模式分类：机器学习与特征提取的关键问题

数据挖掘

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"模式分类是数据挖掘领域的一个关键主题，涉及机器学习、感知与认知等多个方面的理论和技术。本文档提供了一个全面的概述，包括模式分类的各个子问题、学习与适应的不同类型，以及相关的挑战和考量因素。" 正文: 模式分类是机器学习中的核心任务，它涉及到将输入数据分配到预定义的类别中。这个过程在很多实际应用中至关重要，如图像识别、语音识别、文本分类等。"Introduction"章节中，作者首先引出模式识别的概念，指出其在日常生活中的普遍性，如识别人脸、理解语言、辨别物体等。 "Machine Perception"部分讨论了机器如何模拟人类的感知能力来理解和解析环境中的模式。这通常需要通过传感器和数据处理技术来实现。 "An Example"章节可能详细介绍了某个具体的模式分类问题，比如图像分类，并可能探讨了与之相关的其他领域，如计算机视觉和自然语言处理。接着，"The Sub-problems of Pattern Classiﬁcation"部分列出了模式分类面临的挑战。其中，"Feature Extraction"是指从原始数据中提取有用的特征，这是分类器性能的关键；"Noise"则指数据中的不确定性或错误，需要有噪声处理策略；"Overfitting"是模型训练中的常见问题，可能导致模型在新数据上的表现不佳；"Model Selection"涉及选择最佳的模型结构和参数；"Prior Knowledge"强调利用先验知识可以提高分类效果；"Missing Features"处理的是数据缺失问题；"Mereology"可能涉及到对象的部分与整体关系；"Segmentation"通常用于图像分析，将图像分割成有意义的部分；"Context"考虑了上下文信息对分类的影响；"Invariances"是指模型应具备对特定变换不变的能力，如旋转、缩放不变性；"Evidence Pooling"涉及如何整合不同来源的证据；"Costs and Risks"提醒我们在分类决策时要考虑代价和风险；而"Computational Complexity"讨论了算法的计算复杂度和效率。 "Learning and Adaptation"章节涵盖了三种主要的学习方式："Supervised Learning"依赖于带标签的数据来训练模型；"Unsupervised Learning"则在无标签数据上进行，目标是发现数据的内在结构；"Reinforcement Learning"通过与环境的交互，让模型学习最优策略。 "Conclusion"章节总结了前文内容，并为后续章节提供了概述。"Summary by Chapters"可能给出了各章节要点的精炼概括，而"Bibliographical and Historical Remarks"提供了相关领域的文献和历史背景。最后，"Bibliography"和"Index"分别提供了参考文献列表和词汇索引，方便读者深入研究。这篇文档深入探讨了模式分类的各个方面，不仅关注技术细节，也强调了实践中可能遇到的问题和解决策略，对于理解和应用数据挖掘中的模式分类具有重要的指导价值。

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4 CHAPTER 1. INTRODUCTION

images — variations in lighting, position of the ﬁsh on the conveyor, even “static”

due to the electronics of the camera itself.

Given that there truly are diﬀerences between the population of sea bass and that

of salmon, we view them as having diﬀerent models — diﬀerent descriptions, whichmodel

are typically mathematical in form. The overarching goal and approach in pattern

classiﬁcation is to hypothesize the class of these models, process the sensed data

to eliminate noise (not due to the models), and for any sensed pattern choose the

model that corresponds best. Any techniques that further this aim should be in the

conceptual toolbox of the designer of pattern recognition systems.

Our prototype system to perform this very speciﬁc task might well have the form

shown in Fig. 1.1. First the camera captures an image of the ﬁsh. Next, the camera’s

signals are preprocessed to simplify subsequent operations without loosing relevantpre-

processing information. In particular, we might use a segmentation operation in which the images

segmentation

of diﬀerent ﬁsh are somehow isolated from one another and from the background. The

information from a single ﬁsh is then sent to a feature extractor, whose purpose is to

feature

extraction

reduce the data by measuring certain “features” or “properties.” These features

(or, more precisely, the values of these features) are then passed to a classiﬁer that

evaluates the evidence presented and makes a ﬁnal decision as to the species.

The preprocessor might automatically adjust for average light level, or threshold

the image to remove the background of the conveyor belt, and so forth. For the

moment let us pass over how the images of the ﬁsh might be segmented and consider

how the feature extractor and classiﬁer might be designed. Suppose somebody at the

ﬁsh plant tells us that a sea bass is generally longer than a salmon. These, then,

give us our tentative models for the ﬁsh: sea bass have some typical length, and this

is greater than that for salmon. Then length becomes an obvious feature, and we

might attempt to classify the ﬁsh merely by seeing whether or not the length l of

a ﬁsh exceeds some critical value l

∗

. To choose l

∗

we could obtain some design or

training samples of the diﬀerent types of ﬁsh, (somehow) make length measurements,training

samples and inspect the results.

Suppose that we do this, and obtain the histograms shown in Fig. 1.2. These

disappointing histograms bear out the statement that sea bass are somewhat longer

than salmon, on average, but it is clear that this single criterion is quite poor; no

matter how we choose l

∗

, we cannot reliably separate sea bass from salmon by length

alone.

Discouraged, but undeterred by these unpromising results, we try another feature

— the average lightness of the ﬁsh scales. Now we are very careful to eliminate

variations in illumination, since they can only obscure the models and corrupt our

new classiﬁer. The resulting histograms, shown in Fig. 1.3, are much more satisfactory

— the classes are much better separated.

So far we have tacitly assumed that the consequences of our actions are equally

costly: deciding the ﬁsh was a sea bass when in fact it was a salmon was just as

undesirable as the converse. Such a symmetry in the cost is often, but not invariablycost

the case. For instance, as a ﬁsh packing company we may know that our customers

easily accept occasional pieces of tasty salmon in their cans labeled “sea bass,” but

they object vigorously if a piece of sea bass appears in their cans labeled “salmon.”

If we want to stay in business, we should adjust our decision boundary to avoid

antagonizing our customers, even if it means that more salmon makes its way into

the cans of sea bass. In this case, then, we should move our decision boundary x

∗

smaller values of lightness, thereby reducing the number of sea bass that are classiﬁed

as salmon (Fig. 1.3). The more our customers object to getting sea bass with their

1.2. AN EXAMPLE 7

2 4 6 8 10

Width

Lightness

salmon sea bass

Figure 1.4: The two features of lightness and width for sea bass and salmon. The

dark line might serve as a decision boundary of our classiﬁer. Overall classiﬁcation

error on the data shown is lower than if we use only one feature as in Fig. 1.3, but

there will still be some errors.

of more than one feature at a time.

In our search for other features, we might try to capitalize on the observation that

sea bass are typically wider than salmon. Now we have two features for classifying

ﬁsh — the lightness x

and the width x

. If we ignore how these features might be

measured in practice, we realize that the feature extractor has thus reduced the image

of each ﬁsh to a point or feature vector x in a two-dimensional feature space, where

x =





Our problem now is to partition the feature space into two regions, where for all

patterns in one region we will call the ﬁsh a sea bass, and all points in the other we

call it a salmon. Suppose that we measure the feature vectors for our samples and

obtain the scattering of points shown in Fig. 1.4. This plot suggests the following rule

for separating the ﬁsh: Classify the ﬁsh as sea bass if its feature vector falls above the

decision boundary shown, and as salmon otherwise. decision

boundary

This rule appears to do a good job of separating our samples and suggests that

perhaps incorporating yet more features would be desirable. Besides the lightness

and width of the ﬁsh, we might include some shape parameter, such as the vertex

angle of the dorsal ﬁn, or the placement of the eyes (as expressed as a proportion of

the mouth-to-tail distance), and so on. How do we know beforehand which of these

features will work best? Some features might be redundant: for instance if the eye

color of all ﬁsh correlated perfectly with width, then classiﬁcation performance need

not be improved if we also include eye color as a feature. Even if the diﬃculty or

computational cost in attaining more features is of no concern, might we ever have

too many features?

Suppose that other features are too expensive or expensive to measure, or provide

little improvement (or possibly even degrade the performance) in the approach de-

scribed above, and that we are forced to make our decision based on the two features

in Fig. 1.4. If our models were extremely complicated, our classiﬁer would have a

decision boundary more complex than the simple straight line. In that case all the

8 CHAPTER 1. INTRODUCTION

2 4 6 8 10

Width

Lightness

salmon sea bass

Figure 1.5: Overly complex models for the ﬁsh will lead to decision boundaries that are

complicated. While such a decision may lead to perfect classiﬁcation of our training

samples, it would lead to poor performance on future patterns. The novel test point

marked ? is evidently most likely a salmon, whereas the complex decision boundary

shown leads it to be misclassiﬁed as a sea bass.

training patterns would be separated perfectly, as shown in Fig. 1.5. With such a

“solution,” though, our satisfaction would be premature because the central aim of

designing a classiﬁer is to suggest actions when presented with novel patterns, i.e.,

ﬁsh not yet seen. This is the issue of generalization. It is unlikely that the complexgeneral-

ization decision boundary in Fig. 1.5 would provide good generalization, since it seems to be

“tuned” to the particular training samples, rather than some underlying characteris-

tics or true model of all the sea bass and salmon that will have to be separated.

Naturally, one approach would be to get more training samples for obtaining a

better estimate of the true underlying characteristics, for instance the probability

distributions of the categories. In most pattern recognition problems, however, the

amount of such data we can obtain easily is often quite limited. Even with a vast

amount of training data in a continuous feature space though, if we followed the

approach in Fig. 1.5 our classiﬁer would give a horrendously complicated decision

boundary — one that would be unlikely to do well on novel patterns.

Rather, then, we might seek to “simplify” the recognizer, motivated by a belief

that the underlying models will not require a decision boundary that is as complex as

that in Fig. 1.5. Indeed, we might be satisﬁed with the slightly poorer performance

on the training samples if it means that our classiﬁer will have better performance

on novel patterns.

∗

But if designing a very complex recognizer is unlikely to give

good generalization, precisely how should we quantify and favor simpler classiﬁers?

How would our system automatically determine that the simple curve in Fig. 1.6

is preferable to the manifestly simpler straight line in Fig. 1.4 or the complicated

boundary in Fig. 1.5? Assuming that we somehow manage to optimize this tradeoﬀ,

can we then predict how well our system will generalize to new patterns? These are

some of the central problems in statistical pattern recognition.

For the same incoming patterns, we might need to use a drastically diﬀerent cost

∗

The philosophical underpinnings of this approach derive from William of Occam (1284-1347?), who

advocated favoring simpler explanations over those that are needlessly complicated — Entia non

sunt multiplicanda praeter necessitatem (“Entities are not to be multiplied without necessity”).

Decisions based on overly complex models often lead to lower accuracy of the classiﬁer.

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