ON FACTOR ANALYSIS AND FISHER'S LINEAR DISCRIMINANT ANALYSIS
Filomena De Santis, ALFONSO PAGLIUCA · Cybernetics & Systems · 1982
In communication theory the Kaihunen-Löve expansion is a widely used procedure for data compression and it can be shown to be optimal when signal distortion is the essential constraint. In pattern recognition applications emphasis is usually on discrimination rather than faithful representation of data. In previous works various advantages of the factor analysis model over the KL expansion for error-reduction in statistical pattern recognition and clustering have been discussed. It has been shown that the factor analysis model can be viewed as a linear filter which eliminates from the input variables a certain amount of uncorrected information. The remaining signal has been shown to have the essential property of enhancing existing correlations between variables used to describe and discriminate objects in a given collection. Moreover, when clustering problems are involved, results obtained by a factor analysis application are equivalent to those obtained by a Fisher discriminant analysis application in the sense that Fisher directions are contained in the factor plane. Some numerical examples support the above mentioned equivalence.