Análise dos componentes principais supervisionada: uma abordagem não-paramétrica

Abstract

Problems of classification of data become more commonly used. Classification task has a broader range of applications, ranging from detection of spam emails to classification of malignant and benign tumors. In these problems, the quantity of characteristics plays a fundamental role both in the quality and performance of the classifiers. Data having a high dimensionality tends to have lower accuracy and longer processing time. Feature extraction techniques are excellent solutions to this situation, generating a new set of features and selecting the best ones for classification. Principal Component Analysis (PCA) is one of the most common feature extraction techniques. In general, PCA presents excellent results, but because it is an unsupervised technique there are situations where the method can not extract discriminant features. We developed a supervised version of the PCA using Bayesian classification with the kernel density estimation (KDE) to select features. This method has emerged as an extension of the Minimum Classification Error PCA (MCPCA). MCPCA also uses the Bayesian error as a metric however it presents a series of constraints. Comparing the exposed method with PCA, MCPCA and Supervised PCA (SPCA), another supervised approach to PCA, comparing the accuracy by characteristics in four classifiers to sixteen databases. The proposed method presented the greater accuracy in 72% of the cases. For PCA, MCPCA, and SPCA this number is 31%, 36%, 12%, respectively. When using a single extracted feature, the maximum accuracy if achieved is 89%, 14%, 37%, and 25% of the cases for proposed method, PCA, MCPCA, and SPCA, respectively.