Each normalised library mineral band D,j is then compared with each normalised unknown spectrum band 
Di- 
Ej = 1 - £j = i I Djj - Dj I (2) 
Ej = Total error comparing mineral j spectrum with the unknown spectrum 
D,j = Normalised data value of band i for library mineral j 
Dj = Normalised data value of band i of the unknown 
n = Number of bands 
The term Ej can vary between 1 and -1 for each of the j minerals. An Ej of one is a perfect correlation, of 
zero shows no correlation and of minus one a perfect mirror image (a negative correlation). An Ej below 
zero is considered a reject. The identity of the mineral with the highest Ej greater than zero is assigned to 
the matched unknown spectrum. 
Two output maps are produced, a mineral map showing the matched pixels and their 
identities and a map of the error term (Ej) for the identified (non-rejected) pixels in an AVIRIS image for 
example. 
3.2.2. Problems of use. The possible problems are, 
1. Due to the unweighted nature of the comparison of the spectra each band equally affects the error term 
Ej. Therefore mis-classifications between minerals which are very similar over the whole curve shape 
but slightly different in a significant absorption are possible (for example between kaolinite and 
dickite, with the same chemical formula but small structural differences). 
2. The normalisation produces curves with the same mean value losing important information on 
absorption depths and overall flatness of the spectral curve. This can lead to mis-classification in some 
cases. 
3.2.3. Advantages of cross-correlation. The advantages are, 
1. The classification is relatively insensitive to noise spikes or noise generally in the spectrum. The noise 
will increase the error term of matching the data substantially before a mis-match occurs. 
2. It is relatively robust in dealing with mixtures of minerals where there is a spectrally dominant mineral 
component down to a 60-40 ratio in the case of muscovite and dolomite mixtures. 
3. It produces an error term which is a direct representation of the goodness of fit. 
3.3. Neural Networks 
There are many different neural network architectures, each architecture operates in a different manner 
with the input data. This paper will cover one particular architecture in detail, that of the Cerebellar 
Model Articulation Controller (CMAC) developed by Albus (1975). This network creates a data structure 
in memory during training that is accessed using the reflectance values of the unknown spectrum as an 
address in a Look-Up-Table (LUT) manner. 
3.3.1. Method. The reflectance spectral library of minerals (plus Gaussian noise at the level expected in 
the data to be classified) is presented as a long series of training examples to the network. Each presented 
spectrum forms an N-Band address (in the case of the AVIRIS sub-section of data used in this paper N = 
38). To produce generalisation in this network (generalisation is necessary to obtain a correct answer from 
an approximately correct input), a calculation is made using the original N-Band address. An example 
using a three band input spectrum to show the operation is given in figure 1. 
In this figure the three band input spectrum forms the three value STATE vector. These 
values are converted into a three value BASE vector as follows, 
BASE(n) = ((truncated integer(STATE(n) / NUMCEL)) * NUMCEL) - 1 (3) 
Where NUMCEL is the generalisation factor (ie. the number of virtual addresses to create from the BASE 
address), n is the number of bands in the vector. From this three value BASE vector, NUMCEL virtual 
addresses are created using the calculation,