高效KPCA算法：基于特征相关性的评估与应用
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本文是一篇发表在《神经计算与应用》(Neural Computing and Applications, ISSN: 0941-0643)的研究论文，标题为“基于特征相关性评估的高效KPCA算法”。KPCA（Kernel Principal Component Analysis）是一种常用的非线性降维技术，在数据挖掘和机器学习领域中占有重要地位。本文主要贡献是提出了一种新的高效KPCA算法，该算法特别关注特征之间的相关性评估。
首先，文章介绍了传统的KPCA方法，它通过构建高维特征空间中的内积核函数来实现非线性映射，从而保留数据的复杂结构。然而，当处理大规模数据或具有高度相关性的特征时，传统KPCA可能会面临计算效率低下的问题。作者意识到，对特征之间的相关性进行有效利用可以优化算法性能。
该高效KPCA算法的核心在于特征相关性评估步骤，这可能包括计算特征间的相关系数、识别冗余或弱相关的特征，以及选择一个能最大化数据投影信息保留度的子集。这样做的目的是减少计算量，同时保持或提高模型的预测精度。算法可能采用启发式方法或者统计学方法来量化和选择特征，比如皮尔逊相关系数、斯皮尔曼等级相关等。
论文作者Zizhu Fan、Jinghua Wang、Baogen Xu和Pengzhi Tang在2012年12月4日提交了这篇研究，并于后续获得了接受。他们强调，新算法不仅在理论上有创新，而且在实际应用中也展示了优越的性能，尤其是在处理大量相关特征数据集时，能够显著提升KPCA的执行速度。
值得注意的是，作者提醒读者，此篇文章受到版权保护，个人使用仅限于非电子存储，并且必须遵守Springer-Vergag的发布规定。在接受的稿件版本上传到个人网站或存储库时，应在12个月后或更晚的时间进行，并确保对原始出版源给出认可，并在Springer的网页链接上添加相应文字声明。
这篇论文为改进KPCA算法提供了新的视角，通过考虑特征相关性，优化了计算效率，对于处理大规模和高度相关特征的数据具有实际价值。对于从事机器学习、数据挖掘或计算机视觉领域的研究人员来说，这篇工作提供了有价值的技术参考和潜在的研究方向。
ORIGINAL ARTICLE
An efficient KPCA algorithm based on feature correlation
evaluation
Zizhu Fan
•
Jinghua Wang
•
Baogen Xu
•
Pengzhi Tang
Received: 4 December 2012 / Accepted: 20 April 2013
Springer-Verlag London 2013
Abstract Classic kernel principal component analysis
(KPCA) is less computationally efficient when extracting
features from large data sets. In this paper, we propose an
algorithm, that is, efficient KPCA (EKPCA), that enhances
the computational efficiency of KPCA by using a linear
combination of a small portion of training samples, referred
to as basic patterns, to approximately express the KPCA
feature extractor, that is, the eigenvector of the covariance
matrix in the feature extraction. We show that the feature
correlation (i.e., the correlation between different feature
components) can be evaluated by the cosine distance
between the kernel vectors, which are the column vectors
in the kernel matrix. The proposed algorithm can be easily
implemented. It first uses feature correlation evaluation to
determine the basic patterns and then uses these to recon-
struct the KPCA model, perform feature extraction, and
classify the test samples. Since there are usually many
fewer basic patterns than training samples, EKPCA feature
extraction is much more computationally efficient than that
of KPCA. Experimental results on several benchmark data
sets show that EKPCA is much faster than KPCA while
achieving similar classification performance.
Keywords Kernel principal component analysis (KPCA)
Feature extraction Feature correlation Cosine distance
1 Introduction
Kernel principal component analysis (KPCA) [1–7]isan
effective approach to feature extraction and has been used
with success in a variety of pattern recognition problems as
well as in numerous image-related machine learning appli-
cations [8–16]. KPCA is a nonlinear generalization of clas-
sical principal component analysis (PCA), which seeks to
extract a certain number of the most representative features
from data [17–20]. Basically, in KPCA, the input data are first
transformed into a high or even infinite dimensional feature
space F through a nonlinear mapping, and then classic PCA is
performed in the feature space F. KPCA employs an appro-
priately chosen kernel function to stand for inner products of
sample vectors in the feature space, which means that it does
not need to explicitly carry out the nonlinear mapping [21, 22].
KPCA often outperforms the classical PCA because it can
effectively extract the nonlinear features of a sample, but
KPCA-based feature extraction is computationally expensive
since its computational efficiency is inversely proportional to
the number of training samples [23]. Inevitably then, the
greater the number of training samples, the lower the effi-
ciency of feature extraction.
A number of reformulated algorithms [24–32] have
recently been proposed to improve the computational
efficiency of KPCA. Rosipal and Girolami [24] proposed to
improve the training efficiency of KPCA using an expec-
tation maximization approach. Zheng et al. [25] enhanced
the training efficiency of KPCA by grouping the training
samples. Schraudolph et al. [26] improved the convergence
of the kernel Hebbian algorithm (KHA) for iterative kernel
PCA. Moerland described how an expectation–maximiza-
tion algorithm for classical PCA could be adapted to kernel
PCA without having to store the kernel matrix [27]. These
methods, however, do not consider the feature extraction
Z. Fan (&) B. Xu P. Tang
School of Basic Science, East China Jiaotong University,
Nanchang 330013, China
e-mail: zzfan3@yahoo.com.cn
J. Wang
Department of Computing, The Hong Kong Polytechnic
University, Kowloon, Hong Kong, China
123
Neural Comput & Applic
DOI 10.1007/s00521-013-1424-9
Author's personal copy
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