# Igor AizenbergManhattan College · Department of Computer Science

Igor Aizenberg

PhD

## About

133

Publications

20,226

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2,343

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Citations since 2017

Introduction

Igor Aizenberg currently works at the Department of Computer Science, Manhattan College as Professor and Department Chair. Igor does research in Complex-Valued Artificial Neural Networks and their applications. His current major project is 'Intelligent image filtering; Deep learning with MLMVN; Analysis of EEG using MLMVN'.

Additional affiliations

March 2006 - present

## Publications

Publications (133)

The main objective of this paper is to propose two innovative monitoring methods for electrical disturbances in low-voltage networks. The two approaches present a focus on the classification of voltage signals in the frequency domain using machine learning techniques. The first technique proposed here uses the Fourier transform (FT) of the voltage...

In this paper, a monitoring method for DC-DC converters in photovoltaic applications is presented. The primary goal is to prevent catastrophic failures by detecting malfunctioning conditions during the operation of the electrical system. The proposed prognostic procedure is based on machine learning techniques and focuses on the variations of passi...

In this paper, we present a new method designed to recognize single parametric faults in analog circuits. The technique follows a rigorous approach constituted by three sequential steps: calculating the testability and extracting the ambiguity groups of the circuit under test (CUT); localizing the failure and putting it in the correct fault class (...

A smart monitoring system capable of detecting and classifying the health conditions of MV (Medium Voltage) underground cables is presented in this work. Using the analysis technique proposed here, it is possible to prevent the occurrence of catastrophic failures in medium voltage underground lines, for which it is generally difficult to realize ma...

A procedure for the identification of lumped models of distributed parameter electromagnetic systems is presented in this paper. A Frequency Response Analysis (FRA) of the device to be modeled is performed, executing repeated measurements or intensive simulations. The method can be used to extract the values of the components. The fundamental brick...

In classical multiple-valued logic its values are encoded by integers. This complicates the use of multiple-valued logic as a basic model, which can be utilized in an artificial neuron, because the values of k-valued logic encoded by integers 0, 1, 2, ..., k are not normalized. To overcome this obstacle, it was suggested to encode the values of k-v...

Image filtering, regardless of whether it is denoising (low pass filtering) or edge detection (high pass filtering) can be considered as a machine learning problem. In fact, filtering is a process of approximation of a desirable result. A filter is considered good, if it approaches this ideal result better than other filters. But any machine learni...

In this paper, we consider a modified error-correction learning rule for the multilayer neural network with multivalued neurons (MLMVN). This modification is based on the soft margins technique, which leads to the minimization of the distance between a cluster center and the learning samples belonging to this cluster. MLMVN has a derivative-free le...

The fifteen papers in this special issue focus on complex and hyper-complex neural network applications. Complex-valued neural networks (CVNNs) exhibit very desirable characteristics in their learning, self-organizing, and processing dynamics, which makes them attractive for applications in various areas in science and technology. For example, they...

In this paper, we discuss the long-term time series forecasting using a Multilayer Neural Network with Multi-Valued Neurons (MLMVN). This is complex-valued neural network with a derivative-free backpropagation learning algorithm. We evaluate the proposed approach using a real-world data set describing the dynamic behavior of an oilfield asset locat...

In this paper, we consider a modified error-correction learning rule for the multilayer neural network with multi-valued neurons (MLMVN). MLMVN is a neural network with a standard feedforward organization, but based on the multi-valued neuron (MVN). MVN is a neuron with complex-valued weights and inputs/output, which are located on the unit circle....

In this paper, we observe some important aspects of Hebbian and error-correction learning rules for complex-valued neurons. These learning rules, which were previously considered for the multi-valued neuron (MVN) whose inputs and output are located on the unit circle, are generalized for a complex-valued neuron whose inputs and output are arbitrary...

In this paper, a modified learning algorithm for the multilayer neural network with the multi-valued neurons (MLMVN) is presented.
The MLMVN, which is a member of complex-valued neural networks family, has already demonstrated a number of important advantages
over other techniques. A modified learning algorithm for this network is based on the intr...

In this paper, we solve the impulse noise detection problem using an
intelligent approach. We use a multilayer neural network based on
multi-valued neurons (MLMVN) as an intelligent impulse noise detector.
MLMVN was already used for point spread function identification and
intelligent edge enhancement. So it is very attractive to apply it for
solvi...

In this paper, we consider the problem of blurred texture classification using a multilayer neural network based on multi-valued neurons (MLMVN). We use the frequency domain as a feature space. The low frequency part of the Fourier phase spectrum of a blurred image remains almost unaffected by blur. This means that phases corresponding to the lowes...

In this paper, we consider a problem of blurred image recognition using a multilayer neural network based on multi-valued neurons (MLMVN). Recognition of blurred images is a challenging problem because it is difficult or even impossible to find any relevant space of features for solving this problem in the spatial domain. The first crucial point of...

In this paper, we observe some important aspects of Hebbian and errorcorrection learning rules for the multi-valued neuron
with complex-valued weights. It is shown that Hebbian weights are the best starting weights for the errorcorrection learning.
Both learning rules are also generalized for a complex-valued neuron whose inputs and output are arbi...

In this paper, we observe a new approach to learn non-linearly separable problems using a single multi-valued neuron. It is
shown that a k-valued problem, which is non-linearly separable in the n-dimensional space can be projected into an m-valued (where m = kl) linearly separable problem in the same space. This projection can be utilized through a...

In this paper, we solve the edge enhancement problem using an intelligent approach. We use a multilayer neural network based on multi-valued neurons (MLMVN) as an intelligent edge enhancer. The problem of neural edge enhancement using a classical multilayer feedforward neural network (MLF) was already considered by some authors. Since MLMVN signifi...

Why We Need Complex-Valued Neural Networks?.- The Multi-Valued Neuron.- MVN Learning.- Multilayer Feedforward Neural Network based on Multi-Valued Neurons (MLMVN).- Multi-Valued Neuron with a Periodic Activation Function.- Applications of MVN and MLMVN.

In this Chapter, we consider all aspects of the MVN learning. We start in Section 3.1 from the specific theoretical aspects
of MVN learning and from the representation of the MVN learning algorithm. Then we describe the MVN learning rules. In Section
3.2, we consider the first learning rule, which is based on the adjustment of the weights depending...

In this Chapter, we will consider some applications of MVN and MLMVN. In Chapters 2-5 we have introduced MVN, we have deeply
considered all aspects of its learning, we have also introduced MLMVN and its derivative-free backpropagation learning algorithm;
finally we have introduced MVN-P, the multi-valued neuron with a periodic activation function a...

This chapter is introductory. A brief observation of neurons and neural networks is given in Section 1.1. We explain what
is a neuron, what is a neural network, what are linearly separable and non-linearly separable input/output mappings. How a
neuron learns is considered in Section 1.2, where Hebbian learning, the perceptron, and the error-correct...

In this chapter, we introduce the multi-valued neuron. First of all, in Section 2.1 we consider the essentials of the theory
of multiple-valued logic over the field of complex numbers. Then we define a threshold function of multiple-valued logic.
In Section 2.2, we define the discrete-valued multi-valued neuron whose input/output mapping is always...

In this Chapter, we consider one of the most interesting applications of MVN - its use as a basic neuron in a multilayer neural network based on multi-valued neurons (MLMVN). In Section 4.1, we consider basic ideas of the derivative-free backpropagation learning algorithm for MLMVN. In Section 4.2, we derive the error backpropagation rule for MLMVN...

In this paper, we consider a new periodic activation function for the multivalued neuron (MVN). The MVN is a neuron with complex-valued weights and inputs/output, which are located on the unit circle. Although the MVN outperforms many other neurons and MVN-based neural networks have shown their high potential, the MVN still has a limited capability...

In this paper, we further develop a complex-valued neuron paradigm. It is shown how a single multi-valued neuron with a periodic activation function may learn multiple-valued nonlinearly separable problems. One of the classical nonlinearly separable problems - mod k addition of n variables is considered in detail. It is shown that to be able to lea...

In this paper, we observe two artificial neurons with complex-valued weights. There are a multi-valued neuron and a universal
binary neuron. Both neurons have activation functions depending on the argument (phase) of the weighted sum. A multi-valued
neuron may learn multiple-valued threshold functions. A universal binary neuron may learn arbitrary...

In this paper, a theory of multiple-valued threshold functions over the field of complex numbers is further developed. k-valued threshold functions over the field of complex numbers can be learned using a single multi-valued neuron (MVN). We propose a new approach for the projection of a k-valued function, which is not a threshold one, to m-valued...

In this paper, a new activation function for the multi-valued neuron (MVN) is presented. The MVN is a neuron with complex-valued weights and inputs/output, which are located on the unit circle. Although the MVN has a greater functionality than a sigmoidal or radial basis function neurons, it has a limited capability of learning highly nonlinear fun...

This paper presents an efficient method of quasi-periodic noise detection and filtering. Taking into account that periodic noise leaves peaks in the amplitude spectrum, the proposed approach focuses on their detection and elimination. The detection is performed semi-automatically using a local median whereupon the localized peaks are eliminated by...

This paper focuses on neural networks with complex-valued (CV) neurons as well as on selected aspects of neural networks learning, pruning and rule extraction. CV neurons can be used as versatile substitutes in real-valued perceptron networks. Learning of CV layers is discussed in context of traditional multilayer feedforward architecture. Such lea...

Prediction methods that can be reduced to learning of partially defined multiple-valued functions have become very popular. In this paper, we consider a prediction problem related to DNA replication, which is essential for the reproduction of many viruses. Procedures to find replication origins are important for controlling such viruses. This paper...

A multilayer neural network based on multivalued neurons (MLMVN) is a neural network with a traditional feedforward architecture. At the same time, this network has a number of specific different features. Its backpropagation learning algorithm is derivative-free. The functionality of MLMVN is superior to that of the traditional feedforward neural...

A universal binary neuron (UBN) operates with complex-valued weights and a complex-valued activation function, which is the
function of the argument of the weighted sum. The activation function of the UBN separates a whole complex plane onto equal
sectors, where the activation function is equal to either 1 or −1 depending on the sector parity (even...

A universal binary neuron (UBN) operates with complex-valued weights and a complex-valued activation function, which is the function of the argument of the weighted sum. The activation function of the UBN separates a whole complex plane onto equal sectors, where the activation function is equal to either 1 or −1 depending on the sector parity (even...

A multilayer neural network based on multi-valued neurons (MLMVN) is a new powerful tool for solving classification, recognition and prediction problems. This network has a number of specific properties and advantages that follow from the nature of a multi-valued neuron (complex- valued weights and inputs/outputs lying on the unit circle). Its back...

The genetic code is the four-letter nucleic acid code, and it is translated into a 20-letter amino acid code from proteins (each of 20 amino acids is coded by the triplet of four nucleic acids). Thus, it is possible to consider the genetic code as a partially defined multiple-valued function of a 20-valued logic. It is shown in the paper that a mod...

A multilayer neural network based on multi-valued neurons is considered in the paper. A multi- valued neuron (MVN) is based on the principles of multiple-valued threshold logic over the field of the complex numbers. The most important properties of MVN are: the complex-valued weights, inputs and output coded by the kth roots of unity and the activa...

This paper discusses neural networks with complex-valued neurons with both discrete and continuous outputs. It reviews existing
methods of their applications in fully coupled associative memories. Such memories are able to process multiple gray levels
when applied for image de-noising. In addition, when complex-valued neurons are generalized to tak...

Received Abstract. It is shown in this paper that a model of multiple- valued logic over the field of complex numbers is the most appropriate for the representation of the genetic code as a multiple-valued function. The genetic code is considered as a partially defined multiple-valued function of three variables. The genetic code is the four-letter...

The idea of generalized Fresnel functions, which traces back to expressing a discrete transform as a linear convolution, is developed in this paper. The generalized discrete Fresnel functions and the generalized discrete Fresnel transforms for an arbitrary basis are considered. This problem is studied using a general algebraic approach to signal pr...

Futheron development of the Multi-Valued and Universal Binary Neurons conception with basic arithmetic over Complex Numbers Field is presented in this paper. Lot of attention is devoted to Universal Binary Neurons. New high-effective fast convergenced learning algorithm based on Error-correction rule is considered. It is shown that any non-threshol...

Classification of microarray gene expression data is a common problem in bioinformatics. Classification problems with more than two output classes require more attention than the normal binary classification. Here we apply a multilayer neural network based on multi-valued neurons (MLMVN) to the multiclass classification of microarray gene expressio...

A multilayer neural network based on multivalued neurons (MLMVN) is a neural network with a traditional feedforward architecture. At the same time this network has a number of specific properties and advantages. Its backpropagation learning algorithm does not require differentiability of the activation function. The functionality of MLMVN is higher...

A universal binary neuron (UBN) operates with the complex-valued weights and the complex-valued activation function, which is the function of the argument of the weighted sum. This makes possible the implementation of the nonlinearly separable (non-threshold) Boolean functions on the single neuron. Hence the functionality of the UBN is incompatibly...

A prior knowledge about the distorting operator and its parameters is of crucial importance in blurred image restoration. In this paper the continuous- valued multilayer neural network based on multi-valued neurons (MLMVN) is exploited for identification of a type of blur among six trained blurs and of its parameters. This network has a number of s...

A new impulsive noise detection technique is presented here. Preserving edges and details in the process of impulsive noise filtering is an important problem. To avoid image smoothing, only corrupted pixels must be filtered. In order to identify the corrupted pixels, a new impulse detector is proposed. This detector is based on a comparison of sign...

A feedforward neural network based on multi-valued neurons is considered in the paper. It is shown that using a traditional feedforward architecture and a high functionality multi-valued neuron, it is possible to obtain a new powerful neural network. Its learning does not require a derivative of the activation function and its functionality is high...

A new superresolution technique based on the iterative extrapolation of the image spectrum to the high frequency domain is proposed. It is shown that this algorithm gives a better result than commonly used interpolation and superresolution techniques, because it restores an image spectrum with higher precision. Moreover, if the result of any interp...

Impulsive noise filtering is an important problem of image processing. The problem of noise elimination is closely connected with the problem of maximal preservation of image edges. The requirement of maximal preservation of edges is especially important for images corrupted by impulsive noise with a low corruption rate. To avoid smoothing of the i...

As it is known, the impulsive noise appears on the image in the form of randomly distributed pixels of random brightness. Impulses themselves usually differ much from the surrounding pixels in brightness. The main topic of the paper is the introduction of the new impulse detection criteria, and their application to such filters as median, rank-orde...

The original solution of the blur and blur parameters identification problem is presented in this paper. A neural network
based on multi-valued neurons is used for the blur and blur parameters identification. It is shown that using simple single-layered
neural network it is possible to identify the type of the distorting operator. Four types of bl...

Multi-valued and universal binary neurons (MVN and UBN) are the neural processing elements with the complex-valued weights and high functionality. It is possible to implement an arbitrary mapping described by partially defined multiple-valued function on the single MVN. An arbitrary mapping described by partially defined or fully defined Boolean fu...

There are different techniques available for solving of the restoration problem including Fourier domain techniques, regularization methods, recursive and iterative filters to name a few. But without knowing at least approximate parameters of the blur, these methods often show poor results.. If incorrect blur model is chosen then the image will be...

As a rule, blur is a form of bandwidth reduction of an ideal image owing to the imperfect image formation process. It can be caused by relative motion between the camera and the original scene, or by an optical system that is out of focus. Today there are different techniques available for solving of the restoration problem including Fourier domain...

A new approach to impulsive noise filtering is considered in the paper. It is known that the median filter is a sliding window filter, with a window N X N. As it is known, the impulsive noise is a 'big' and unusual jump of brightness. So if the central pixel in the window is noisy, its value belongs to one of the ends of the variation representatio...

Removal of periodic and quasi-periodic patterns from photographs is an
important problem. There are a lot of sources of this periodic noise,
e.g. the resolution of the scanner used to scan the image affects the
high frequency noise pattern in the acquired image and can produce moire
patterns. It is also characteristic of gray scale images obtained...

In order to reconstruct the establishment of the body pattern over time in Drosophila embryos, we have developed automated methods for detecting the age of an embryo on the basis of knowledge about its gene expression patterns. In this paper we perform temporal classification of confocal images of expression patterns of genes controlling segmentati...

Multi-valued neurons (MVN) are the neural processing elements with complex-valued weights and high functionality. It is possible to implement an arbitrary mapping described by partial-defined multiple-valued function on the single MVN. The MVN-based neural networks are applied to temporal classification of images of gene expression patterns, obtain...

The principal constituents of computational intelligence are fuzzy logic, neural networks and evolutionary algorithms, with emphasis in their mutual enhancement. The present paper reviews some applications of these formalisms in the area of medical image processing, where advantage is taken from the ability of fuzzy logic to work with imprecise inf...

Multi-valued neurons (MVN) are the neural processing elements with complex-valued weights and high functionality. It is possible to implement an arbitrary mapping described by partial-defined multiple-valued function on the single MVN. The MVN-based neural networks are applied to temporal classification of images of gene expression patterns, obtain...

Multi-valued neurons (MVN) and universal binary neurons (UBN) are neural elements with complex-valued weights and high functionality.
It is possible to implement the arbitrary mapping described by partially defined multiple-valued function on the single MVN
and the arbitrary mapping described by Boolean function (which may not be threshold) on the...

Some important ideas of image recognition using neural network based on multi-valued neurons are being developed in this paper.
We are going to discuss the recognition of color images, distortion (blur) types, distortion parameters and recognition of
images with distorted training set.

A new approach to nonlinear filtering is considered in the paper. The key point of this approach is a combination of spatial and frequency domain filtering. The following filtering technique is proposed for noise reduction. On the first stage a noisy image has to be processed using some powerful nonlinear spatial-domain filter. Since the image will...

Some important ideas of image recognition using neural network based on multi-valued neurons are being developed in this paper. We are going to discuss the recognition of color images, which is reduced to recognition of gray-scale images. An approach, which has been developed, is illustrated by simulation results. Recognition of distortion (blur) t...

Multi-valued neurons (MVN) are the neural processing elements with complex-valued weights and high functionality. It is possible
to implement an arbitrary mapping described by partial-defined multiple-valued function on the single MVN. The MVN-based neural
networks are applied to temporal classification of images of gene expression patterns, obtain...