Koel Das

An efficient discriminant-based solution for small sample size problem

Classification of high-dimensional statistical data is usually not amenable to standard pattern recognition techniques because of an underlying small sample size problem. To address the problem of high-dimensional data classification in the face of a limited number of samples, a novel principal component analysis (PCA) based feature extraction/classification scheme is proposed. The proposed method yields a piecewise linear feature subspace and is particularly well-suited to difficult recognition problems where achievable classification rates are intrinsically low. Such problems are often encountered in cases where classes are highly overlapped, or in cases where a prominent curvature in data renders a projection onto a single linear subspace inadequate. The proposed feature extraction/classification method uses class-dependent PCA in conjunction with linear discriminant feature extraction and performs well on a variety of real-world datasets, ranging from digit recognition to classification of high-dimensional bioinformatics and brain imaging data.

Approximate information discriminant analysis: A computationally simple heteroscedastic feature extraction technique

In this article we develop a novel linear dimensionality reduction technique for classification. The technique utilizes the first two statistical moments of data and retains the computational simplicity, characteristic of second-order techniques, such as linear discriminant analysis. Formally, the technique maximizes a criterion that belongs to the class of probability dependence measures, and is naturally defined for multiple classes. The criterion is based on an approximation of an information-theoretic measure and is capable of handling heteroscedastic data. The performance of our method, along with similar feature extraction approaches, is demonstrated based on experimental results with real-world datasets. Our method compares favorably to similar second-order linear dimensionality techniques.

A Classwise PCA-based Recognition of Neural Data for Brain-Computer Interfaces

We present a simple, computationally efficient recognition algorithm that can systematically extract useful information from any large-dimensional neural datasets. The technique is based on classwise Principal Component Analysis, which employs the distribution characteristics of each class to discard non-informative subspace. We propose a two-step procedure, comprising of removal of sparse non-informative subspace of the large-dimensional data, followed by a linear combination of the data in the remaining subspace to extract meaningful features for efficient classification. Our method produces significant improvement over the standard discriminant analysis based methods. The classification results are given for iEEG and EEG signals recorded from the human brain.

Sketching Free-form Surfaces Using Network of Curves

This work addresses the issue of generating free-form surfaces using a 2D sketch interface. As the first step in this process, we develop a methodology to sketch 3D space curves from 2D sketches. Since the inverse projection from 2D sketches to 3D curve or surface is a one to many function, there is no unique solution. Hence we propose to interpret the given 2D curve to be the projection of the 3D curve that has minimum curvature among all the candidates in 3D. We present an algorithm to efficiently find a close approximation of this minimum curvature 3D space curve. In the second step, this network of curves along with the boundary information are given to the surface fitting method to generate free-form surfaces.

Mental State Estimation for Brain--Computer Interfaces

Mental state estimation is potentially useful for the development of asynchronous brain-computer interfaces. In this study, four mental states have been identified and decoded from the electrocorticograms (ECoGs) of six epileptic patients, engaged in a memory reach task. A novel signal analysis technique has been applied to high-dimensional, statistically sparse ECoGs recorded by a large number of electrodes. The strength of the proposed technique lies in its ability to jointly extract spatial and temporal patterns, responsible for encoding mental state differences. As such, the technique offers a systematic way of analyzing the spatiotemporal aspects of brain information processing and may be applicable to a wide range of spatiotemporal neurophysiological signals.

Analysis of large-scale brain data for brain-computer interfaces.

We present a systematic technique for extraction of useful information from large-scale neural data in the context of brain-computer interfaces. The technique is based on a direct linear discriminant analysis, recently developed for face recognition problems. We show that this technique is capable of extracting useful information from brain data in a systematic fashion and can serve as a general analytical tool for other types of biomedical data, such as images and collections of images (movies). The performance of the method is tested on intracranial electroencephalographic data recorded from the human brain

Automated cell classification and visualization for analyzing remyelination therapy

Remyelination therapy is a state-of-the-art technique for treating spinal cord injury (SCI). Demyelination—the loss of myelin sheath that insulates axons, is a prominent feature in many neurological disorders resulting in SCI. This lost myelin sheath can be replaced by remyelination. In this paper, we propose an algorithm for efficient automated cell classification and visualization to analyze the progress of remyelination therapy in SCI. Our method takes as input the images of the cells and outputs a density map of the therapeutically important oligodendrocyte-remyelinated axons (OR-axons) which is used for efficacy analysis of the therapy. Our method starts with detecting cell boundaries using a robust, shape-independent algorithm based on iso-contour analysis of the image at progressively increasing intensity levels. The detected boundaries of spatially clustered cells are then separated using the Delaunay triangulation based contour separation method. Finally, the OR-axons are identified and a density map is generated for efficacy analysis of the therapy. Our efficient automated cell classification and visualization of remyelination analysis significantly reduces error due to human subjectivity. We validate the accuracy of our results by extensive cross-verification by the domain experts.

Automated analysis of remyelination therapy for spinal cord injury

Demyelination- the loss of myelin sheath that insulates axons, is a prominent feature in many neurological disorders resulting in spinal cord injury (SCI). The lost myelin sheath can be replaced by remyelination, used in SCI treatment. In this paper, we propose an algorithm for efficient automated analysis of remyelination therapy. We use a robust, shape-independent algorithm based on iso-contour analysis of the image at progressively increasing intensity levels for detecting cell boundaries. The detected boundaries of spatially clustered cells are then separated using Delaunay triangulation based contour separation method. The therapeutically important oligodendrocyte-remyelinated axons (OR-axons) are identified and a density map is generated for efficacy analysis of the therapy. Our efficient automated remyelination analysis significantly reduces error due to human subjectivity. We corroborate the accuracy of our results by extensive cross-verification by the domain experts.

A Nonlinear Technique for Analysis of Big Data in Neuroscience

Recent technological advances have paved the way for big data analysis in the field of neuroscience. Machine learning techniques can be used effectively to explore the relationship between large-scale neural and behavorial data. In this chapter, we present a computationally efficient nonlinear technique which can be used for big data analysis. We demonstrate the efficacy of our method in the context of brain computer interface. Our technique is piecewise linear and computationally inexpensive and can be used as an analysis tool to explore any generic big data.

A computationally efficient order statistics based outlier detection technique for EEG signals.

Detecting artifacts in EEG data produced by muscle activity, eye blinks and electrical noise is a common and important problem in EEG applications. We present a novel outlier detection method based on order statistics. We propose a 2 step procedure comprising of detecting noisy EEG channels followed by detection of noisy epochs in the outlier channels. The performance of our method is tested systematically using simulated and real EEG data. Our technique produces significant improvement in detecting EEG artifacts over state-of-the-art outlier detection technique used in EEG applications. The proposed method can serve as a general outlier detection tool for different types of noisy signals.