Optimal design of an unsupervised adaptive classifier with unknown priors

An adaptive detection scheme for M hypotheses was analyzed. It was assumed that the probability density function under each hypothesis was known, and that the prior probabilities of the M hypotheses were unknown and sequentially estimated. Each observation vector was classified using the current estimate of the prior probabilities. Using a set of nonlinear transformations, and applying stochastic approximation theory, an optimally converging adaptive detection and estimation scheme was designed. The optimality of the scheme lies in the fact that convergence to the true prior probabilities is ensured, and that the asymptotic error variance is minimum, for the class of nonlinear transformations considered. An expression for the asymptotic mean square error variance of the scheme was also obtained

Recursive estimation of prior probabilities using the mixture approach

The problem of estimating the prior probabilities q sub k of a mixture of known density functions f sub k(X), based on a sequence of N statistically independent observations is considered. It is shown that for very mild restrictions on f sub k(X), the maximum likelihood estimate of Q is asymptotically efficient. A recursive algorithm for estimating Q is proposed, analyzed, and optimized. For the M = 2 case, it is possible for the recursive algorithm to achieve the same performance with the maximum likelihood one. For M 2, slightly inferior performance is the price for having a recursive algorithm. However, the loss is computable and tolerable

Evolutionary Granular Kernel Machines

Kernel machines such as Support Vector Machines (SVMs) have been widely used in various data mining applications with good generalization properties. Performance of SVMs for solving nonlinear problems is highly affected by kernel functions. The complexity of SVMs training is mainly related to the size of a training dataset. How to design a powerful kernel, how to speed up SVMs training and how to train SVMs with millions of examples are still challenging problems in the SVMs research. For these important problems, powerful and flexible kernel trees called Evolutionary Granular Kernel Trees (EGKTs) are designed to incorporate prior domain knowledge. Granular Kernel Tree Structure Evolving System (GKTSES) is developed to evolve the structures of Granular Kernel Trees (GKTs) without prior knowledge. A voting scheme is also proposed to reduce the prediction deviation of GKTSES. To speed up EGKTs optimization, a master-slave parallel model is implemented. To help SVMs challenge large-scale data mining, a Minimum Enclosing Ball (MEB) based data reduction method is presented, and a new MEB-SVM algorithm is designed. All these kernel methods are designed based on Granular Computing (GrC). In general, Evolutionary Granular Kernel Machines (EGKMs) are investigated to optimize kernels effectively, speed up training greatly and mine huge amounts of data efficiently

Modeling, Simulation, and Analysis of Optical Remote Sensing Systems

Remote Sensing of the Earth\u27s resources from space-based sensors has evolved in the past twenty years from a scientific experiment to a commonly used technological tool. The scientific applications and engineering aspects of remote sensing systems have been studied extensively. However, most of these studies have been aimed at understanding individual aspects of the remote sensing process while relatively few have studied their interrelations. A motivation for studying these interrelationships has arisen with the advent of highly sophisticated configurable sensors as part of the Earth Observing System (EOS) proposed by NASA for the 1990\u27s. These instruments represent a tremendous advance in sensor technology with data gathered In nearly 200 spectral bands, and with the ability for scientists to specify many observational parameters. It will be increasingly necessary for users of remote sensing systems to understand the tradeoffs and interrelationships of system parameters. In this report, two approaches to investigating remote sensing systems are developed. In one approach, detailed models of the scene, the sensor, and the processing aspects of the system are implemented In a discrete simulation, This approach is useful in creating simulated images with desired characteristics for use in sensor or processing algorithm development. A less complete, but computationally simpler method based on a parametric model of the system is also developed. In this analytical model the various informational classes are parameterized by their spectral mean vector and covariance matrix. These Class statistics are modified by models for the atmosphere, the sensor, and processing algorithms and an estimate made of the resulting classification accuracy among the informational classes. Application of these models is made to the study of the proposed High Resolution Imaging Spectrometer (HIRIS).; The interrelationships among observational conditions, sensor effects, and processing choices are investigated with several interesting results. Reduced classification accuracy in hazy atmospheres is seen to be due not only to sensor noise, but also to the increased path radiance scattered from the surface. The effect of the atmosphere is also seen in its relationship to view angle. In clear atmospheres, increasing the zenith view angle is seen to result in an increase in classification accuracy due to the reduced scene variation as the ground size of image pixels is increased. However, in hazy atmospheres the reduced transmittance and increased path radiance counter this effect and result in decreased accuracy with increasing view angle. The relationship between the Signal-to:Noise Ratio (SNR) and classification accuracy is seen to depend in a complex manner on spatial parameters and feature selection. Higher SNR values are seen to hot always result in higher accuracies, and even in cases of low SNR feature sets chosen appropriately can lead to high accuracies