Data clustering amounts to a combinatorial optimization problem to reduce thecomplexity of a data representation and to increase its precision. Central and pairwise data clustering are studied in the maximum entropy framework.For central clustering we derive a set of reestimation equations and a minimization procedure which yields an optimal number ofclusters, their centers and their cluster probabilities. A meanfield approximation for pairwise clustering is used to estimate assignment probabilities. A se1fconsistent solution to multidimensional scaling and pairwise clustering is derived which yields an optimal embedding and clustering of data points in a d-dimensional Euclidian space. 1 Introduction A central problem in information processing is the reduction of the data complexity with minimal loss in precision to discard noise and to reveal basic structure of data sets. Data clustering addresses this tradeoff by optimizing a cost function which preserves the original data as complete as possible and which simultaneously favors prototypes with minimal complexity (Linde et aI., 1980; Gray, 1984; Chou et aI., 1989; Rose et ai., 1990). We discuss anobjective function for the joint optimization of distortion errors and the complexity of a reduced data representation.

In this work we apply a texture classification network to remote sensing image analysis. The goal is to extract the characteristics of the area depicted in the input image, thus achieving a segmented map of the region. We have recently proposed a combined neural network and rule-based framework for texture recognition. The framework uses unsupervised and supervised learning, and provides probability estimates for the output classes. We describe the texture classification network and extend it to demonstrate its application to the Landsat and Aerial image analysis domain. 1 INTRODUCTION In this work we apply a texture classification network to remote sensing image analysis. The goal is to segment the input image into homogeneous textured regions and identify each region as one of a prelearned library of textures, e.g.

In this work we apply a texture classification network to remote sensing image analysis. The goal is to extract the characteristics of the area depicted in the input image, thus achieving a segmented map of the region. We have recently proposed a combined neural network and rule-based framework for texture recognition. The framework uses unsupervised and supervised learning, and provides probability estimates for the output classes. We describe the texture classification network and extend it to demonstrate its application to the Landsat and Aerial image analysis domain. 1 INTRODUCTION In this work we apply a texture classification network to remote sensing image analysis. The goal is to segment the input image into homogeneous textured regions and identify each region as one of a prelearned library of textures, e.g.

In this work we apply a texture classification network to remote sensing image analysis.The goal is to extract the characteristics of the area depicted in the input image, thus achieving a segmented map of the region. We have recently proposed a combined neural network and rule-based framework for texture recognition. The framework uses unsupervised and supervised learning, and provides probability estimates for the output classes. We describe the texture classification network and extend it to demonstrate its application to the Landsat and Aerial image analysis domain. 1 INTRODUCTION In this work we apply a texture classification network to remote sensing image analysis. The goal is to segment the input image into homogeneous textured regions and identify each region as one of a prelearned library of textures, e.g.

"vector quantization", and "unsupervised learning" are all words which descn'be the same process: assigning a few exemplars to represent a large set of samples. Perfonning that process is the subject of a substantial body of literature. In this paper, we are concerned with the comparison of various clustering techniques to a particular, practical application: color clustering. The color clustering problem is as follows: an image is recorded in full color -- that is, three components, RED, GREEN, and BLUE, each of which has been measured to 8 bits of precision. Thus, each pixel is a 24 bit quantity. We must find a representation in which 2563 possible colors are represented by only 8 bits per pixel. That is, for a problem with 256000 variables (512 x 512) variables, assign each variable to one of only 256 classes. The color clustering problem is currently of major economic interest since millions of display systems are sold each year which can only store 8 bits per pixel, but on which users would like to be able to display "true" color (or at least as near true color as possible). In this study, we have approached the problem using the standard techniques from the literature (including k-means -- ISODATA clustering[1,3,61, LBG[4]), competitive learning (referred to as CL herein) [2], and Kohonen feature maps [5,7,9].

We present and compare learning rate schedules for stochastic gradient descent, a general algorithm which includes LMS, online backpropagation and k-means clustering as special cases. We introduce "search-thenconverge" type schedules which outperform the classical constant and "running average" (1ft) schedules both in speed of convergence and quality of solution.

"vector quantization", and "unsupervised learning" are all words which descn'be the same process: assigning a few exemplars to represent a large set of samples. Perfonning that process is the subject of a substantial body of literature. In this paper, we are concerned with the comparison of various clustering techniques to a particular, practical application: color clustering. The color clustering problem is as follows: an image is recorded in full color -- that is, three components, RED, GREEN, and BLUE, each of which has been measured to 8 bits of precision. Thus, each pixel is a 24 bit quantity. We must find a representation in which 2563 possible colors are represented by only 8 bits per pixel. That is, for a problem with 256000 variables (512 x 512) variables, assign each variable to one of only 256 classes. The color clustering problem is currently of major economic interest since millions of display systems are sold each year which can only store 8 bits per pixel, but on which users would like to be able to display "true" color (or at least as near true color as possible). In this study, we have approached the problem using the standard techniques from the literature (including k-means -- ISODATA clustering[1,3,61, LBG[4]), competitive learning (referred to as CL herein) [2], and Kohonen feature maps [5,7,9].

We present and compare learning rate schedules for stochastic gradient descent, a general algorithm which includes LMS, online backpropagation and k-means clustering as special cases. We introduce "search-thenconverge" type schedules which outperform the classical constant and "running average" (1ft) schedules both in speed of convergence and quality of solution.

Background The overall aim of our work is to develop fast and flexible systems for image recognition, usually for commercial inspection tasks. There is an urgent need for automatic learning systems in such applications, since at present most systems employ heuristic classification techniques. This approach requires an extensive development effort for each new application, which exaggerates implementation costs; and for many tasks, there are no clearly defined features which can be employed for classification. Enquiring of a human expert will often only produce "good" and "bad" examples of each class and not the underlying strategies which he may employ. Our approach is to model in a quite abstract way the perceptual networks found in the mammalian brain for vision. A back-propagation network could be employed to generalise about the input pattern space, and it would find some useful representations. However, there are many difficulties with this approach, since the network structure assumes nothing about the input space and it can be difficult to bound complicated feature clusters using hyperplanes. The mammalian brain is a layered structure, and so another model may be proposed which involves the application of many two-dimensional feature maps. Each map takes information from the output of the preceding one and performs some type of clustering analysis in order to reduce the dimensionality of the input information.

Background The overall aim of our work is to develop fast and flexible systems for image recognition, usually for commercial inspection tasks. There is an urgent need for automatic learning systems in such applications, since at present most systems employ heuristic classification techniques. This approach requires an extensive development effort for each new application, which exaggerates implementation costs; and for many tasks, there are no clearly defined features which can be employed for classification. Enquiring of a human expert will often only produce "good" and "bad" examples of each class and not the underlying strategies which he may employ. Our approach is to model in a quite abstract way the perceptual networks found in the mammalian brain for vision. A back-propagation network could be employed to generalise about the input pattern space, and it would find some useful representations. However, there are many difficulties with this approach, since the network structure assumes nothing about the input space and it can be difficult to bound complicated feature clusters using hyperplanes. The mammalian brain is a layered structure, and so another model may be proposed which involves the application of many two-dimensional feature maps. Each map takes information from the output of the preceding one and performs some type of clustering analysis in order to reduce the dimensionality of the input information.