The primary goal of pattern recognition is supervised or unsupervised classification. Among the various frameworks in which pattern recognition has been traditionally formulated, the statistical approach has been most intensively studied and used in practice. More recently, neural network techniques and methods imported from statistical learning theory have been receiving increasing attention. The design of a recognition system requires careful attention to the following issues: definition of pattern classes, sensing environment, pattern representation, feature extraction and selection, cluster analysis, classifier design and learning, selection of training and test samples, and performance evaluation. In spite of almost 50 years of research and development in this field, the general problem of recognizing complex patterns with arbitrary orientation, location, and scale remains unsolved. New and emerging applications, such as data mining, web searching, retrieval of multimedia data, face recognition, and cursive handwriting recognition, require robust and efficient pattern recognition techniques. The objective of this review paper is to summarize and compare some of the well-known methods used in various stages of a pattern recognition system and identify research topics and applications which are at the forefront of this exciting and challenging field.

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Statistical pattern recognition: a review

Planning algorithms are impacting technical disciplines and industries around the world, including robotics, computer-aided design, manufacturing, computer graphics, aerospace applications, drug design, and protein folding. This coherent and comprehensive book unifies material from several sources, including robotics, control theory, artificial intelligence, and algorithms. The treatment is centered on robot motion planning but integrates material on planning in discrete spaces. A major part of the book is devoted to planning under uncertainty, including decision theory, Markov decision processes, and information spaces, which are the “configuration spaces” of all sensor-based planning problems. The last part of the book delves into planning under differential constraints that arise when automating the motions of virtually any mechanical system. Developed from courses taught by the author, the book is intended for students, engineers, and researchers in robotics, artificial intelligence, and control theory as well as computer graphics, algorithms, and computational biology.

Planning Algorithms: Introductory Material

Gradient Boosting Decision Tree (GBDT) is a popular machine learning algorithm, and has quite a few effective implementations such as XGBoost and pGBRT. Although many engineering optimizations have been adopted in these implementations, the efficiency and scalability are still unsatisfactory when the feature dimension is high and data size is large. A major reason is that for each feature, they need to scan all the data instances to estimate the information gain of all possible split points, which is very time consuming. To tackle this problem, we propose two novel techniques: Gradient-based One-Side Sampling (GOSS) and Exclusive Feature Bundling (EFB). With GOSS, we exclude a significant proportion of data instances with small gradients, and only use the rest to estimate the information gain. We prove that, since the data instances with larger gradients play a more important role in the computation of information gain, GOSS can obtain quite accurate estimation of the information gain with a much smaller data size. With EFB, we bundle mutually exclusive features (i.e., they rarely take nonzero values simultaneously), to reduce the number of features. We prove that finding the optimal bundling of exclusive features is NP-hard, but a greedy algorithm can achieve quite good approximation ratio (and thus can effectively reduce the number of features without hurting the accuracy of split point determination by much). We call our new GBDT implementation with GOSS and EFB LightGBM. Our experiments on multiple public datasets show that, LightGBM speeds up the training process of conventional GBDT by up to over 20 times while achieving almost the same accuracy.

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LightGBM: a highly efficient gradient boosting decision tree

may 7th, 1986, Professor A. F. M. Smith in the Chair] SUMMARY A continuous two-dimensional region is partitioned into a fine rectangular array of sites or "pixels", each pixel having a particular "colour" belonging to a prescribed finite set. The true colouring of the region is unknown but, associated with each pixel, there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model. The aim is to reconstruct the true scene, with the additional knowledge that pixels close together tend to have the same or similar colours. In this paper, it is assumed that the local characteristics of the true scene can be represented by a nondegenerate Markov random field. Such information can be combined with the records by Bayes' theorem and the true scene can be estimated according to standard criteria. However, the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field. Thus, a simple, iterative method of reconstruction is proposed, which does not depend on these large-scale characteristics. The method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field. Some complications, including parameter estimation, are discussed. Potential applications are mentioned briefly.

https://stat.duke.edu/~scs/Courses/Stat376/Papers/GibbsFieldEst/BesagDirtyPicsJRSSB1986.pdf

On the statistical analysis of dirty pictures

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Semi-Supervised Learning Literature Survey

A new covariance matrix estimator useful for designing classifiers with limited training data is developed. In experiments, this estimator achieved higher classification accuracy than the sample covariance matrix and common covariance matrix estimates. In about half of the experiments, it achieved higher accuracy than regularized discriminant analysis, but required much less computation.

Covariance matrix estimation and classification with limited training data

As the number of spectral bands of high-spectral resolution data increases, the ability to detect more detailed classes should also increase, and the classification accuracy should increase as well. Often the number of labelled samples used for supervised classification techniques is limited, thus limiting the precision with which class characteristics can be estimated. As the number of spectral bands becomes large, the limitation on performance imposed by the limited number of training samples can become severe. A number of techniques for case-specific feature extraction have been developed to reduce dimensionality without loss of class separability. Most of these techniques require the estimation of statistics at full dimensionality in order to extract relevant features for classification. If the number of training samples is not adequately large, the estimation of parameters in high-dimensional data will not be accurate enough. As a result, the estimated features may not be as effective as they could be. This suggests the need for reducing the dimensionality via a preprocessing method that takes into consideration high-dimensional feature-space properties. Such reduction should enable the estimation of feature-extraction parameters to be more accurate. Using a technique referred to as projection pursuit (PP), such an algorithm has been developed. This technique is able to bypass many of the problems of the limitation of small numbers of training samples by making the computations in a lower-dimensional space, and optimizing a function called the projection index. A current limitation of this method is that, as the number of dimensions increases, it is likely that a local maximum of the projection index will be found that does not enable one to fully exploit hyperspectral-data capabilities.

Hyperspectral data analysis and supervised feature reduction via projection pursuit

220 Band AVIRIS Hyperspectral Image Data Set: June 12, 1992 Indian Pine Test Site 3

Through a series of specific examples, some characteristics encountered in analyzing high-dimensional multispectral data are illustrated. The increased importance of the second-order statistics in analyzing high-dimensional data is shown, as is the shortcoming of classifiers such as the minimum distance classifier, which rely on first-order variations alone. It is also shown how inaccurate estimation of first- and second-order statistics, e.g., from use of training sets which are too small, affects the performance of a classifier. Recognizing the importance of second-order statistics on the one hand, but the increased difficulty in perceiving and comprehending information present in statistics derived from high-dimensional data on the other, the authors propose a method to aid visualization of high-dimensional statistics using a color coding scheme. >

Analyzing high-dimensional multispectral data

An adaptive Bayesian contextual classification procedure that utilizes both spectral and spatial interpixel dependency contexts in estimation of statistics and classification is proposed. Essentially, this classifier is the constructive coupling of an adaptive classification procedure and a Bayesian contextual classification procedure. In this classifier, the joint prior probabilities of the classes of each pixel and its spatial neighbors are modeled by the Markov random field. The estimation of statistics and classification are performed in a recursive manner to allow the establishment of the positive-feedback process in a computationally efficient manner. Experiments with real hyperspectral data show that, starting with a small training sample set, this classifier can reach classification accuracies similar to that obtained by a pixelwise maximum likelihood pixel classifier with a very large training sample set. Additionally, classification maps are produced that have significantly less speckle error.

David A. Landgrebe

Papers

Covariance matrix estimation and classification with limited training data

Hyperspectral data analysis and supervised feature reduction via projection pursuit

220 Band AVIRIS Hyperspectral Image Data Set: June 12, 1992 Indian Pine Test Site 3

Analyzing high-dimensional multispectral data

Adaptive Bayesian contextual classification based on Markov random fields