Matlab手册：模式识别与聚类、特征选择方法

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《模式识别MATLAB手册》(Pattern Recognition Matlab Manual)由Aggelos Pikrakis、Sergios Theodoridis、Kostantinos Koutroumbas和Dionisis Cavouras合作编写，于2009年二月出版。该书是Theodoridis的经典著作《模式识别》(Pattern Recognition)的第四版，由Elsevier Inc.版权所有。本书详细介绍了在计算机视觉和机器学习领域中，模式识别方法和算法如何在MATLAB环境中实现。第1章为引言，涵盖基础知识和背景，解释了模式识别的重要性，以及MATLAB作为工具在该领域的应用价值。它可能包括了对MATLAB环境的优势、编程技巧以及如何利用其强大的数学和图形处理能力来处理模式识别任务。第二部分着重于聚类分析，共包含多个实用函数： - BSAS.m: 可能是一种基于样本平均的自适应分割方法。 - reassign.m: 用于重分配数据到不同的簇。 - GMDAS.m: 可能是全局最大差分分析（Global Maximal Difference Algorithm for Segmentation）的MATLAB实现。 - gustkess.m: 可能是基于 Gustafson-Kessel 算法的聚类。 - kmeans.m: 众所周知的K-means聚类算法，用于将数据分成预定义数量的类别。 - possibi.m: 可能是概率模型评估或潜在类别的计算工具。 - kmedoids.m: 使用质心替代中心点的K-medoids聚类算法。 - spectralNcut2.m 和相关函数：可能涉及谱聚类，如Normalized Cut方法，用于无监督图像分割。 - competitive.m: 可能涉及到竞争性学习算法，用于解决分类问题。第三部分讨论特征选择，这是数据分析中的关键步骤： - simpleOutlierRemoval.m: 简单的异常值检测算法。 - normalizeStd.m、normalizeMnmx.m 和 normalizeSoftmax.m: 数据标准化的不同方法，用于提高特征的可比性和减少噪声影响。 - ROC.m: 接收者操作特征曲线（Receiver Operating Characteristic Curve），用于评估分类器性能。 - divergence.m 和 divergenceBhata.m: 可能是计算不同类型的相似度或距离度量，如Bhattacharyya距离。 - ScatterMatrices.m: 可能是散点矩阵的生成，用于可视化特征之间的关系。 - ScalarFeatureSelectionRanking.m 和其他函数：采用不同的统计方法进行特征排名和选择。第四部分专门探讨图像特征提取技术： - generate.m: 可能是用于生成图像特征的通用函数，可以是局部特征（如SIFT、SURF等）或全局特征（如颜色直方图、纹理描述符）。这些函数提供了深入理解并应用模式识别理论到实际项目中的实践案例，帮助读者掌握如何通过MATLAB平台构建和优化自己的模式识别系统。无论是聚类、特征选择还是图像处理，此手册都是一个宝贵的资源，适合研究人员、学生和工程师进一步探索和应用。

• Input:

– X : an l × N dimensional matrix each column of which corresponds to a data vector.

– u: an N ×m dimensional matrix whose (i, j) element is an initial estimate of the “grade of membership”

of the i-th data vector to the j-th cluster (all elements of u are in the interval [0, 1] and the entries of

each row sum up to unity).

– c: an l × m dimensional matrix whose j-th column is an initial estimate of the center for the j-th

cluster.

– S: an l × l × m dimensional matrix whose j-th l × l two-dimensional “slice” is an initial estimate of

the covariance for the j-th cluster.

– q: the fuzziﬁer parameter.

– e: the parameter used in the termination criterion of the algorithm. (the algorithm terminates when

the summation of the absolute diﬀerences of u’s between two successive iterations is less than e).

• Output:

– u: an N × m dimensional matrix with the ﬁnal estimates of the grade of memberships of each vector

to each cluster.

– c: an l × m dimensional matrix with the ﬁnal estimates of the centers of the clusters.

– S: an l × l × m dimensional matrix whose j-th l × l two-dimensional “slice” is a ﬁnal estimate of the

covariance for the j-th cluster.

– NOTE: This function calls dgk.m function for the computation of the distance of a point from a

cluster.

2.5 k means.m

• Syntax: [w,bel]=k means(X,w)

• Description: This function implements the k-means algorithm, which requires as input the number of clus-

ters underlying the data set. The algorithm starts with an initial estimation of the cluster representatives

and iteratively tries to move them into regions that are “dense” in data vectors, so that a suitable cost

function is minimized. This is achieved by performing (usually) a few passes on the data set. The algo-

rithm terminates when the values of the cluster representatives remain unaltered between two successive

iterations.

• Input:

– X : an l × N dimensional matrix, each column of which corresponds to an l-dimensional data vector.

– w: a matrix, whose columns contain the l-dimensional (mean) representatives of the clusters.

• Output:

– w: a matrix, whose columns contain the ﬁnal estimates of the representatives of the clusters.

– bel: an N-dimensional vector, whose i-th element indicates the cluster where the i-th data vector has

been assinged.

Theodoridis, Pattern Recognition 4e,

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Theodoridis, Pattern Recognition 4e,

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Theodoridis, Pattern Recognition 4e,

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2.6 possibi.m

• Syntax: [U,w]=possibi(X,m,eta,q,sed,init proc,e thres)

• Description: Implements the possibilistic algorithm, when the squared Euclidean distance is adopted. The

algorithm moves iteratively the cluster representatives to regions that are “dense” in data, so that a suitable

cost function is minimized. It terminates when no signiﬁcant diﬀerence in the values of the representatives

is encountered between two successive iterations. Once more, the number of clusters is a priori required.

However, when it is overestimated, the algorithm has the ability to return a solution where more than one

representatives coincide.

• Input:

– X : an l × N dimensional matrix, each column of which corresponds to a data vector.

– m: the number of clusters.

– eta: an m-dimensional array of the eta parameters of the clusters.

– q: the q parameter of the algorithm. When this is not equal to 0 the original cost function is

considered, while if it is 0 the alternative one is considered.

– sed: a scalar integer, which is used as the seed for the random generator function “rand”.

– init proc: an integer taking values “1”, “2” or “3” with

- “1” corresponding to the rand init.m initialization procedure (this procedure chooses randomly m

vectors from the smallest hyperrectangular that contains all the vectors of X and its sides are parallel

to the axes).

- “2” corresponding to rand data init.m (this procedure chooses randomly m vectors among the vectors

of X) and

- “3” corresponding to distant init.m (this procedure chooses the m vectors of X that are “most

distant” from each other. This is a more computationally demanding procedure).

– e thres: The threshold controlling the termination of the algorithm. Speciﬁcally, the algorithm termi-

nates when the sum of the absolute diﬀerences of the representatives between two successive iterations

is smaller than e thres.

• Output:

– U : an N ×m dimensional matrix, whose (i, j) element denotes the possibility that the i-th data vector

belongs to the j-th cluster, after the convergence of the algorithm.

– w: an l × m dimensional matrix, each column of which corresponds to a cluster representative, after

the convergence of the algorithm.

– NOTE: This function calls rand init.m, rand data init.m and distant init.m.

2.7 k medoids.m

• Syntax: [bel,cost,w,a]=k medoids(X,m,sed)

• Description: This function implements the k-medoids algorithm. The aim of this algorihm is the same as

with k-means, i.e., to move iteratively the cluster representatives to regions that are “dense” in data, so

that a suitable cost function is minimized. However, now, the represenatives are constrained to be vectors

Theodoridis, Pattern Recognition 4e,

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Theodoridis, Pattern Recognition 4e,

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Theodoridis, Pattern Recognition 4e,

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