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pattern recognition and machine learning PDF 下载
 失效链接处理 pattern recognition and machine learning PDF 下载 本站整理下载：   相关截图： 主要内容： The problem of searching for patterns in data is a fundamental one and has a long and successful history. For instance, the extensive astronomical observations of Tycho Brahe in the 16th century allowed Johannes Kepler to discover the empirical laws of planetary motion, which in turn provided a springboard for the development of clas￾sical mechanics. Similarly, the discovery of regularities in atomic spectra played a key role in the development and verification of quantum physics in the early twenti￾eth century. The field of pattern recognition is concerned with the automatic discov￾ery of regularities in data through the use of computer algorithms and with the use of these regularities to take actions such as classifying the data into different categories. Consider the example of recognizing handwritten digits, illustrated in Figure 1.1. Each digit corresponds to a 28×28 pixel image and so can be represented by a vector x comprising 784 real numbers. The goal is to build a machine that will take such a vector x as input and that will produce the identity of the digit 0,..., 9 as the output. This is a nontrivial problem due to the wide variability of handwriting. It could be 1 2 1. INTRODUCTION Figure 1.1 Examples of hand-written dig￾its taken from US zip codes. tackled using handcrafted rules or heuristics for distinguishing the digits based on the shapes of the strokes, but in practice such an approach leads to a proliferation of rules and of exceptions to the rules and so on, and invariably gives poor results. Far better results can be obtained by adopting a machine learning approach in which a large set of N digits {x1,..., xN } called a training set is used to tune the parameters of an adaptive model. The categories of the digits in the training set are known in advance, typically by inspecting them individually and hand-labelling them. We can express the category of a digit using target vector t, which represents the identity of the corresponding digit. Suitable techniques for representing cate￾gories in terms of vectors will be discussed later. Note that there is one such target vector t for each digit image x. The result of running the machine learning algorithm can be expressed as a function y(x) which takes a new digit image x as input and that generates an output vector y, encoded in the same way as the target vectors. The precise form of the function y(x) is determined during the training phase, also known as the learning phase, on the basis of the training data. Once the model is trained it can then de￾termine the identity of new digit images, which are said to comprise a test set. The ability to categorize correctly new examples that differ from those used for train￾ing is known as generalization. In practical applications, the variability of the input vectors will be such that the training data can comprise only a tiny fraction of all possible input vectors, and so generalization is a central goal in pattern recognition. For most practical applications, the original input variables are typically prepro￾cessed to transform them into some new space of variables where, it is hoped, the pattern recognition problem will be easier to solve. For instance, in the digit recogni￾tion problem, the images of the digits are typically translated and scaled so that each digit is contained within a box of a fixed size. This greatly reduces the variability within each digit class, because the location and scale of all the digits are now the same, which makes it much easier for a subsequent pattern recognition algorithm to distinguish between the different classes. This pre-processing stage is sometimes also called feature extraction. Note that new test data must be pre-processed using the same steps as the training data. Pre-processing might also be performed in order to speed up computation. For example, if the goal is real-time face detection in a high-resolution video stream, the computer must handle huge numbers of pixels per second, and presenting these directly to a complex pattern recognition algorithm may be computationally infeasi￾ble. Instead, the aim is to find useful features that are fast to compute, and yet that 1. INTRODUCTION 3 also preserve useful discriminatory information enabling faces to be distinguished from non-faces. These features are then used as the inputs to the pattern recognition algorithm. For instance, the average value of the image intensity over a rectangular subregion can be evaluated extremely efficiently (Viola and Jones, 2004), and a set of such features can prove very effective in fast face detection. Because the number of such features is smaller than the number of pixels, this kind of pre-processing represents a form of dimensionality reduction. Care must be taken during pre-processing because often information is discarded, and if this information is important to the solution of the problem then the overall accuracy of the system can suffer. Applications in which the training data comprises examples of the input vectors along with their corresponding target vectors are known as supervised learning problems. Cases such as the digit recognition example, in which the aim is to assign each input vector to one of a finite number of discrete categories, are called classification problems. If the desired output consists of one or more continuous variables, then the task is called regression. An example of a regression problem would be the prediction of the yield in a chemical manufacturing process in which the inputs consist of the concentrations of reactants, the temperature, and the pressure. In other pattern recognition problems, the training data consists of a set of input vectors x without any corresponding target values. The goal in such unsupervised learning problems may be to discover groups of similar examples within the data, where it is called clustering, or to determine the distribution of data within the input space, known as density estimation, or to project the data from a high-dimensional space down to two or three dimensions for the purpose of visualization.
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