Vishnu Menon

Vishnu Menon, Gokularam M, Sheetal Kalyani

Subspace clustering, the task of clustering high dimensional data when the data points come from a union of subspaces is one of the fundamental tasks in unsupervised machine learning. Most of the existing algorithms for this task require prior knowledge of the number of clusters along with few additional parameters which need to be set or tuned apriori according to the type of data to be clustered. In this work, a parameter free method for subspace clustering is proposed, where the data points are clustered on the basis of the difference in statistical distribution of the angles subtended by the data points within a subspace and those by points belonging to different subspaces. Given an initial fine clustering, the proposed algorithm merges the clusters until a final clustering is obtained. This, unlike many existing methods, does not require the number of clusters apriori. Also, the proposed algorithm does not involve the use of an unknown parameter or tuning for one. %through cross validation. A parameter free method for producing a fine initial clustering is also discussed, making the whole process of subspace clustering parameter free. The comparison of proposed algorithm's performance with that of the existing state-of-the-art techniques in synthetic and real data sets, shows the significance of the proposed method.

Vishnu Menon, Sheetal Kalyani

Robust PCA, the problem of PCA in the presence of outliers has been extensively investigated in the last few years. Here we focus on Robust PCA in the outlier model where each column of the data matrix is either an inlier or an outlier. Most of the existing methods for this model assumes either the knowledge of the dimension of the lower dimensional subspace or the fraction of outliers in the system. However in many applications knowledge of these parameters is not available. Motivated by this we propose a parameter free outlier identification method for robust PCA which a) does not require the knowledge of outlier fraction, b) does not require the knowledge of the dimension of the underlying subspace, c) is computationally simple and fast d) can handle structured and unstructured outliers. Further, analytical guarantees are derived for outlier identification and the performance of the algorithm is compared with the existing state of the art methods in both real and synthetic data for various outlier structures.

Vishnu Menon, Sheetal Kalyani

Robust PCA, the problem of PCA in the presence of outliers has been extensively investigated in the last few years. Here we focus on Robust PCA in the column sparse outlier model. The existing methods for column sparse outlier model assumes either the knowledge of the dimension of the lower dimensional subspace or the fraction of outliers in the system. However in many applications knowledge of these parameters is not available. Motivated by this we propose a parameter free outlier identification method for robust PCA which a) does not require the knowledge of outlier fraction, b) does not require the knowledge of the dimension of the underlying subspace, c) is computationally simple and fast. Further, analytical guarantees are derived for outlier identification and the performance of the algorithm is compared with the existing state of the art methods.