A Trimmed Clustering-Based l1-Principal Component Analysis Model for Image Classification and Clustering Problems with Outliers
Department of Mathematics and Statistics, The Hang Seng University of Hong Kong, Hong Kong, China
Author to whom correspondence should be addressed.
Received: 4 February 2019 / Revised: 1 April 2019 / Accepted: 10 April 2019 / Published: 15 April 2019
PDF [1998 KB, uploaded 23 April 2019]
Different versions of principal component analysis (PCA) have been widely used to extract important information for image recognition and image clustering problems. However, owing to the presence of outliers, this remains challenging. This paper proposes a new PCA methodology based on a novel discovery that the widely used
-PCA is equivalent to a two-groups
-means clustering model. The projection vector of the
-PCA is the vector difference between the two cluster centers estimated by the clustering model. In theory, this vector difference provides inter-cluster information, which is beneficial for distinguishing data objects from different classes. However, the performance of
-PCA is not comparable with the state-of-the-art methods. This is because the
-PCA can be sensitive to outliers, as the equivalent clustering model is not robust to outliers. To overcome this limitation, we introduce a trimming function to the clustering model and propose a trimmed-clustering based
-PCA (TC-PCA). With this trimming set formulation, the TC-PCA is not sensitive to outliers. Besides, we mathematically prove the convergence of the proposed algorithm. Experimental results on image classification and clustering indicate that our proposed method outperforms the current state-of-the-art methods.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
Share & Cite This Article
MDPI and ACS Style
Lam, B.S.Y.; Choy, S.K. A Trimmed Clustering-Based l1-Principal Component Analysis Model for Image Classification and Clustering Problems with Outliers. Appl. Sci. 2019, 9, 1562.
Lam BSY, Choy SK. A Trimmed Clustering-Based l1-Principal Component Analysis Model for Image Classification and Clustering Problems with Outliers. Applied Sciences. 2019; 9(8):1562.
Lam, Benson S.Y.; Choy, S. K. 2019. "A Trimmed Clustering-Based l1-Principal Component Analysis Model for Image Classification and Clustering Problems with Outliers." Appl. Sci. 9, no. 8: 1562.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
For more information on the journal statistics, click here
Multiple requests from the same IP address are counted as one view.