This paper presents a constructive method for deriving an updated discriminant eigenspace for classification, when bursts of data that contains new classes is being added to an initial discriminant eigenspace in the form of random chunks. Basically, we propose an incremental linear discriminant analysis (ILDA) in its two forms: a sequential ILDA; and a Chunk ILDA. In experiments, we have tested ILDA using datasets with a small number of classes and smalldimensional features, as well as datasets with a large number of classes and large-dimensional features. We have compared the proposed ILDA against the traditional batch LDA in terms of discriminability, execution time and memory usage with the increasing volume of data addition. The results show that the proposed ILDA can effectively evolve a discriminant eigenspace over a fast and large data stream, and extract features with superior discriminability in classification, when compared with other methods.

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Principle Component Analysis (PCA) is a mathematical procedure widely used in exploratory data analysis, signal processing, etc. However, it is often considered a black box operation whose results and procedures are difficult to understand. The goal of this paper is to provide a detailed explanation of PCA based on a designed visual analytics tool that visualizes the results of principal component analysis and supports a rich set of interactions to assist the user in better understanding and utilizing PCA. The paper begins by describing the relationship between PCA and single vector decomposition (SVD), the method used in our visual analytics tool. Then a detailed explanation of the interactive visual analytics tool, including advantages and limitations, is provided. 1.

Principle Component Analysis (PCA) is a widely used mathematical technique in many fields for factor and trend analysis, dimension reduction, etc. However, it is often considered to be a “black box ” operation whose results are difficult to interpret and sometimes counter-intuitive to the user. In order to assist the user in better understanding and utilizing PCA, we have developed a system that visualizes the results of principal component analysis using multiple coordinated views and a rich set of user interactions. Our design philosophy is to support analysis of multivariate datasets through extensive interaction with the PCA output. To demonstrate the usefulness of our system, we performed a comparative user study with a known commercial system, SAS/INSIGHT’s Interactive Data Analysis. Participants in our study solved a number of high-level analysis tasks with each interface and rated the systems on ease of learning and usefulness. Based on the participants ’ accuracy, speed, and qualitative feedback, we observe that our system helps users to better understand relationships between the data and the calculated eigenspace, which allows the participants to more accurately analyze the data. User feedback suggests that the interactivity and transparency of our system are the key strengths of our approach. Categories and Subject Descriptors (according to ACM CCS): H.5.2 [User Interfaces]: Interaction styles (e.g., commands, menus, forms, direct manipulation) I.3.6 [Methodology and Techniques]: Interaction techniques 1.

A new general dimension reduction framework based on similar and dissimilar metric learning is proposed in this paper which allows us to exploit the geometry of data to reduce the data dimension for classification and visualization. The general formulation can unify the existing dimension reduction algorithms within a common framework. Furthermore, this metric learning framework can be used as a general platform for developing new dimension reduction algorithms. By utilizing this framework as a tool, we propose a novel supervised dimension reduction algorithm named Sub-Manifold Preserving Analysis (SMPA) in which the intrinsic sub-manifold structure will be preserved while the margin of interclass will be separated. Experimental evidences show that performance of our proposed SMPA algorithm is better than other algorithms. 1.