Mitra Basu

Complexity measures of supervised classification problems

We studied a number of measures that characterize the difficulty of a classification problem, focusing on the geometrical complexity of the class boundary. We compared a set of real-world problems to random labelings of points and found that real problems contain structures in this measurement space that are significantly different from the random sets. Distributions of problems in this space show that there exist at least two independent factors affecting a problems difficulty. We suggest using this space to describe a classifiers domain of competence. This can guide static and dynamic selection of classifiers for specific problems as well as subproblems formed by confinement, projection, and transformations of the feature vectors.

Gaussian-based edge-detection methods-a survey

The Gaussian filter has been used extensively in image processing and computer vision for many years. We discuss the various features of this operator that make it the filter of choice in the area of edge detection. Despite these desirable features of the Gaussian filter, edge detection algorithms which use it suffer from many problems. We review several linear and nonlinear Gaussian-based edge detection methods.

Data Complexity in Pattern Recognition

Theory and Methodology.- Measures of Geometrical Complexity in Classification Problems.- Object Representation, Sample Size, and Data Set Complexity.- Measures of Data and Classifier Complexity and the Training Sample Size.- Linear Separability in Descent Procedures for Linear Classifiers.- Data Complexity, Margin-Based Learning, and Poppers Philosophy of Inductive Learning.- Data Complexity and Evolutionary Learning.- Classifier Domains of Competence in Data Complexity Space.- Data Complexity Issues in Grammatical Inference.- Applications.- Simple Statistics for Complex Feature Spaces.- Polynomial Time Complexity Graph Distance Computation for Web Content Mining.- Data Complexity in Clustering Analysis of Gene Microarray Expression Profiles.- Complexity of Magnetic Resonance Spectrum Classification.- Data Complexity in Tropical Cyclone Positioning and Classification.- Human-Computer Interaction for Complex Pattern Recognition Problems.- Complex Image Recognition and Web Security.

Measures of Geometrical Complexity in Classification Problems

When popular classifiers fail to perform to perfect accuracy in a practical application, possible causes can be deficiencies in the algorithms, intrinsic difficulties in the data, and a mismatch between methods and problems. We propose to address this mystery by developing measures of geometrical and topological characteristics of point sets in high-dimensional spaces. Such measures provide a basis for analyzing classifier behavior beyond estimates of error rates. We discuss several measures useful for this characterization, and their utility in analyzing data sets with known or controlled complexity. Our observations confirm their effectiveness and suggest several future directions.

The learning behavior of single neuron classifiers on linearly separable or nonseparable input

Determining linear separability is an important way of understanding structures present in data. We explore the behavior of several classical descent procedures for determining linear separability and training linear classifiers in the presence of linearly nonseparable input. We compare the adaptive procedures to linear programming methods using many pairwise discrimination problems from a public database. We found that the adaptive procedures have serious implementation problems which make them less preferable than linear programming.

Gaussian derivative model for edge enhancement

Abstract In this paper we report the result of a set of computer experiments carried out to enhance edges in digital images. We use a special line-weight function, which is a combination of zero- and second-order Hermite functions. We are motivated by the physiological evidence reported in R. A. Young, Spatial Vision 2 (4), 273–293 (1987), that visual receptive fields in the primate eye are shaped like the sum of a Gaussian function and its Laplacian. This function can also be derived mathematically when the contrast sensitivity experiments in psychophysics are posed as an eigenvalue problem (A. L. Stewart and R. Pinkham, Biological Cybernetics , to appear). We introduce the concept of multi-scale analysis into the line weight function. We have attempted to understand the role played by the weight associated with each term of the proposed function. The experimental results with one- and two-dimensional data show that the proposed function has extremely good localization capability (i.e. the points marked by the operator is as close as possible to the center of the true edge).

Measuring the complexity of classification problems

We study a number of measures that characterize the difficulty of a classification problem. We compare a set of real world problems to random combinations of points in this measurement space and found that real problems contain structures that are significantly different from the random sets. Distribution of problems in this space reveals that there exist at least two independent factors affecting a problems difficulty, and that they have notable joint effects. We suggest using this space to describe a classifier domain of competence. This can guide static and dynamic selection of classifiers for specific problems as well as sub-problems formed by confinement, projections, and transformations of the feature vectors.

Application of neural network to gene expression data for cancer classification

The goal of the work is to explore the use of gene expression data in discriminating two types of very similar cancers-acute myeloid leukemia (AML) and acute lymphoblastic leukemia (ALL). Classification results are reported in Golub et al. (1999) using methods other than neural networks. Here, we explore the role of the feature vector in classification. Each feature vector consists of 6817 elements which are gene expression data for 6817 genes. We show in this preliminary experiment that learning using neural networks is possible when the input vector contains the correct number of gene expression data. This result is very promising because of the nature of the data (available in large amounts and more new information becomes available with better technology and better understanding of the problem). Thus, it is absolutely essential to employ an automated recognition system that has learning capability.

Gating improves neural network performance

Our first purpose is to study the performance of gating network functions in a committee machine setting. The problem of image deblurring is used to test the capability of such a system. Input clustering divides the task of deblurring into several subtasks. Each subtask is performed by a projection pursuit learning network (Basu and Su, 1999). We use a dynamic gating structure to combine outputs from various committee members. Our second purpose is to study the possibility of extending the role of the input signal beyond the decision making stage in the gating structure. Input data contain crucial structural information and characteristics of the data in a degraded form. The novel aspect of this work is the use of input signal with the output from the gating structure to produce the overall output. Resulting images show significant improvement over images that are produced from the output of the gating structure alone.

Image enhancement using a human visual system model

Abstract In this paper we report the result of a set of computer experiments carried out to enhance digital images. We use a special line weight function (LWF) which is a combination of zero- and second-order Hermite functions. We are motivated by the physiological evidence reported in R. A. Young, Spatial Vision 2(4), 273–293 (1987), that visual receptive fields are shaped like the sum of a Gaussian function and its Laplacian. This function can also be derived mathematically when the contrast sensitivity experiments in psychophysics are posed as an eigenvalue problem (A. L. Stewart and R. Pinkham, Biol. Cybernetics 64, 373–379 (1991). Analyses of the edge location error show that the proposed function has extremely good localization capability (i.e. the points marked by the operator is as close as possible to the center of the true edge). We also show that the LWF does not detect phantom edges which do not correspond to significant image intensity changes.