Available with Spatial Analyst license.
The input raster bands to the classification must influence the categorization of the classification. The desired input bands are entered in a multiband raster and individual single band rasters.
Generally, the data for the input bands should be normally distributed for optimal results. If the data is not, you could apply a transformation to it. To see if the data is normally distributed, you can use the graphing tools available in ArcGIS.
The input bands should not be derived from one another. For example, some will argue that slope, aspect, curvature, and elevation should not all be input into the multivariate classification since slope, aspect, and curvature are all derived from elevation.
One way to explore the correlations in the input bands is to use a scatterplot graph. In the graphs, the x-axis should represent one band's variables, and the y-axis represents another. If the low values in one band always correspond to the low values in the second, and the high in both bands correspond, the data may be correlated and redundant.