Classification approach based on non-negative least squares

A non-negative least squares classifier is proposed in this paper for classifying under-complete data. The idea is that unknown samples can be approximated by sparse non-negative linear combinations of few training samples. Based on sparse coefficient vectors representing the training data, a sparse interpreter can then be used to predict the class label. We have devised new sparse methods which can learn data containing missing value, which can be trained on over-complete data, and which also apply to tensor data and to multi-class data. Permutation test shows that our approach requires a small number of training samples to obtain significant accuracy. Statistical comparisons on various data shows that our methods perform as well as support vector machines while being faster. Our approach is very robust to missing values and noise. We also show that with appropriate kernel functions, our methods perform very well on three-dimensional tensor data and run fairly fast.