In recent years the Probabilistic Neural Network (PPN) has been used in a large number of applications due to its simplicity and efficiency. PNN assigns the test data to the class with maximum likelihood compared with other classes. Likelihood of the test data to each training data is computed in the pattern layer through a kernel density estimation using a simple Bayesian rule. The kernel is usually a standard probability distribution function such as a Gaussian function. A spread parameter is used as a global parameter which determines the width of the kernel. The Bayesian rule in the pattern layer estimates the conditional probability of each class given an input vector without considering any probable local densities or heterogeneity in the training data. In this paper, an enhanced and generalized PNN (EPNN) is presented using local decision circles (LDCs) to overcome the aforementioned shortcoming and improve its robustness to noise in the data. Local decision circles enable EPNN to incorporate local information and non-homogeneity existing in the training population. The circle has a radius which limits the contribution of the local decision. In the conventional PNN the spread parameter can be optimized for maximum classification accuracy. In the proposed EPNN two parameters, the spread parameter and the radius of local decision circles, are optimized to maximize the performance of the model. Accuracy and robustness of EPNN are compared with PNN using three different benchmark classification problems, iris data, diabetic data, and breast cancer data, and five different ratios of training data to testing data: 90:10, 80:20, 70:30, 60:40, and 50:50. EPNN provided the most accurate results consistently for all ratios. Robustness of PNN and EPNN is investigated using different values of signal to noise ratio (SNR). Accuracy of EPNN is consistently higher than accuracy of PNN at different levels of SNR and for all ratios of training data to testing data.

Enhanced probabilistic neural network with local decision circles: A robust classifier

What are quantum fluctuations

Digital Hardware Evolution.- An Online EHW Pattern Recognition System Applied to Sonar Spectrum Classification.- Design of Electronic Circuits Using a Divide-and-Conquer Approach.- Implementing Multi-VRC Cores to Evolve Combinational Logic Circuits in Parallel.- An Intrinsic Evolvable Hardware Based on Multiplexer Module Array.- Estimating Array Connectivity and Applying Multi-output Node Structure in Evolutionary Design of Digital Circuits.- Research on the Online Evaluation Approach for the Digital Evolvable Hardware.- Research on Multi-objective On-Line Evolution Technology of Digital Circuit Based on FPGA Model.- Evolutionary Design of Generic Combinational Multipliers Using Development.- Analog Hardware Evolution.- Automatic Synthesis of Practical Passive Filters Using Clonal Selection Principle-Based Gene Expression Programming.- Research on Fault-Tolerance of Analog Circuits Based on Evolvable Hardware.- Analog Circuit Evolution Based on FPTA-2.- Bio-inspired Systems.- Knowledge Network Management System with Medicine Self Repairing Strategy.- Design of a Cell in Embryonic Systems with Improved Efficiency and Fault-Tolerance.- Design on Operator-Based Reconfigurable Hardware Architecture and Cell Circuit.- Bio-inspired Systems with Self-developing Mechanisms.- Development of a Tiny Computer-Assisted Wireless EEG Biofeedback System.- Steps Forward to Evolve Bio-inspired Embryonic Cell-Based Electronic Systems.- Evolution of Polymorphic Self-checking Circuits.- Mechanical Hardware Evolution.- Sliding Algorithm for Reconfigurable Arrays of Processors.- System-Level Modeling and Multi-objective Evolutionary Design of Pipelined FFT Processors for Wireless OFDM Receivers.- Reducing the Area on a Chip Using a Bank of Evolved Filters.- Evolutionary Design.- Walsh Function Systems: The Bisectional Evolutional Generation Pattern.- Extrinsic Evolvable Hardware on the RISA Architecture.- Evolving and Analysing "Useful" Redundant Logic.- Adaptive Transmission Technique in Underwater Acoustic Wireless Communication.- Autonomous Robot Path Planning Based on Swarm Intelligence and Stream Functions.- Research on Adaptive System of the BTT-45 Air-to-Air Missile Based on Multilevel Hierarchical Intelligent Controller.- The Design of an Evolvable On-Board Computer.- Evolutionary Algorithms in Hardware Design.- Extending Artificial Development: Exploiting Environmental Information for the Achievement of Phenotypic Plasticity.- UDT-Based Multi-objective Evolutionary Design of Passive Power Filters of a Hybrid Power Filter System.- Designing Electronic Circuits by Means of Gene Expression Programming II.- Designing Polymorphic Circuits with Evolutionary Algorithm Based on Weighted Sum Method.- Robust and Efficient Multi-objective Automatic Adjustment for Optical Axes in Laser Systems Using Stochastic Binary Search Algorithm.- Minimization of the Redundant Sensor Nodes in Dense Wireless Sensor Networks.- Evolving in Extended Hamming Distance Space: Hierarchical Mutation Strategy and Local Learning Principle for EHW.- Hardware Implementation of Evolutionary Algorithms.- Adaptive and Evolvable Analog Electronics for Space Applications.- Improving Flexibility in On-Line Evolvable Systems by Reconfigurable Computing.- Evolutionary Design of Resilient Substitution Boxes: From Coding to Hardware Implementation.- A Sophisticated Architecture for Evolutionary Multiobjective Optimization Utilizing High Performance DSP.- FPGA-Based Genetic Algorithm Kernel Design.- Using Systolic Technique to Accelerate an EHW Engine for Lossless Image Compression.

Evolvable systems : from biology to hardware : 7th International Conference, ICES 2007, Wuhan, China, September 21-23, 2007 : proceedings

Complex-valued neural networks is a rapidly developing neural network framework that utilizes complex arithmetic, exhibiting specific characteristics in its learning, self-organizing, and processing dynamics. They are highly suitable for processing complex amplitude, composed of amplitude and phase, which is one of the core concepts in physical systems to deal with electromagnetic, light, sonic/ ultrasonic waves as well as quantum waves, namely, electron and superconducting waves. This fact is a critical advantage in practical applications in diverse fields of engineering, where signals are routinely analyzed and processed in time/space, frequency, and phase domains.

Complex-Valued Neural Networks: Advances and Applications

Global µ-stability criteria for quaternion-valued neural networks with unbounded time-varying delays

Quaternion neural networks are models in which computations of the neurons are based on quaternions, the four-dimensional equivalents of imaginary numbers. This paper shows by experiments that the quaternion-version of the Back Propagation (BP) algorithm achieves correct geometrical transformations in three-dimensional space, as well as in color space for an image compression problem, whereas real-valued BP algorithms fail. The quaternion neural network also performs superior in terms of convergence speed to a real-valued neural network with respect to the 3-bit parity check problem, as simulations show.

Quaternion neural network with geometrical operators

Quaternion neural networks are models of which computations in the neurons is based on quaternions, the four-dimensional equivalents of imaginary numbers. This paper shows by experiments that the quaternion-version of the Back Propagation (BP) algorithm achieves correct geometrical transformations in color space for an image compression problem, whereas real-valued BP algorithms fail.

Quaternion Neural Network and Its Application

Associative memory networks based on quaternionic Hopfield neural network are investigated in this paper. These networks are composed of quaternionic neurons, and input, output, threshold, and connection weights are represented in quaternions, which is a class of hypercomplex number systems. The energy function of the network and the Hebbian rule for embedding patterns are introduced. The stable states and their basins are explored for the networks with three neurons and four neurons. It is clarified that there exist at most 16 stable states, called multiplet components, as the degenerated stored patterns, and each of these states has its basin in the quaternionic networks.

Associative memory in quaternionic Hopfield neural network.

Asynchronous cellular arrays have gained attention as promising architectures for nanocomputers, because of their lack of a clock, which facilitates low power designs, and their regular structure, which potentially allows manufacturing techniques based on molecular self-organization. With the increase in integration density comes a decrease in the reliability of the components from which computers are built, and implementations based on cellular arrays are no exception to this. This paper advances asynchronous cellular arrays that are tolerant to transient errors in up to one third of the information stored by its cells. The cellular arrays require six rules to describe the interactions between the cells, implying less complexity of the cells as compared to a previously proposed (nonfault-tolerant) asynchronous cellular array that employs nine rules.

Fault-tolerance in nanocomputers: a cellular array approach

Complex numbers play an important role in practical applications and fundamental theorems in various fields of engineering such as electromagnetics, communication, control theory, and quantum mechanics. The application of complex numbers to neural networks has recently attracted attention because they tend to improve the learning ability and conform to the abovementioned applications (Hirose, 2003) (Rao, Nitta & Murthy, 2008). ABSTrACT

Teijiro Isokawa

Papers

Quaternion neural network with geometrical operators

Quaternion Neural Network and Its Application

Associative memory in quaternionic Hopfield neural network.

Fault-tolerance in nanocomputers: a cellular array approach

Quaternionic Neural Networks: Fundamental Properties and Applications