Adaptive second order self-organizing mapping for 2D pattern representation

The problem of unsupervised classifying a set data and identifying the natural principal direction of each class at the same time is studied. A new adaptive unsupervised learning model called adaptive second order self-organizing map (ASOSOM) is proposed for this problem. ASOSOM combines the advantages of the self-organizing mapping with Karhunen-Loeve (KL) transformation. Instead of having one neuron representing each class, an additional neuron is introduced to cooperate with the class neuron for identifying the principal direction. Furthermore, a new performance measurement based on the co-variance between the natural principal direction and its perpendicular direction is introduced. This new model is applied to several applications and the obtained results are better than KL and MKL transformations.