Proceedings of the
The Nineteenth International Conference on Computational Intelligence and Security (CIS 2023)
December 1 – 4, 2023, Haikou, China
Kernel Non-negative Matrix Factorization using Modified Cosine Similarity
1School of Mathematical Sciences, Shenzhen University, China /EADDRESS/2Guangdong Key Laboratory of Intelligent Information Processing, Shenzhen University, China.
ABSTRACT
Kernel-based non-negative matrix factorization (KNMF) methods mostly utilize the Frobenius norm to measure the loss of the matrix decomposition. However, Euclidean distance is sensitive to illumination variation for the images. To solve this problem, this paper presents a modified cosine metric-induced KNMF (CSKNMF) approach for nonlinear feature extraction. The modified cosine similarity-induced metric is invariant to the rotation and dilation of the data, which is beneficial for improving the performance of the KNMF algorithm. The proposed CSKNMF model is established in a polynomial kernel feature space. The update rules for the basis matrix and the feature matrix are acquired by means of the auxiliary function technique. The property of the auxiliary functions ensures the convergence of our CSKNMF algorithm. Several experiments are conducted using facial image data to reveal its good performance in the aspects of convergence, illumination variation, etc. The results also imply that the proposed CSKNMF algorithm outperforms all the compared algorithms.
Keywords: Non-negative matrix factorization, Face recognition, Cosine similarity induced metric.
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1School of Mathematical Sciences, Shenzhen University, China /EADDRESS/2Guangdong Key Laboratory of Intelligent Information Processing, Shenzhen University, China.
ABSTRACT
Kernel-based non-negative matrix factorization (KNMF) methods mostly utilize the Frobenius norm to measure the loss of the matrix decomposition. However, Euclidean distance is sensitive to illumination variation for the images. To solve this problem, this paper presents a modified cosine metric-induced KNMF (CSKNMF) approach for nonlinear feature extraction. The modified cosine similarity-induced metric is invariant to the rotation and dilation of the data, which is beneficial for improving the performance of the KNMF algorithm. The proposed CSKNMF model is established in a polynomial kernel feature space. The update rules for the basis matrix and the feature matrix are acquired by means of the auxiliary function technique. The property of the auxiliary functions ensures the convergence of our CSKNMF algorithm. Several experiments are conducted using facial image data to reveal its good performance in the aspects of convergence, illumination variation, etc. The results also imply that the proposed CSKNMF algorithm outperforms all the compared algorithms.
Keywords: Non-negative matrix factorization, Face recognition, Cosine similarity induced metric.
Download PDF