Gaussian Windows: A Multivariate Exploratory Method,
Abstract
This paper presents a method for interactively exploring a large set of quantitative multivariate data, in order to estimate the shape of the underlying density function. It is assumed that the density function is more or less smooth. The local structure of the data in a given region may be examined by viewing the data through a Gaussian window, whose location and shape are chosen by the user. The method, which is applicable in any number of dimensions, can be used to find and describe simple structural features such as peaks, valleys, and saddle points in the density function, and also extended structures such as ridges and analogous structures in higher dimensions. A Gaussian window is defined by giving each data point a weight based on a multivariate Gaussian function. The weighted sample mean and sample covariance matrix are then computed, using the weights attached to the data points. These quantities are used to compute an estimate of the shape of the density function in the window region. The local structure of the data is described by a method similar to the method of principal components. Thus we can apply our geometrical intuition to the structural features we find in the data, in any number of dimensions. By taking many such local views of the data, we can form an idea of the structure of the data set. Since the computations involved are relatively simple, the method can be implemented on a small computer.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1992
- Accession Number
- ADP007106
Entities
People
- Louis A. Jaeckel
Organizations
- National Aeronautics and Space Administration