Principal component analysis is one of the most important and powerful methods in chemometrics as well as in a wealth of other areas. This paper provides a description of how to understand, use, and interpret principal component analysis. The paper focuses on the use of principal component analysis in typical chemometric areas but the results are generally applicable.

/pdf/principal-component-analysis-1sba76ou47.pdf

Principal component analysis

This paper is concerned with the problem of stability of neural networks with time-varying delays. A novel Lyapunov-Krasovskii functional decomposing the delays in all integral terms is proposed. By exploiting all possible information and considering independent upper bounds of the delay derivative in various delay intervals, some new generalized delay-dependent stability criteria are established, which are different from the existing ones and improve upon previous results. Numerical examples are finally given to demonstrate the effectiveness and the merits of the proposed method.

Complete Delay-Decomposing Approach to Asymptotic Stability for Neural Networks With Time-Varying Delays

Computer-implemented systems and methods for analyzing activities associated with accesses of a computer network. A computer-implemented method can be configured to receive data related to the activities associated with the accesses of a computer network. The network activities data are segmented into a plurality of network activities segments. For each of the network activities segments, an anomaly detection predictive model is generated. The generated predictive models are for use in analyzing the activities associated with the computer network.

Computer-implemented modeling systems and methods for analyzing and predicting computer network intrusions

Systems and methods for performing fraud detection. As an example, a system and method can be configured to contain a raw data repository for storing raw data related to financial transactions. A data store contains rules to indicate how many generations or to indicate a time period within which data items are to be stored in the raw data repository. Data items stored in the raw data repository are then accessed by a predictive model in order to perform fraud detection.

Computer-Implemented Data Storage Systems and Methods for Use with Predictive Model Systems

Systems and methods are provided for evaluating risks associated with alternative strategies for assessing an entity with respect to a predetermined objective. A system includes an action table that contains a plurality of possible actions that can be taken with respect to the predetermined objective for various entity profiles. One or more statistical data stores are configured to contain risk amounts associated with each entity profile, where the one or more statistical data stores are configured to contain inferred percentage distribution of applicants associated with each entity profile. One or more profile identification data stores contain entity identification information for use in determining an action for the entity. One or more improvement data stores provide an indication in the improvement in risk based upon a change in one or more characteristics for an entity profile.

Computer-Implemented Risk Evaluation Systems And Methods

We discuss a new approach to self-organization that leads to novel adaptive algorithms for generalized eigen-decomposition and its variance for a single-layer linear feedforward neural network. First, we derive two novel iterative algorithms for linear discriminant analysis (LDA) and generalized eigen-decomposition by utilizing a constrained least-mean-squared classification error cost function, and the framework of a two-layer linear heteroassociative network performing a one-of-m classification. By using the concept of deflation, we are able to find sequential versions of these algorithms which extract the LDA components and generalized eigenvectors in a decreasing order of significance. Next, two new adaptive algorithms are described to compute the principal generalized eigenvectors of two matrices (as well as LDA) from two sequences of random matrices. We give a rigorous convergence analysis of our adaptive algorithms by using stochastic approximation theory, and prove that our algorithms converge with probability one.

M.D. Zoltowski

Papers

Self-organizing algorithms for generalized eigen-decomposition