Abstract
Dimensionality reduction, also called feature extraction, is an important issue in pattern recognition. However, many existing dimensionality reduction methods, such as principal component analysis, fail when there exist noises in data, especially for noise caused by outliers or corruption. Recently, a robust method, named low-rank embedding (LRE) is proposed, which uses the nuclear norm for characterizing the low rank structure hided in the data. However, one major limitation of the nuclear norm is that each singular value is treated equally, since the nuclear norm is defined as the sum of all singular values. Thus the rank function may not be well approximated in practice. To overcome this drawback, this paper presents a truncated nuclear norm based low rank embedding (Truncated-LRE). The truncated nuclear norm can approximate the rank function more accurately than nuclear norm. Experimental results show encouraging results of the proposed methods in comparison with the state-of-the-art matrix dimensionality reduction methods.
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Acknowledgments
This work is supported by the University Natural Science Fund of Jiangsu Province (Grant No. 16KJB520020), the National Key R&D Program (Grant No. 2017YFC0804002), the National Science Fund of China (Grant Nos. 61603192, 61772277, 61462064), and the Natural Science Fund of Jiangsu Province (Grant Nos. BK20161580, BK20171494).
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Zhang, F., Chang, H., Yang, G., Yang, Z., Wan, M. (2017). Truncated Nuclear Norm Based Low Rank Embedding. In: Zhou, J., et al. Biometric Recognition. CCBR 2017. Lecture Notes in Computer Science(), vol 10568. Springer, Cham. https://doi.org/10.1007/978-3-319-69923-3_76
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DOI: https://doi.org/10.1007/978-3-319-69923-3_76
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