Sparse Support Matrix Machines for the Classification of Corrupted Data
- Publication Type:
- Thesis
- Issue Date:
- 2019
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Support matrix machine is fragile to the presence of outliers: even few corrupted data points can arbitrarily alter the quality of the approximation, What if a fraction of columns are corrupted? In real world, the data is noisy and most of the features may be redundant as well as may be useless, which in turn affect the classification performance. Thus, it is important to perform robust feature selection under robust metric learning to filter out redundant features and ignore the noisy data points for more interpretable modelling. To overcome this challenge, in this work, we propose a new model to address the classification problem of high dimensionality data by jointly optimizing the both regularizer and hinge loss. We combine the hinge loss and regularization terms as spectral elastic net penalty. The regularization term which promotes the structural sparsity and shares similar sparsity patterns across multiple predictors. It is a spectral extension of the conventional elastic net that combines the property of low-rank and joint sparsity together, to deal with complex high dimensional noisy data. We further extends this approach by combining the recovery along with feature selection and classification could significantly improve the performance based on the assumption that the data consists of a low rank clean matrix plus a sparse noise matrix. We perform matrix recovery, feature selection and classification through joint minimization of p,q-norm and nuclear norm under the incoherence and ambiguity conditions and able to recover intrinsic matrix of higher rank and recover data with much denser corruption. Although, above both methods takes full advantage of low rank assumption to exploit the strong correlation between columns and rows of each matrix and able to extract useful features, however, are originally built for binary classification problems. To improve the robustness against data that is rich in outliers, we further extend this problem and present a novel multiclass support matrix machine by utilizing the maximization of the inter-class margins (i.e. margins between pairs of classes). We demonstrate the significance and advantage of our methods on different available benchmark datasets such as person identification, face recognition and EEG classification. Results showed that our methods achieved significantly better performance both in terms of time and accuracy for solving the classification problem of highly correlated matrix data as compared to state-of-the-art methods.
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