Abstract: Twin support vector machine (TWSVM) is a recent hot spot in the field of machine learning.TWSVM achieves fast training speed and good performance for data classification.However,it does not take full advantage of the statistical information in training samples.As an improved algorithm of TWSVM,mahalanobis distance-based twin support vector machine (TMSVM) takes the covariance of each class of data into consideration and is suitable for many real problems.However,the learning speed of TMSVW remains to be improved.Moreover,the approach only deals with binary classification problems.To solve these problems,this paper formulated a least squares version of TMSVM by considering equality type constraints instead of inequalities of TMSVM,which makes the solution follow from solving a set of linear equations instead of quadratic programming,and extended the binary classier into a new multiclass classification algorithm with directed acyclic graph (DAG).In order to reduce error accumulation in DAG structure,a mahalanobis distance-based distance measure was designed as the class separability criterion.The experimental results on toy dataset and UCI datasets show that the proposed algorithm is efficient and has better classification accuracy than traditional multi-class SVM.

Key words: Twin support vector machine,Mahalanobis distance,Multi-class classification,Directed acyclic graph