A novel dictionary learning method based on total least squares approach with application in high dimensional biological data

In recent years dictionary learning has become a favorite sparse feature extraction technique. Dictionary learning represents each data as a sparse combination of atoms (columns) of the dictionary matrix. Usually, the input data is contaminated by errors that affect the quality of the obtained dictionary and so sparse features. This effect is especially critical in applications with high dimensional data such as gene expression data. Therefore, some robust dictionary learning methods have investigated. In this study, we proposed a novel robust dictionary learning algorithm, based on the total least squares, that could consider the inexactness of data in modeling. We confirm that standard and some robust dictionary learning models are the particular cases of our proposed model. Also, the results on various data indicate that our method performs better than other dictionary learning methods on high dimensional data.