Independent Subspace Analysis using Locally Linear Embedding

While Independent Subspace Analysis provides a means of blindly separating sound souces from a single channel signal, it does have a number of problems. In particular the amount of information required for separation of sources varies with the signal. This is a result of the variance-based nature of Principal Component Analysis, which is used for dimensional reduction in the Independent Subspace Analysis algorithm. In an attempt to overcome this problem the use of a non-variance based dimensional reduction method, Locally Linear Embedding, is proposed. Locally Linear Embedding is a geometry based dimensional reduction technique. The use of this approach is demonstrated by its application to single channel source separation and its merits discusse

GEOGRAPHICALLY WEIGHTED REGRESSION PRINCIPAL COMPONENT ANALYSIS (GWRPCA) PADA PEMODELAN PENDAPATAN ASLI DAERAH DI JAWA TENGAH

Linear Regression Analysis is a method for modeling the relation between a response variable with two or more independent variables. Geographically Weighted Regression (GWR) is a development of the regression model where each observation location has different regression parameter values because of the effects of spatial heterogenity. Regression Principal Component Analysis (PCA) is a combination of PCA and are used to remove the effect of multicolinearity in regression. Geographically Weighted Regression Principal Component Analysis (GWRPCA) is a combination of PCA and GWR if spatial heterogenity and local multicolinearity occured. Estimation parameters for the GWR and GWRPCA using Weighted Least Square (WLS). Weighting use fixed gaussian kernel function through selection of the optimum bandwidth is 0,08321242 with minimum Cross Validation (CV) is 3,009035. There are some variables in PCA that affect locally-generated revenue in Central Java on 2012 and 2013, which can be represented by PC1 that explained the total variance data about 71,4%. GWRPCA is a better model for modeling locally-generated revenue for the districts and cities in Central Java than RPCA because it has the the smallest Akaike Information Criterion (AIC) and the largest R2.. Keywords : Spatial Heterogenity, Local Multicolinearity, Principal Component Analysis, Geographically Weighted Regression Principal Component Analysis

Geographically Weighted Regression Principal Component Analysis (Gwrpca) Pada Pemodelan Pendapatan Asli Daerah Di Jawa Tengah

Linear Regression Analysis is a method for modeling the relation between a response variable with two or more independent variables. Geographically Weighted Regression (GWR) is a development of the regression model where each observation location has different regression parameter values because of the effects of spatial heterogenity. Regression Principal Component Analysis (PCA) is a combination of PCA and are used to remove the effect of multicolinearity in regression. Geographically Weighted Regression Principal Component Analysis (GWRPCA) is a combination of PCA and GWR if spatial heterogenity and local multicolinearity occured. Estimation parameters for the GWR and GWRPCA using Weighted Least Square (WLS). Weighting use fixed gaussian kernel function through selection of the optimum bandwidth is 0,08321242 with minimum Cross Validation (CV) is 3,009035. There are some variables in PCA that affect locally-generated revenue in Central Java on 2012 and 2013, which can be represented by PC1 that explained the total variance data about 71,4%. GWRPCA is a better model for modeling locally-generated revenue for the districts and cities in Central Java than RPCA because it has the the smallest Akaike Information Criterion (AIC) and the largest R2

The spectrum of kernel random matrices

We place ourselves in the setting of high-dimensional statistical inference where the number of variables $p$ in a dataset of interest is of the same order of magnitude as the number of observations $n$. We consider the spectrum of certain kernel random matrices, in particular $n\times n$ matrices whose $(i,j)$th entry is $f(X_i'X_j/p)$ or $f(\Vert X_i-X_j\Vert^2/p)$ where $p$ is the dimension of the data, and $X_i$ are independent data vectors. Here $f$ is assumed to be a locally smooth function. The study is motivated by questions arising in statistics and computer science where these matrices are used to perform, among other things, nonlinear versions of principal component analysis. Surprisingly, we show that in high-dimensions, and for the models we analyze, the problem becomes essentially linear--which is at odds with heuristics sometimes used to justify the usage of these methods. The analysis also highlights certain peculiarities of models widely studied in random matrix theory and raises some questions about their relevance as tools to model high-dimensional data encountered in practice.Comment: Published in at http://dx.doi.org/10.1214/08-AOS648 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Nonlinear modal analysis using pattern recognition

The main objective of nonlinear modal analysis is to formulate a mathematical model of a nonlinear dynamical structure based on observations of input/output data from the dynamical system. Most theories regarding structural modal analysis are centred on the linear modal analysis which has proved to now to be the method of choice for the analysis of linear dynamic structures. However, for the majority of other structures, where the effect of nonlinearity becomes significant, then nonlinear modal analysis is a necessity. The objective of the current paper is to demonstrate a machine learning approach to output-only nonlinear modal decomposition using kernel independent component analysis and locally linear embedding analysis. The key element is to demonstrate a pattern recognition approach which exploits the idea of independence of principal components by learning the nonlinear manifold between the variables

Visualizing dimensionality reduction of systems biology data

One of the challenges in analyzing high-dimensional expression data is the detection of important biological signals. A common approach is to apply a dimension reduction method, such as principal component analysis. Typically, after application of such a method the data is projected and visualized in the new coordinate system, using scatter plots or profile plots. These methods provide good results if the data have certain properties which become visible in the new coordinate system and which were hard to detect in the original coordinate system. Often however, the application of only one method does not suffice to capture all important signals. Therefore several methods addressing different aspects of the data need to be applied. We have developed a framework for linear and non-linear dimension reduction methods within our visual analytics pipeline SpRay. This includes measures that assist the interpretation of the factorization result. Different visualizations of these measures can be combined with functional annotations that support the interpretation of the results. We show an application to high-resolution time series microarray data in the antibiotic-producing organism Streptomyces coelicolor as well as to microarray data measuring expression of cells with normal karyotype and cells with trisomies of human chromosomes 13 and 21