抄録
A principal component analysis using a fuzzy covariance for multivariate interval-valued image data is presented. A fuzzy covariance for interval-valued data is defined by assuming uniform distribution for each interval of an object. Since the principal component analysis measures similarity among observations in a projection space from a higher dimensional space, in which the observation exists and the metric projections are monotone and non-expansive, the result of the principal component analysis does not always show the real similarity of the data. In order to solve this problem, we use weights which can show the similarity structure in the higher observational space to the empirical joint function for interval-valued data and then calculate the weighted covariance for the principal component analysis. Numerical examples using multivariate interval-valued image data show a better performance.
