Independent Subspace Analysis to Rotate Multidimensional Space for Visualization of Color Symbolism

Ordinary independent component analysis cannot suitably handle the spherically symmetrical distributed subspaces that reflect the hue relations. Therefore, a method based on independent subspace analysis or multidimensional independent component analysis is presented for rotating a configuration in which color symbolism is visualized. Assuming two-dimensional spherically symmetric distributions for some pairs of dimensions, the proposed method aligns the axes into mutually independent spherically symmetrical spaces and sparse dimensions. The L2-norm of the data points in the spherically symmetric subspace is assumed to follow a Weibull distribution, and the distributions in the sparse dimensions are assumed to follow a generalized normal distribution. To process the heterogeneous dimensions/dimension pairs and to rotate an unwhitened configuration, the scaling parameters of dimensions/dimension pairs are estimated in addition to the orthonormal matrix by fully maximizing the likelihood function to rotate the space representing color symbolism. Two applications for this method are presented, whereby the configurations of color-emotion associations and color-shape associations obtained by correspondence analysis are rotated by the proposed method. The characteristics of these associations are clearly shown in the obtained configurations. The proposed method provides potentially advantageous options for rotating a configuration for the visualization of color symbolism.