Non-Linear Embeddings and the Underlying Dimensionality of Reflectance Spectra and Chromaticity Histograms

摘要

We have used the locally linear embedding and Isomap techniques to process high-dimensional color and spectral data. These techniques allowed us to create low-dimensional embeddings of the original data. In particular, the dimensionality is significantly lower than that obtained by principal components analysis. The data that we processed included spectral reflectances, illuminant spectra (both 101 dimensional) and chromaticity histograms (251 dimensional). Isomap was useful in determining the dimensionality of the data in question. Using the Isomap technique, we found that the dimensionality for the spectral reflectances is between 3 and 4. For the chromaticity histograms, we found that the 251 original histogram dimensions were transformed into 5 to 6 dimensional space. In addition to providing an estimate of the underlying dimensionality of the data, both Isomap and LLE technique were used in producing the low-dimensional embeddings of the high dimensional data.