Dimension Reduction for Non-Gaussian Data by Adaptive Discriminative Analysis

Abstract

High-dimensional non-Gaussian data are ubiquitous in many real applications. Face recognition is a typical example of such scenarios. The sampled face images of each person in the original data space are more closely located to each other than to those of the same individuals due to the changes of various conditions like illumination, pose variation, and facial expression. They are often non-Gaussian and differentiating the importance of each data point has been recognized as an effective approach to process the high-dimensional non-Gaussian data. In this paper, to embed non-Gaussian data well, we propose a novel unified framework named adaptive discriminative analysis (ADA), which combines the sample's importance measurement and subspace learning in a unified framework. Therefore, our ADA can preserve the within-class local structure and learn the discriminative transformation functions simultaneously by minimizing the distances of the projected samples within the same classes while maximizing the between-class separability. Meanwhile, an efficient method is developed to solve our formulated problem. Comprehensive analyses, including convergence behavior and parameter determination, together with the relationship to other related approaches, are as well presented. Systematical experiments are conducted to understand the work of our proposed ADA. Promising experimental results on various types of real-world benchmark data sets are provided to examine the effectiveness of our algorithm. Furthermore, we have also evaluated our method in face recognition. They all validate the effectiveness of our method on processing the high-dimensional non-Gaussian data.

Feature extraction based ondeep‐convolutional neural network for face recognition

“…The method based on algebraic features is mainly implemented by grayscale change or matrix decomposition of a picture to be processed, such as PCA 13 and the Linear Discriminant Analysis. 14,15 Method based on space-frequency transform to extract local features of face details, such as Fourier Transform. 16 In some practical applications, there are problems such as illumination, expression, and occlusion in face images, and the extraction of local features of faces is considered by researchers to be robust to the illumination and expression changes of faces, and more commonly used facial features including LBP features, Gabor wavelet features.…”

“…The former indicates the proportion of correctly identified positive case data in actual positive case data, and the latter indicates the proportion of false-positive instances identified in all negative instances. Equations 14- (15) illustrate how FPR and TPR are defined.…”

Robust Bhattacharyya bound linear discriminant analysis through an adaptive algorithm

“…In this subsection, the behaviors of various methods are investigated on two handwritten digit databases, including the MNIST database and the USPS database. (7) 78.22 (7) 75.25 (7) 73.27 (5) 78.22 (7) 78.22 (7…”

“…LDA tries to find an optimal linear transformation by maximizing the quadratic distance between the class means simultaneously minimizing the within-class distance in the projected space. Due to its simplicity and effectiveness, LDA is widely applied in many applications, including image recognition [3][4][5][6], gene expression [7], biological populations [8], image retrieval [9], etc.…”

A bidirectional weighted boundary distance algorithm for time series similarity computation based on optimized sliding window size

“…By this kind of analysis, the deeplevel relations such as the implicit correlation in the time series can be revealed and the internal rules of movement, change, and development of objects also are discovered, which is of great practical significance for people to correctly understand things and make scientific decisions accordingly. Time series mining is one of the most challenging research problems in the field of data mining, the key step is to map the original data from a high-dimensional feature space to a low dimensional space to reduce the time complexity [14], the similarity clustering is an important research direction of time series mining, many other time sequence mining methods are based on it.…”