Online robust dictionary learning with density-based outlier weighing

Online outlier detection is fundamental for expediting the processing of data and focusing processing resources on portions of data that may be most informative. This work develops online robust dictionary learning algorithms that are able to identify outliers in the training data. The algorithms are based on lasso updates for computing the vector of expansion coefficients for a new training vector and gradient descent updates for updating the dictionary. An outlier is identified based on the so-called outlier vector. The weight associated with the group lasso regularizer that encourages an outlier vector to be set to zero is computed based on the outlierness score of the corresponding training data vector. Outlier vectors are thus more likely to be nonzero if they feature a high outlierness score. Outlierness scores are obtained from density-based outlier detection algorithms and help to enhance the selection of outliers. Both soft and hard outlier removal algorithms are developed. In the latter case, outliers are identified and a residual obtained after removing the outlier contribution is used to update the dictionary. The performance of the proposed algorithms is illustrated via numerical experiments on real video data.