Robust and Efficient Subspace Segmentation via Least Squares Regression
This work addresses the subspace segmentation problem for data analysis, offering a more robust and efficient solution compared to existing methods, though it is incremental as it builds on prior objective function frameworks.
The paper tackles subspace segmentation by proposing a Least Squares Regression (LSR) method that leverages data correlation to group highly correlated data, achieving significant improvements in segmentation accuracy and efficiency on the Hopkins 155 and Extended Yale Database B benchmarks.
This paper studies the subspace segmentation problem which aims to segment data drawn from a union of multiple linear subspaces. Recent works by using sparse representation, low rank representation and their extensions attract much attention. If the subspaces from which the data drawn are independent or orthogonal, they are able to obtain a block diagonal affinity matrix, which usually leads to a correct segmentation. The main differences among them are their objective functions. We theoretically show that if the objective function satisfies some conditions, and the data are sufficiently drawn from independent subspaces, the obtained affinity matrix is always block diagonal. Furthermore, the data sampling can be insufficient if the subspaces are orthogonal. Some existing methods are all special cases. Then we present the Least Squares Regression (LSR) method for subspace segmentation. It takes advantage of data correlation, which is common in real data. LSR encourages a grouping effect which tends to group highly correlated data together. Experimental results on the Hopkins 155 database and Extended Yale Database B show that our method significantly outperforms state-of-the-art methods. Beyond segmentation accuracy, all experiments demonstrate that LSR is much more efficient.