Spatio-Temporal Multiway Data Decomposition Using Principal Tensor Analysis on k-Modes: The R Package PTAk

The purpose of this paper is to describe the R package {PTAk and how the spatio-temporal context can be taken into account in the analyses. Essentially PTAk() is a multiway multidimensional method to decompose a multi-entries data-array, seen mathematically as a tensor of any order. This PTAk-modes method proposes a way of generalizing SVD (singular value decomposition), as well as some other well known methods included in the R package, such as PARAFAC or CANDECOMP and the PCAn-modes or Tucker-n model. The example datasets cover different domains with various spatio-temporal characteristics and issues: (i)~medical imaging in neuropsychology with a functional MRI (magnetic resonance imaging) study, (ii)~pharmaceutical research with a pharmacodynamic study with EEG (electro-encephaloegraphic) data for a central nervous system (CNS) drug, and (iii)~geographical information system (GIS) with a climatic dataset that characterizes arid and semi-arid variations. All the methods implemented in the R package PTAk also support non-identity metrics, as well as penalizations during the optimization process. As a result of these flexibilities, together with pre-processing facilities, PTAk constitutes a framework for devising extensions of multidimensional methods such ascorrespondence analysis, discriminant analysis, and multidimensional scaling, also enabling spatio-temporal constraints.

Analyze of Classification Accaptence Subsidy Food Using Kernel Discriminant

Subsidy food is government program for social protection to poor households. The aims of this program are to effort households from starve and to decrease poverty. Less precisely target of this program has negative impact. So that to successful program, it’s important to know accuracy classification of admission subsidy food. The variables classification are number of household members, number of household member in work, average expenditure capita, weighted household, and floor area. Discriminant analysis is a multivariate statistical technique which can be used to classify the new observation into a specific group. Kernel discriminant analysis is a non-parametric method which is flexible because it does not have to concern about assumption from certain distribution and equal variance matrices as in parametric discriminant analysis. The classification using the kernel discriminant analysis with the normal kernel function with optimum bandwidth 0.6 gives accurate classification 75.35%

Penalized Orthogonal Iteration for Sparse Estimation of Generalized Eigenvalue Problem

We propose a new algorithm for sparse estimation of eigenvectors in generalized eigenvalue problems (GEP). The GEP arises in a number of modern data-analytic situations and statistical methods, including principal component analysis (PCA), multiclass linear discriminant analysis (LDA), canonical correlation analysis (CCA), sufficient dimension reduction (SDR) and invariant co-ordinate selection. We propose to modify the standard generalized orthogonal iteration with a sparsity-inducing penalty for the eigenvectors. To achieve this goal, we generalize the equation-solving step of orthogonal iteration to a penalized convex optimization problem. The resulting algorithm, called penalized orthogonal iteration, provides accurate estimation of the true eigenspace, when it is sparse. Also proposed is a computationally more efficient alternative, which works well for PCA and LDA problems. Numerical studies reveal that the proposed algorithms are competitive, and that our tuning procedure works well. We demonstrate applications of the proposed algorithm to obtain sparse estimates for PCA, multiclass LDA, CCA and SDR. Supplementary materials are available online

Revisiting Classical Multiclass Linear Discriminant Analysis with a Novel Prototype-based Interpretable Solution

Linear discriminant analysis (LDA) is a fundamental method for feature extraction and dimensionality reduction. Despite having many variants, classical LDA has its own importance, as it is a keystone in human knowledge about statistical pattern recognition. For a dataset containing C clusters, the classical solution to LDA extracts at most C-1 features. Here, we introduce a novel solution to classical LDA, called LDA++, that yields C features, each interpretable as measuring similarity to one cluster. This novel solution bridges dimensionality reduction and multiclass classification. Specifically, we prove that, for homoscedastic Gaussian data and under some mild conditions, the optimal weights of a linear multiclass classifier also make an optimal solution to LDA. In addition, we show that LDA++ reveals some important new facts about LDA that remarkably changes our understanding of classical multiclass LDA after 75 years of its introduction. We provide a complete numerical solution for LDA++ for the cases 1) when the scatter matrices can be constructed explicitly, 2) when constructing the scatter matrices is infeasible, and 3) the kernel extension

Bandwidth Allocation Mechanism based on Users' Web Usage Patterns for Campus Networks

Managing the bandwidth in campus networks becomes a challenge in recent years. The limited bandwidth resource and continuous growth of users make the IT managers think on the strategies concerning bandwidth allocation. This paper introduces a mechanism for allocating bandwidth based on the users’ web usage patterns. The main purpose is to set a higher bandwidth to the users who are inclined to browsing educational websites compared to those who are not. In attaining this proposed technique, some stages need to be done. These are the preprocessing of the weblogs, class labeling of the dataset, computation of the feature subspaces, training for the development of the ANN for LDA/GSVD algorithm, visualization, and bandwidth allocation. The proposed method was applied to real weblogs from university’s proxy servers. The results indicate that the proposed method is useful in classifying those users who used the internet in an educational way and those who are not. Thus, the developed ANN for LDA/GSVD algorithm outperformed the existing algorithm up to 50% which indicates that this approach is efficient. Further, based on the results, few users browsed educational contents. Through this mechanism, users will be encouraged to use the internet for educational purposes. Moreover, IT managers can make better plans to optimize the distribution of bandwidth