionally to the experimentally induced illusory colored aftereffects known as McCollough effects (MEs). To test these proposals, we develop a neural network model which incorporates many of the receptive-field (RF) profiles of neurons in primate color vision. The model is composed of two parallel processing streams which encode complementary sets of stimulus features: one stream encodes color contrasts to facilitate filling-in and color constancy; the other stream selectively encodes (spurious) color fringes at luminance boundaries, and learns to inhibit the filling-in of these colors within the first stream. Computer simulations of the model illustrate how complementary color-spatial interactions between error-correction and filling-in operations (a) facilitate color constancy, (b) reveal functional links between color constancy and the ME, and (c) reconcile previously reported anomalies in the local (edge) and global (spreading) properties of the ME. We discuss the broader implications of these findings by considering the complementary functional roles performed by RFs mediating color-spatial interactions in the primate visual system. (C) 2002 Elsevier Science Ltd. All rights reserved.

Learning the dynamics of embedded clauses

Recent work by Siegelmann has shown that the computational power of recurrent neural networks matches that of Turing Machines. One important implication is that complex language classes (infinite languages with embedded clauses) can be represented in neural networks. Proofs are based on a fractal encoding of states to simulate the memory and operations of stacks. In the present work, it is shown that similar stack-like dynamics can be learned in recurrent neural networks from simple sequence prediction tasks. Two main types of network solutions are found and described qualitatively as dynamical systems: damped oscillation and entangled spiraling around fixed points. The potential and limitations of each solution type are established in terms of generalization on two different context-free languages. Both solution types constitute novel stack implementations - generally in line with Siegelmann's theoretical work - which supply insights into how embedded structures of languages can be handled in analog hardware.

Document retrieval for e-mail search and discovery using Formal Concept Analysis

This paper discusses a document discovery tool based on Conceptual Clustering by Formal Concept Analysis. The program allows users to navigate e-mail using a visual lattice metaphor rather than a tree. It implements a virtual. le structure over e-mail where files and entire directories can appear in multiple positions. The content and shape of the lattice formed by the conceptual ontology can assist in e-mail discovery. The system described provides more flexibility in retrieving stored e-mails than what is normally available in e-mail clients. The paper discusses how conceptual ontologies can leverage traditional document retrieval systems and aid knowledge discovery in document collections.

Human brain regions required for the dividing and switching of attention between two features of a single object

This combined PET and ERP study was designed to identify the brain regions activated in switching and divided attention between different features of a single object using matched sensory stimuli and motor response. The ERP data have previously been reported in this journal [64]. We now present the corresponding PET data. We identified partially overlapping neural networks with paradigms requiring the switching or dividing of attention between the elements of complex visual stimuli. Regions of activation were found in the prefrontal and temporal cortices and cerebellum. Each task resulted in different prefrontal cortical regions of activation lending support to the functional subspecialisation of the prefrontal and temporal cortices being based on the cognitive operations required rather than the stimuli themselves. (C) 2003 Elsevier Science B.V. All rights reserved.

Speeding up the EM algorithm for mixture model-based segmentation of magnetic resonance images

Mixture models implemented via the expectation-maximization (EM) algorithm are being increasingly used in a wide range of problems in pattern recognition such as image segmentation. However, the EM algorithm requires considerable computational time in its application to huge data sets such as a three-dimensional magnetic resonance (MR) image of over 10 million voxels. Recently, it was shown that a sparse, incremental version of the EM algorithm could improve its rate of convergence. In this paper, we show how this modified EM algorithm can be speeded up further by adopting a multiresolution kd-tree structure in performing the E-step. The proposed algorithm outperforms some other variants of the EM algorithm for segmenting MR images of the human brain. (C) 2004 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.

The philosophical significance of Cox's theorem

Cox's theorem states that, under certain assumptions, any measure of belief is isomorphic to a probability measure. This theorem, although intended as a justification of the subjectivist interpretation of probability theory, is sometimes presented as an argument for more controversial theses. Of particular interest is the thesis that the only coherent means of representing uncertainty is via the probability calculus. In this paper I examine the logical assumptions of Cox's theorem and I show how these impinge on the philosophical conclusions thought to be supported by the theorem. I show that the more controversial thesis is not supported by Cox's theorem. (C) 2003 Elsevier Inc. All rights reserved.

Multivariate monitoring of a biological wastewater treatment process: a case study at Melbourne Water's Western Treatment Plant

Biological wastewater treatment is a complex, multivariate process, in which a number of physical and biological processes occur simultaneously. In this study, principal component analysis (PCA) and parallel factor analysis (PARAFAC) were used to profile and characterise Lagoon 115E, a multistage biological lagoon treatment system at Melbourne Water's Western Treatment Plant (WTP) in Melbourne, Australia. In this study, the objective was to increase our understanding of the multivariate processes taking place in the lagoon. The data used in the study span a 7-year period during which samples were collected as often as weekly from the ponds of Lagoon 115E and subjected to analysis. The resulting database, involving 19 chemical and physical variables, was studied using the multivariate data analysis methods PCA and PARAFAC. With these methods, alterations in the state of the wastewater due to intrinsic and extrinsic factors could be discerned. The methods were effective in illustrating and visually representing the complex purification stages and cyclic changes occurring along the lagoon system. The two methods proved complementary, with each having its own beneficial features. (C) 2003 Elsevier B.V. All rights reserved.

Hybrid knowledge representation in a blackboard KBS for liquid retaining structure design

This paper highlights the importance of design expertise, for designing liquid retaining structures, including subjective judgments and professional experience. Design of liquid retaining structures has special features different from the others. Being more vulnerable to corrosion problem, they have stringent requirements against serviceability limit state of crack. It is the premise of the study to transferring expert knowledge in a computerized blackboard system. Hybrid knowledge representation schemes, including production rules, object-oriented programming, and procedural methods, are employed to express engineering heuristics and standard design knowledge during the development of the knowledge-based system (KBS) for design of liquid retaining structures. This approach renders it possible to take advantages of the characteristics of each method. The system can provide the user with advice on preliminary design, loading specification, optimized configuration selection and detailed design analysis of liquid retaining structure. It would be beneficial to the field of retaining structure design by focusing on the acquisition and organization of expert knowledge through the development of recent artificial intelligence technology. (C) 2003 Elsevier Ltd. All rights reserved.

A conceptual model of personalized virtual learning environments

The Virtual Learning Environment (VLE) is one of the fastest growing areas in educational technology research and development. In order to achieve learning effectiveness, ideal VLEs should be able to identify learning needs and customize solutions, with or without an instructor to supplement instruction. They are called Personalized VLEs (PVLEs). In order to achieve PVLEs success, comprehensive conceptual models corresponding to PVLEs are essential. Such conceptual modeling development is important because it facilitates early detection and correction of system development errors. Therefore, in order to capture the PVLEs knowledge explicitly, this paper focuses on the development of conceptual models for PVLEs, including models of knowledge primitives in terms of learner, curriculum, and situational models, models of VLEs in general pedagogical bases, and particularly, the definition of the ontology of PVLEs on the constructivist pedagogical principle. Based on those comprehensive conceptual models, a prototyped multiagent-based PVLE has been implemented. A field experiment was conducted to investigate the learning achievements by comparing personalized and non-personalized systems. The result indicates that the PVLE we developed under our comprehensive ontology successfully provides significant learning achievements. These comprehensive models also provide a solid knowledge representation framework for PVLEs development practice, guiding the analysis, design, and development of PVLEs. (c) 2005 Elsevier Ltd. All rights reserved.

Multiple paths extraction in images using a constrained expanded trellis

Single shortest path extraction algorithms have been used in a number of areas such as network flow and image analysis. In image analysis, shortest path techniques can be used for object boundary detection, crack detection, or stereo disparity estimation. Sometimes one needs to find multiple paths as opposed to a single path in a network or an image where the paths must satisfy certain constraints. In this paper, we propose a new algorithm to extract multiple paths simultaneously within an image using a constrained expanded trellis (CET) for feature extraction and object segmentation. We also give a number of application examples for our multiple paths extraction algorithm.

Multiplication and comultiplication of beliefs

Multiplication and comultiplication of beliefs represent a generalisation of multiplication and comultiplication of probabilities as well as of binary logic AND and OR. Our approach follows that of subjective logic, where belief functions are expressed as opinions that are interpreted as being equivalent to beta probability distributions. We compare different types of opinion product and coproduct, and show that they represent very good approximations of the analytical product and coproduct of beta probability distributions. We also define division and codivision of opinions, and compare our framework with other logic frameworks for combining uncertain propositions. (C) 2004 Elsevier Inc. All rights reserved.

The correspondence framework for 3D surface matching algorithms

Beyond the inherent technical challenges, current research into the three dimensional surface correspondence problem is hampered by a lack of uniform terminology, an abundance of application specific algorithms, and the absence of a consistent model for comparing existing approaches and developing new ones. This paper addresses these challenges by presenting a framework for analysing, comparing, developing, and implementing surface correspondence algorithms. The framework uses five distinct stages to establish correspondence between surfaces. It is general, encompassing a wide variety of existing techniques, and flexible, facilitating the synthesis of new correspondence algorithms. This paper presents a review of existing surface correspondence algorithms, and shows how they fit into the correspondence framework. It also shows how the framework can be used to analyse and compare existing algorithms and develop new algorithms using the framework's modular structure. Six algorithms, four existing and two new, are implemented using the framework. Each implemented algorithm is used to match a number of surface pairs. Results demonstrate that the correspondence framework implementations are faithful implementations of existing algorithms, and that powerful new surface correspondence algorithms can be created. (C) 2004 Elsevier Inc. All rights reserved.

A cognitive genetic algorithm for power distribution system planning

Power systems are large scale nonlinear systems with high complexity. Various optimization techniques and expert systems have been used in power system planning. However, there are always some factors that cannot be quantified, modeled, or even expressed by expert systems. Moreover, such planning problems are often large scale optimization problems. Although computational algorithms that are capable of handling large dimensional problems can be used, the computational costs are still very high. To solve these problems, in this paper, investigation is made to explore the efficiency and effectiveness of combining mathematic algorithms with human intelligence. It had been discovered that humans can join the decision making progresses by cognitive feedback. Based on cognitive feedback and genetic algorithm, a new algorithm called cognitive genetic algorithm is presented. This algorithm can clarify and extract human's cognition. As an important application of this cognitive genetic algorithm, a practical decision method for power distribution system planning is proposed. By using this decision method, the optimal results that satisfy human expertise can be obtained and the limitations of human experts can be minimized in the mean time.

The development of retinotectal maps: A review of models based on molecular gradients

Information about the world is often represented in the brain in the form of topographic maps. A paradigm example is the topographic representation of the visual world in the optic tectum/superior colliculus. This map initially forms during neural development using activity-independent molecular cues, most notably some type of chemospecific matching between molecular gradients in the retina and corresponding gradients in the tectum/superior colliculus. Exactly how this process might work has been studied both experimentally and theoretically for several decades. This review discusses the experimental data briefly, and then in more detail the theoretical models proposed. The principal conclusions are that (1) theoretical models have helped clarify several important ideas in the field, (2) earlier models were often more sophisticated than more recent models, and (3) substantial revisions to current modelling approaches are probably required to account for more than isolated subsets of the experimental data.