Covariance and PCA for Categorical Variables
نویسندگان
چکیده
Covariances from categorical variables are defined using a regular simplex expression for categories. The method follows the variance definition by Gini, and it gives the covariance as a solution of simultaneous equations. The calculated results give reasonable values for test data. A method of principal component analysis (RS-PCA) is also proposed using regular simplex expressions, which allows easy interpretation of the principal components. The proposed methods apply to variable selection problem of categorical data USCensus1990 data. The proposed methods give appropriate criterion for the variable selection problem of categorical
منابع مشابه
Maximally Correlated Principal Component Analysis
In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance of the data. However, PCA has two major weaknesses. Firstly, it only considers linear correlations among variables (features), and secondly it is not suitable...
متن کاملSwitching principal component analysis for modeling means and covariance changes over time.
Many psychological theories predict that cognitions, affect, action tendencies, and other variables change across time in mean level as well as in covariance structure. Often such changes are rather abrupt, because they are caused by sudden events. To capture such changes, one may repeatedly measure the variables under study for a single individual and examine whether the resulting multivariate...
متن کاملePCA: High Dimensional Exponential Family PCA
Many applications involve large collections of high-dimensional datapoints with noisy entries from exponential family distributions. It is of interest to estimate the covariance and principal components of the noiseless distribution. In photon-limited imaging (e.g. XFEL) we want to estimate the covariance of the pixel intensities of 2-D images, where the pixels are low-intensity Poisson variabl...
متن کاملA New Feature Extraction Method Based on the Information Fusion of Entropy Matrix and Covariance Matrix and Its Application in Face Recognition
The classic principal components analysis (PCA), kernel PCA (KPCA) and linear discriminant analysis (LDA) feature extraction methods evaluate the importance of components according to their covariance contribution, not considering the entropy contribution, which is important supplementary information for the covariance. To further improve the covariance-based methods such as PCA (or KPCA), this...
متن کاملModel Identification and Error Covariance Matrix Estimation from Noisy Data Using Pca
Principal Components Analysis (PCA) is increasingly being used for reducing the dimensionality of multivariate data, process monitoring, model identification, and fault diagnosis. However, in the mode that PCA is currently used, it can be statistically justified only if measurement errors in different variables are assumed to be i.i.d. In this paper, we develop the theoretical basis and an iter...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005