Semi-supervised distance metric learning based on local linear regression for data clustering

Distance metric plays an important role in many machine learning tasks. The distance between samples is mostly measured with a predefined metric, ignoring how the samples distribute in the feature space and how the features are correlated. This paper proposes a semi-supervised distance metric learning method by exploring feature correlations. Specifically, unlabeled samples are used to calculate the prediction error by means of local linear regression. Labeled samples are used to learn discriminative ability, that is, maximizing the between-class covariance and minimizing the within-class covariance. We then fuse the knowledge learned from both labeled and unlabeled samples into an overall objective function which can be solved by maximum eigenvectors. Our algorithm explores both labeled and unlabeled information as well as data distribution. Experimental results demonstrates the superiority of our method over several existing algorithms.