Hyperspectral Data

In existing studies, hyperspectral data are usually modeled as random vectors whose dimension equals to the number of spectral bands. Some mathematically tractable multivariate probability distributions have been proposed to fit this type of data, such as multivariate normal distribution or more generally, elliptically contoured family.

Hyperspectral data are collected over a consecutive period of time (e.g. every 15 minutes), yielding a natural multivariate time series data set. In fact, correlations between different spectral channels in hyperspectral signature measured at one time, and auto-correlations over time points for each wave length do exist in the real data, as is shown below. Thus, multivariate time series are reasonable description of hyperspectral data.

An interesting analogy of hyperspectral signatures of a certain plant collecting over time would the stock prices of a particular portfolio, as is shown in the following figure (produced by R package mvtsplot). This stock portfolio data set is contributed by R. Peng. He collected daily price data for a portfolio consisting of an S&P 500 index exchange traded fund, two bond exchange traded funds and nine real estate investment trusts over the period 2006-2007. For hypersepctral data, each band channel can be viewed as one portfolio components. Multivariate time series analysis has been widely used in financial data analysis, so similar methods could be transplant in the study of hyperspectral data at early period of investigation.