Novel Approximate Statistical Algorithm for Large Complex Datasets

In the field of pattern recognition, principal component analysis (PCA) is one of the most well-known feature extraction methods for reducing the dimensionality of high-dimensional datasets. Simple-PCA (SPCA), which is a faster version of PCA, performs effectively with iterative operated learning. However, SPCA might not be efficient when input data are distributed in a complex manner because it learns without using the class information in the dataset. Thus, SPCA cannot be said to be optimal from the perspective of feature extraction for classification. In this study, we propose a new learning algorithm that uses the class information in the dataset. Eigenvectors spanning the eigenspace of the dataset are produced by calculating the data variations within each class. We present our proposed algorithm and discuss the results of our experiments that used UCI datasets to compare SPCA and our proposed algorithm

Feature Generation by Simple FLD

This paper presents a new algorithm for feature generation, which is approximately derived based on geometrical interpretation of the Fisher linear discriminant analysis. In a field of pattern recognition or signal processing, the principal component analysis (PCA) is often used for data compression and feature extraction. Furthermore, iterative learning algorithms for obtaining eigenvectors have been presented in pattern recognition and image analysis. Their effectiveness has been demonstrated on computational time and pattern recognition accuracy in many applications. However, recently the Fisher linear discriminant (FLD) analysis has been used in such a field, especially face image analysis. The drawback of FLD is a long computational time in compression of large-sized between-class and within-class covariance matrices. Usually FLD has to carry out minimization of a within-class variance. However in this case the inverse matrix of the within-class covariance matrix cannot be obtained, since data dimension is higher than the number of data and then it includes many zero eigenvalues. In order to overcome this difficulty, a new iterative feature generation method, a simple FLD is introduced and its effectiveness is demonstrated