Recursive Sample Scaling Low-Rank Representation

Abstract

The low-rank representation (LRR) method has recently gained enormous popularity due to its robust approach in solving the subspace segmentation problem, particularly those concerning corrupted data. In this paper, the recursive sample scaling low-rank representation (RSS-LRR) method is proposed. The advantage of RSS-LRR over traditional LRR is that a cosine scaling factor is further introduced, which imposes a penalty on each sample to minimize noise and outlier influence better. Specifically, the cosine scaling factor is a similarity measure learned to extract each sample’s relationship with the low-rank representation’s principal components in the feature space. In order words, the smaller the angle between an individual data sample and the low-rank representation’s principal components, the more likely it is that the data sample is clean. Thus, the proposed method can then effectively obtain a good low-rank representation influenced mainly by clean data. Several experiments are performed with varying levels of corruption on ORL, CMU PIE, COIL20, COIL100, and LFW in order to evaluate RSS-LRR’s effectiveness over state-of-the-art low-rank methods. The experimental results show that RSS-LRR consistently performs better than the compared methods in image clustering and classification tasks.

Robust Spectral Clustering via Low-Rank Sample Representation

“…In contrast, the nuclear norm regularization approach was proposed in [7] to capture a global data structure, thus providing some robustness against noise and possible outliers. us, the second category contains methods like those in [6,9,11,[15][16][17][18][19][20][21][22][23][24], which apply the aforementioned nuclear norm technique to learn the coefficient matrix. Illustratively, the LapLRR method was proposed in [9] based on the nuclear norm.…”

“…(5) Update U by equation ( 21); (6) Update F by equation (22); Applied Computational Intelligence and Soft Computing were performed on COIL20 (https://www.cs.columbia.edu/ CAVE/software/softlib/coil-20.php), UCI (https://archive. ics.uci.edu/ml/datasets/ Optical+Recognition+of+Handwritten+Digits), ORL (http://cam-orl.co.uk/facedatabase.html), FERET (https:// www.nist.gov/itl/products-and-services/color-FERETdatabase), and BBC (http://mlg.ucd.ie/datasets/segment.…”