Estimating Dimensionality of Hyperspectral Data Using False Neighbour Method

Accurate estimation of dimensionality is a prerequisite step prior to many information extraction methods from hyperspectral images. The estimation is usually conducted through linear transformations. These methods, though manifested in different mathematical forms, are all based on treating hyperspectral images as the data sets produced by linear stochastic processes, which may contradict the physical processes involved in the formation of hyperspectral imagery. We investigate in this study the dimensionality of a hyperspectral data by using a nonlinear time series analysis approach - false neighbour method. The investigation is conducted based on pixels of different land-cover types. It is found that the estimated dimensionality of the hyperspectral data is markedly smaller than that derived based on linear transformations. This indicates that the hyperspectral data can be embedded tightly in a lower dimensional space if nonlinearity is considered. It is also found that dimensionality may change among different land-cover types.