扩展的多尺度主成分分析：理论与在异常检测中的优势

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本文主要探讨了"扩展的多尺度主成分分析方法及其在异常检测中的应用"这一主题，发表在《中国电子学报》2012年第3期。作者们，来自杭州 Hangdian 大学、河南大学和上海电讯大学的 Wen Chenglin、Zhou Funa、Wen Chuanbo 和 Chen Zhiguo，针对多尺度主成分分析（MSPCA）的理论基础尚未完全解决的问题，提出了一个创新的方法——扩展多尺度主成分分析(EMSPCA)。 EMSPCA通过矩阵的谱分解，以及信号的多尺度表示和多尺度变换，深入挖掘多元数据在不同尺度下的信息。与传统的单尺度方法相比，该方法的优势在于能够更好地实现多变量信息的提取，特别是在异常检测任务中。文章的关键贡献在于构建了在EMSPCA统一投影框架下，多尺度检测模型与各个尺度模型之间的关系，这使得异常检测能够在多尺度上更加准确和有效。通过EMSPCA，研究者们探讨了为什么多尺度检测方法相较于单一尺度方法在处理复杂数据集时表现更优。他们可能对信号的频域特性进行了深入分析，并利用了这些特性来设计出适应性更强的异常检测算法。这种方法的应用不仅限于学术研究，还可能在工业界的数据分析和故障诊断等领域展现出实际价值，例如在电力系统监控、网络入侵检测或者金融交易异常识别中。文章的具体内容可能包括多尺度分析的数学原理，如如何通过不同的窗口大小或滤波器选择来捕捉信号的不同频率成分；EMSPCA的具体实施步骤，包括数据预处理、谱分解和多尺度特征提取；以及实验结果的展示，对比EMSPCA与传统方法在不同数据集上的性能差异，以及在实际应用中的鲁棒性和准确性。这篇研究论文深入挖掘了多尺度主成分分析的潜力，为异常检测领域的实践者提供了一个强大的工具和技术支持，同时也为理论研究者探索更深层次的多尺度数据分析方法提供了新的思考方向。通过阅读这篇文章，读者将对如何有效地利用多尺度信息来提高异常检测的敏感性和精度有更深入的理解。

Chinese Journal of Electronics

Vol.21, No.3, July 2012

An Extended Multi-scale Principal Component

Analysis Method and Application in Anomaly

Detection

∗

WEN Chenglin

, ZHOU Funa

,WENChuanbo

and CHEN Zhiguo

(1.Institute of Information and Controll, Hangdian University, Hangzhou 310018, China)

(2.Institute of Advanced Control and Intelligent Information Processing, Henan University, Kaifeng 475004, China)

(3.Electric Engineering College, Shanghai Dianji University, Shanghai 200240, China)

Abstract — Multi-scale principal component analysis

(MSPCA) can well implement multivariate information

extracting on diﬀerent scales, but theory foundation of

MSPCA is still an open question. Using spectral decompo-

sition of a matrix and multi-scale representation of spectral

as well as multi-scale transform of a signal, an Extended

multi-scale PCA (EMSPCA) method is proposed to ana-

lyze the reason why multi-scale detection method does well

than single scale method. Under the uniform projection

frame of EMSPCA, the relation between multi-scale de-

tection model and those on each scale is established. Thus

multi-scale anomaly detection can be implemented without

establishing another new PCA model of the reconstructed

data. Simulation shows the eﬃciency of EMSPCA anomaly

detection algorithm.

Key words — Spectral decomposition, Projection, Ex-

tended multi-scale PCA (EMSPCA), Principal component

analysis (PCA), Fault detection.

I. Introduction

With the development of industry technology, large scale

system becomes more and more complicated and automatic.

All parts of the system are tightly connected, and they are

operating as a whole. Failure in a part may cause breakdown

of the whole system or even result in disastrous accident

[1−3]

Research on fault diagnosis has received widely attention from

experts both in academic and application

[1−8]

Principal component analysis (PCA) is a commonly used

method in the ﬁeld of data driven abnormal detection

[9−13]

Multi-scale principal component analysis (MSPCA) com-

bines the ability of PCA to decorrelate multivariate with

that of wavelet analysis to extract deterministic features.

Simulation shows that MSPCA can well extract feature

information

[14−16]

. But existed methods on MSPCA can’t the-

oretically analyze the intrinsic reason why MSPCA is better

than PCA.

Spectrum decomposition of covariance matrix and multi-

scale decomposition of spectrum are ﬁrst studied. Then ex-

tended MSPCA is established to theoretically analyze the in-

trinsic reason why MSPCA is better than PCA. Finally, an

EMSPCA based abnormal detection algorithm is proposed.

II. PCA

The essence of PCA is a linear transform corresponding to

axis rotation

[9,11,12]

V = B

Y (1)

where Y =[y(1), y(2), ···, y(n)] ∈ R

p×n

is the observation

matrix, p is the number of observation variable, n is the num-

ber of samples; V =[v(1), v(2), ···, v(n)] ∈ R

p×n

is score

matrix.

PCA provides a method of observation matrix decompos-

ing observation in Eq.(2)

Y =



i=1

+ E (2)

where b

=[b

, ···,b

]

is loading vector, is after PCA

transform, eigenvalue corresponding to each b

is descendly

sorted as λ

≥···≥λ

≥ 0. V

=[v

(1), ···,v

(n)] ∈ R

1×n

the projection of Y on b

,thatis

= b

Y (3)

E =



i=υ+1

is the residual matrix, υ is the number of key

principal components

[9−12]

III. MSPCA

MSPCA implement PCA to wavelet coeﬃcients at each

scale to ﬁlter unwanted components. The main idea of

MSPCA can be shown in Fig.1

[13−15]

∗

Manuscript Received Apr. 2011; Accepted Nov. 2011. This work is supported by the National Natural Science Foundation of China

(No.60934009, No.61034006, No.60804026, No.61174112, No.60801048).

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