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  <front>

    <journal-meta>

      <journal-title>Information Technology Journal</journal-title>

      <issn pub-type="ppub">1812-5638</issn>

      <issn pub-type="epub">1812-5646</issn>

      <publisher>

        <publisher-name>Asian Network for Scientific Information</publisher-name>

      </publisher>

    </journal-meta>


    <article-meta>

      <article-id pub-id-type="doi">10.3923/itj.2013.2333.2341</article-id>


      <title-group>

        <article-title><![CDATA[A Kernel Sparse Representation Method Based on Virtual Samples for Use with Face Recognition]]></article-title>

      </title-group>


      <contrib-group>

        <contrib contrib-type="author" xlink:type="simple">


          <name name-style="western">

            <surname>Tang</surname>

            <given-names>Ting</given-names>

          </name>


          <name name-style="western">

            <surname>Zhu</surname>

            <given-names>Ningbo</given-names>

          </name>


          <name name-style="western">

            <surname>Tang</surname>

            <given-names>Shi</given-names>

          </name>


        </contrib>

      </contrib-group>


      <pub-date pub-type="collection">




        <month>12</month>


        <year>2013</year>

      </pub-date>


      <volume>12</volume>

      <issue>12</issue>


      <abstract><![CDATA[<p>Recently, the sparse representation based classification has 
  been proved to be superior to conventional Face Recognition (FR) methods. Though 
  the sparse representation based classification can achieve striking recognition 
  performance, the classification accuracy still has room to grow. To improve 
  the accuracy of FR, a kernel sparse representation method based on virtual samples 
  (KSRVS) is devised here. It first generates virtual samples and then uses a 
  kernel-induced distance to perform FR. Because more training samples can provide 
  more useful information in representing the testing sample and the kernel-induced 
  distance can select the training samples that are truly &#147;near&#148; to 
  the testing sample, the final error ratios obtained using the KSRVS are lower 
  than various sparse representation methods such as the sparse representation 
  method based on virtual samples, kernel-based sparse representation method, 
  two-step test sample sparse representation and the feature space-based representation 
  method, collaborative representation based classification with regularized least 
  square.</p>]]></abstract>


    </article-meta>

  </front>


  <ref-list>




      <ref id="364048">

        <label>1</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Zhao, W., R. Chellappa, P.J. Phillips and A. Rosenfeld,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2003</year>

          <article-title><![CDATA[Face recognition: A literature survey.]]></article-title>

          <source>ACM Comput. Surv.,</source>

          <volume>35</volume>

          <fpage>399</fpage>

          <lpage>458</lpage>

        </citation>

      </ref>


















      <ref id="1148148">

        <label>2</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Xu, Y., A.N. Zhong, J.A. Yang and D. Zhang,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2010</year>

          <article-title><![CDATA[LPP solution schemes for use with face recognition.]]></article-title>

          <source>Pattern Recogn.,</source>

          <volume>43</volume>

          <fpage>4165</fpage>

          <lpage>4176</lpage>

        </citation>

      </ref>


















      <ref id="1148157">

        <label>3</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Yang, J., D. Zhang, X. Yong and J. Yang,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2005</year>

          <article-title><![CDATA[Two-dimensional discriminant transform for face recognition.]]></article-title>

          <source>Pattern Recognit.,</source>

          <volume>38</volume>

          <fpage>1125</fpage>

          <lpage>1129</lpage>

        </citation>

      </ref>


















      <ref id="1148163">

        <label>4</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Xu, Y., D. Zhang, H. Yang and J.Y. Yang,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2008</year>

          <article-title><![CDATA[An approach for directly extracting features from matrix data and its application in face recognition.]]></article-title>

          <source>Neurocomputing,</source>

          <volume>71</volume>

          <fpage>1857</fpage>

          <lpage>1865</lpage>

        </citation>

      </ref>


















      <ref id="1148168">

        <label>5</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Zhang, L., S. Chen and L. Qiao,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[Graph optimization for dimensionality reduction with sparsity constraints.]]></article-title>

          <source>Pattern Recognit.,</source>

          <volume>45</volume>

          <fpage>1205</fpage>

          <lpage>1210</lpage>

        </citation>

      </ref>


















      <ref id="1148175">

        <label>6</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Wang, S.J., J. Yang, M.F. Sun, X.J. Peng, M.M. Sun and C.G. Zhou,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[Sparse tensor discriminant color space for face verification]]></article-title>

          <source>IEEE Trans. Neural Networks Learn. Syst.,</source>

          <volume>23</volume>

          <fpage>876</fpage>

          <lpage>888</lpage>

        </citation>

      </ref>


















      <ref id="1148178">

        <label>7</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Pishchulin, L., T. Gass, P. Dreuw and H. Ney,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[Image warping for face recognition: From local optimality towards global optimization.]]></article-title>

          <source>Pattern Recognit.,</source>

          <volume>45</volume>

          <fpage>3131</fpage>

          <lpage>3140</lpage>

        </citation>

      </ref>


















      <ref id="1148183">

        <label>8</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Kautkar, S.N., G.A. Atkinson and M.L. Smith,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[Face recognition in 2D and 2.5D using ridgelets and photometric stereo.]]></article-title>

          <source>Pattern Recognit.,</source>

          <volume>45</volume>

          <fpage>3317</fpage>

          <lpage>3327</lpage>

        </citation>

      </ref>






















      <ref id="38937">

        <label>9</label>

        <citation citation-type="book" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Moon, H. and P.J. Phillips,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>1998</year>

          <article-title><![CDATA[Analysis of PCA-Based Face Recognition Algorithms.]]></article-title>

          <source>Analysis of PCA-Based Face Recognition Algorithms.</source>

          <volume>1998</volume>

          <fpage>pp: 57-71</fpage>

          <lpage>pp: 57-71</lpage>

        </citation>

      </ref>














      <ref id="895630">

        <label>10</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Sirovich, L. and M. Kirby,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>1987</year>

          <article-title><![CDATA[Low-dimensional procedure for the characterization of human faces.]]></article-title>

          <source>J. Opt. Soc. Am. A,</source>

          <volume>4</volume>

          <fpage>519</fpage>

          <lpage>524</lpage>

        </citation>

      </ref>


















      <ref id="646292">

        <label>11</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Kirby, M. and L. Sirovich,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>1990</year>

          <article-title><![CDATA[Application of the Karhunen-Loeve procedure for the characterization of human faces.]]></article-title>

          <source>IEEE Trans. Pattern Anal. Mach. Intell.,</source>

          <volume>12</volume>

          <fpage>103</fpage>

          <lpage>108</lpage>

        </citation>

      </ref>


















      <ref id="941297">

        <label>12</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Yang, J., D. Zhang, A.F. Frangi and J. Yang,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2004</year>

          <article-title><![CDATA[Two-dimensional PCA: A new approach to appearance-based face representation and recognition.]]></article-title>

          <source>IEEE Trans. Pattern Anal. Mach. Intell.,</source>

          <volume>26</volume>

          <fpage>131</fpage>

          <lpage>137</lpage>

        </citation>

      </ref>






























      <ref id="13331">

        <label>13</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Park, S.W. and M. Savvides,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2010</year>

          <article-title><![CDATA[A multifactor extension of linear discriminant analysis for face recognition under varying pose and illumination.]]></article-title>

          <source>Eurasip J. Adv. Sig. Process.,</source>

          <volume>2010</volume>

        </citation>

      </ref>






      <ref id="1148215">

        <label>14</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Li, M. and B.Z. Yuan,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2005</year>

          <article-title><![CDATA[2D-LDA: A statistical linear discriminant analysis for image matrix.]]></article-title>

          <source>Pattern Recognit. Lett.,</source>

          <volume>26</volume>

          <fpage>527</fpage>

          <lpage>532</lpage>

        </citation>

      </ref>






























      <ref id="13333">

        <label>15</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Xu, Y. and D. Zhang,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2010</year>

          <article-title><![CDATA[Represent and fuse bimodal biometric images at the feature level: Complex-matrix-based fusion scheme]]></article-title>

          <source>Opt. Eng., Vol. 49.</source>

          <volume>2010</volume>

        </citation>

      </ref>






      <ref id="1148434">

        <label>16</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Debruyne, M. and T. Verdonck,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2010</year>

          <article-title><![CDATA[Robust kernel principal component analysis and classification.]]></article-title>

          <source>Adv. Data Anal. Classification,</source>

          <volume>4</volume>

          <fpage>151</fpage>

          <lpage>167</lpage>

        </citation>

      </ref>
























      <ref id="53164">

        <label>17</label>

        <citation citation-type="conference" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Wang, X., J. Wang and C. Li,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[Studies on human face recognition based on greedy kernel principal component analysis.]]></article-title>

          <source>Proceedings of the 24th Chinese Control and Decision Conference,</source>

          <volume>2012</volume>

          <fpage>pp: 1446</fpage>

          <lpage>1449</lpage>

        </citation>

      </ref>


















      <ref id="53165">

        <label>18</label>

        <citation citation-type="conference" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Murthy, K.R. and A. Ghosh,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[An efficient illumination invariant face recognition technique using two dimensional linear discriminant analysis.]]></article-title>

          <source>Proceedings of the 1st International Conference on Recent Advances in Information Technology</source>

          <volume>2012</volume>

          <fpage>pp: 62</fpage>

          <lpage>67</lpage>

        </citation>

      </ref>












      <ref id="1148439">

        <label>19</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Wright, J., Y. Ma, J. Mairal, G. Sapiro, T.S. Huang and S. Yan,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2010</year>

          <article-title><![CDATA[Sparse representation for computer vision and pattern recognition]]></article-title>

          <source>Proc. IEEE,</source>

          <volume>98</volume>

          <fpage>1031</fpage>

          <lpage>1044</lpage>

        </citation>

      </ref>


















      <ref id="847933">

        <label>20</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Wright, J., A.Y. Yang, A. Ganesh, S.S. Sastry and Y. Ma,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2009</year>

          <article-title><![CDATA[Robust face recognition via sparse representation.]]></article-title>

          <source>IEEE Trans. Pattern Anal. Mach. Intell.,</source>

          <volume>31</volume>

          <fpage>210</fpage>

          <lpage>227</lpage>

        </citation>

      </ref>


















      <ref id="1148443">

        <label>21</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Lai, Z., M. Wan, Z. Jin and J. Yang,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2011</year>

          <article-title><![CDATA[Sparse two-dimensional local discriminant projections for feature extraction.]]></article-title>

          <source>Neurocomputing,</source>

          <volume>74</volume>

          <fpage>629</fpage>

          <lpage>637</lpage>

        </citation>

      </ref>






























      <ref id="13339">

        <label>22</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Tang, D., N. Zhu, Y. Fu, W. Chen and T. Tang,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[A novel sparse representation method based on virtual samples for face recognition]]></article-title>

          <source>Neural Comput. Appl.,</source>

          <volume>2012</volume>

        </citation>

      </ref>


















      <ref id="13340">

        <label>23</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Zhu, N.B. and S.T. Li,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[A novel kernel-based sparse representation method for face recognition.]]></article-title>

          <source>Neural Comput. Appl.,</source>

          <volume>2012</volume>

        </citation>

      </ref>






      <ref id="1148462">

        <label>24</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Xu, Y., D. Zhang, J. Yang and J.Y. Yang,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2011</year>

          <article-title><![CDATA[A two-step test sample sparse representation method for use with face recognition.]]></article-title>

          <source>IEEE Trans. Circuits Syst. Video Technol.,</source>

          <volume>21</volume>

          <fpage>1255</fpage>

          <lpage>1262</lpage>

        </citation>

      </ref>






























      <ref id="13343">

        <label>25</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Xu, Y., Z. Fan and Q. Zhu,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[Feature space-based human face image representation and recognition.]]></article-title>

          <source>Opt. Eng., Vol. 51.</source>

          <volume>2012</volume>

        </citation>

      </ref>






      <ref id="1148482">

        <label>26</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Xu, Y., W. Zuo and Z. Fan,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[Supervised sparse representation method with a heuristic strategy and face recognition experiments.]]></article-title>

          <source>Neurocomputing,</source>

          <volume>79</volume>

          <fpage>125</fpage>

          <lpage>131</lpage>

        </citation>

      </ref>


















      <ref id="1148473">

        <label>27</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Lu, C.Y., H. Min, J. Gui, L. Zhu and Y.K. Lei,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[Face recognition via weighted sparse representation.]]></article-title>

          <source>J. Visual Commun. Image Represent.,</source>

          <volume>24</volume>

          <fpage>111</fpage>

          <lpage>116</lpage>

        </citation>

      </ref>






























      <ref id="13344">

        <label>28</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Lai, Z., Y. Li, M. Wan and Z. Jing,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[Local sparse representation projections for face recognition]]></article-title>

          <source>Neural Comput. Appl.,</source>

          <volume>2012</volume>

        </citation>

      </ref>






      <ref id="1068365">

        <label>29</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Xu, Y., X. Zhu, Z. Li, G. Liu, Y. Lu and H. Liu,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2013</year>

          <article-title><![CDATA[Using the original and symmetrical face training samples to perform representation based two-step face recognition.]]></article-title>

          <source>Pattern Recognit.,</source>

          <volume>46</volume>

          <fpage>1151</fpage>

          <lpage>1158</lpage>

        </citation>

      </ref>


















      <ref id="1148480">

        <label>30</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Lai, Z., W.K. Wong, Z. Jin, J. Yang and Y. Xu,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[Sparse approximation to the eigensubspace for discrimination.]]></article-title>

          <source>IEEE Trans. Neural Networks Learn. Syst.,</source>

          <volume>23</volume>

          <fpage>1948</fpage>

          <lpage>1960</lpage>

        </citation>

      </ref>
























      <ref id="49775">

        <label>31</label>

        <citation citation-type="conference" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Zhang, L., M. Yang and X. Feng,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2011</year>

          <article-title><![CDATA[Sparse representation or collaborative representation: Which helps face recognition?]]></article-title>

          <source>Proceedings of the IEEE International Conference on Computer Vision,</source>

          <volume>2011</volume>

          <fpage>pp: 471</fpage>

          <lpage>478</lpage>

        </citation>

      </ref>












      <ref id="1148487">

        <label>32</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Yin, J., Z. Liu, Z. Jin and W. Yang,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[Kernel sparse representation based classification.]]></article-title>

          <source>Neurocomputing,</source>

          <volume>77</volume>

          <fpage>120</fpage>

          <lpage>128</lpage>

        </citation>

      </ref>


















      <ref id="1148513">

        <label>33</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Wagner, A., J. Wright, A. Ganesh, Z. Zihan, H. Mobahi and M. Yi,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[Toward a practical face recognition system: Robust alignment and illumination by sparse representation, pattern analysis and machine intelligence]]></article-title>

          <source>IEEE Trans. Pattern Anal. Mach. Intell.,</source>

          <volume>34</volume>

          <fpage>372</fpage>

          <lpage>386</lpage>

        </citation>

      </ref>


















      <ref id="1148523">

        <label>34</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Lai, J. and X. Jiang,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[Modular weighted global sparse representation for robust face recognition.]]></article-title>

          <source>IEEE Signal Process. Lett.,</source>

          <volume>19</volume>

          <fpage>571</fpage>

          <lpage>574</lpage>

        </citation>

      </ref>
























      <ref id="53166">

        <label>35</label>

        <citation citation-type="conference" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Yang, M., L. Zhang, D. Zhang and S. Wang,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[Relaxed collaborative representation for pattern classification.]]></article-title>

          <source>Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition,</source>

          <volume>2012</volume>

          <fpage>pp: 2224</fpage>

          <lpage>2231</lpage>

        </citation>

      </ref>
























      <ref id="13346">

        <label>36</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Yang, M., L. Zhang, J. Yang and D. Zhang,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[Regularized robust coding for face recognition]]></article-title>

          <source>IEEE Trans. Image Process.,</source>

          <volume>2012</volume>

        </citation>

      </ref>












      <ref id="53168">

        <label>37</label>

        <citation citation-type="conference" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Yang, S.Y., Y. Han and X.R. Zhang,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[A sparse kernel representation method for image classification.]]></article-title>

          <source>Proceedings of the International Joint Conference on Neural Networks,</source>

          <volume>2012</volume>

          <fpage>pp: 1</fpage>

          <lpage>7</lpage>

        </citation>

      </ref>


















      <ref id="33301">

        <label>38</label>

        <citation citation-type="conference" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Gao, S., I.W.H. Tsang and L.T. Chia,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2010</year>

          <article-title><![CDATA[Kernel sparse representation for image classification and face recognition.]]></article-title>

          <source>Proceedings of the 11th European Conference on Computer Vision: Part IV,</source>

          <volume>2010</volume>

          <fpage>pp: 1</fpage>

          <lpage>14</lpage>

        </citation>

      </ref>












      <ref id="1079169">

        <label>39</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Chen, S. and D. Zhang,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2004</year>

          <article-title><![CDATA[Robust image segmentation using FCM with spatial constraints based on new kernel-induced distance measure.]]></article-title>

          <source>IEEE Trans. Syst. Man Cybernet.,</source>

          <volume>34</volume>

          <fpage>1907</fpage>

          <lpage>1916</lpage>

        </citation>

      </ref>


















      <ref id="400853">

        <label>40</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Das, S. and S. Sil,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2010</year>

          <article-title><![CDATA[Kernel-induced fuzzy clustering of image pixels with an improved differential evolution algorithm.]]></article-title>

          <source>Inform. Sci.,</source>

          <volume>180</volume>

          <fpage>1237</fpage>

          <lpage>1256</lpage>

        </citation>

      </ref>


















      <ref id="1148530">

        <label>41</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Xu, Y., D. Zhang, Z. Jin, M. Li and J.Y. Yang,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2006</year>

          <article-title><![CDATA[A fast kernel-based nonlinear discriminant analysis for multi-class problems.]]></article-title>

          <source>Pattern Recogn.,</source>

          <volume>39</volume>

          <fpage>1026</fpage>

          <lpage>1033</lpage>

        </citation>

      </ref>
























      <ref id="53169">

        <label>42</label>

        <citation citation-type="conference" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Kang, C., S. Liao, S. Xiang and C. Pan,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2011</year>

          <article-title><![CDATA[Kernel sparse representation with local patterns for face recognition.]]></article-title>

          <source>Proceedings of the IEEE International Conference on Image Processing,</source>

          <volume>2011</volume>

          <fpage>pp: 3009</fpage>

          <lpage>3012</lpage>

        </citation>

      </ref>
























      <ref id="13347">

        <label>43</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Chen, Y., N.M. Nasrabadi and T.D. Tran,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2012</year>

          <article-title><![CDATA[Kernel sparse representation for hyperspectral target detection, algorithms and technologies for multispectral.]]></article-title>

          <source>Hyperspectral Ultraspectral Imagery, Vol. 18.</source>

          <volume>2012</volume>

        </citation>

      </ref>






      <ref id="1148560">

        <label>44</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Gundimada, S. and V.K. Asari,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2009</year>

          <article-title><![CDATA[Facial recognition using multisensor images based on localized kernel eigen spaces.]]></article-title>

          <source>IEEE Trans. Image Process.,</source>

          <volume>18</volume>

          <fpage>1314</fpage>

          <lpage>1325</lpage>

        </citation>

      </ref>


















      <ref id="1148563">

        <label>45</label>

        <citation citation-type="journal" xlink:type="simple">

          <person-group person-group-type="author">

            <name name-style="western">

              <surname>Xu, Y., J.Y. Yang, J. Lu and D. Yu,</surname>

              <given-names></given-names>

            </name>

          </person-group>

          <year>2004</year>

          <article-title><![CDATA[An efficient renovation on kernel Fisher discriminant analysis and face recognition experiments.]]></article-title>

          <source>Pattern Recognit.,</source>

          <volume>37</volume>

          <fpage>2091</fpage>

          <lpage>2094</lpage>

        </citation>

      </ref>
















  </ref-list>

</article>

