Non-Linear Embeddings and the Underlying Dimensionality of Reflectance
spectra and Chromaticity Histograms
Brian Funt, Dejan Kulpinski and Vlad Cardei "Non-Linear Embeddings and
the Underlying Dimensionality of Reflectance spectra and Chromaticity Histograms,"
Proceedings of the IS&T/SID Ninth Color Imaging Conference: Color Science,
Systems and Applications, 2001, pp 126-129.
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
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.
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Keywords: Spectral representation, color histograms, dimensionality reduction
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