Supervised principal component analysis: Visualization, classification and regression on subspaces and submanifolds
Supervised principal component analysis: Visualization, classification and regression on subspaces and submanifolds
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DOI：
10.1016/j.patcog.2010.12.015
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发表时间：
2011-07-01
影响因子：
8
通讯作者：
Jahromi, Mansoor Zolghadri
中科院分区：
文献类型：
--
作者：
Barshan, Elnaz;Ghodsi, Ali;Jahromi, Mansoor Zolghadri
我们提出了“监督主成分分析（有监督的PCA）”，这是PCA的概括，对于具有高维输入数据的回归和分类问题非常有效。它通过估计对响应变量具有最大依赖性的主组件的序列来起作用。提出的监督PCA可在闭合形式中解决，并且具有双重公式，可显着降低问题的计算复杂性，其中预测变量数量大大超过了观测值的数量（例如DNA微阵列实验）。此外，我们还展示了如何将算法化为算法，这使其适用于非线性降低降低任务。各种可视化，分类和回归问题的实验结果比其他监督方法的准确性和计算效率都显着改善。 （c）2011 Elsevier Ltd.保留所有权利。
We propose "supervised principal component analysis (supervised PCA)", a generalization of PCA that is uniquely effective for regression and classification problems with high-dimensional input data. It works by estimating a sequence of principal components that have maximal dependence on the response variable. The proposed supervised PCA is solvable in closed-form, and has a dual formulation that significantly reduces the computational complexity of problems in which the number of predictors greatly exceeds the number of observations (such as DNA microarray experiments). Furthermore, we show how the algorithm can be kernelized, which makes it applicable to non-linear dimensionality reduction tasks. Experimental results on various visualization, classification and regression problems show significant improvement over other supervised approaches both in accuracy and computational efficiency. (c) 2011 Elsevier Ltd. All rights reserved.