A particular Gaussian mixture model for clustering and its ...
A particular Gaussian mixture model for clustering and its ...
A particular Gaussian mixture model for clustering and its ...
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A <strong>particular</strong> <strong>Gaussian</strong> <strong>mixture</strong> <strong>model</strong> <strong>for</strong> <strong>clustering</strong> <strong>and</strong> <strong>its</strong> application to image retrievalTable 3 This table shows the distribution of the categories (ground truth) through the clusters on the Olivetti set using our <strong>clustering</strong> algorithmCategories 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Totalclusters1 9 . . . . . . . . . . . . . . . . . . . 92 . 10 . . 1 3 . . . 1 . . . . . . . . 3 . 183 . . 10 . . . . . . . . . . . . . . 5 . . 154 . . . 10 . . . . 3 . . . . . . . 2 . . . 155 . . . . 9 . . . . . . . . . . . . . . 1 106 . . . . . . 5 . . . . . . . . . . . . . 57 . . . . . . . . 5 . 2 . . . . . . . . . 78 . . . . . 1 . . . 9 . . . . . . . . . 2 129 . . . . . . . . . . 3 . . . . . . . . . 310 1 . . . . . . . . . . 4 5 . 2 . . . . . 1211 . . . . . . . . . . 5 . . . . . . . . . 512 . . . . . . . . . . . 6 3 . . . . . . . 913 . . . . . . . . . . . . 2 10 . 1 . . . . 1314 . . . . . 1 . . . . . . . . 8 . . . . . 915 . . . . . 1 . . . . . . . . . 9 . . . . 1016 . . . . . 4 1 2 2 . . . . . . . 8 2 . . 1917 . . . . . . . . . . . . . . . . . 3 . 5 818 . . . . . . 4 . . . . . . . . . . . 7 . 1119 . . . . . . . . . . . . . . . . . . . 2 2Total 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10We can see that this distribution is concentrated near the diagonal. The scale parameter σ is set to 24 <strong>and</strong> C = 30. Errors in the cardinality of theclusters are mentioned in boldTable 4 This table shows the distribution of the categories through the clusters on the Columbia set using our <strong>clustering</strong> algorithmCategories 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Totalclusters1 72 . . . . . . . . . . . . . . 722 . 72 . . . . . . . . . . . . . 723 . . 72 . . . . . . . . . . . . 724 . . . 72 . . . . . . . . . . . 725 . . . . 72 . . . . . . . . . . 726 . . . . . 37 . 34 . . . . . . . 717 . . . . . 35 . 38 . . . . . . . 738 . . . . . . 72 . . . . . . . . 729 . . . . . . . . 72 . . . . . . 7210 . . . . . . . . . 72 . . . . . 7211 . . . . . . . . . . 72 . . . . 7212 . . . . . . . . . . . 72 . . . 7213 . . . . . . . . . . . . 30 . . 3014 . . . . . . . . . . . . 42 72 72 186Total 72 72 72 72 72 72 72 72 72 72 72 72 72 72 72We can see that this distribution is concentrated near the diagonal. The scale σ is set to 0.4<strong>and</strong>C = 20. Errors in the cardinality of the clusters arementioned in boldthe expense of few interactions <strong>and</strong> reasonable ef<strong>for</strong>t fromthe user.Figure 5 shows that this heuristic provides “good guess” ofthe scale on the Olivetti <strong>and</strong> Columbia sets as it is close to theoptimal scale shown in Fig. 6. Indeed, the estimated scale inFig. 5 is approximately 24 <strong>and</strong> 0.4 <strong>for</strong>, respectively, Olivetti<strong>and</strong> Columbia sets. For these scales, the number of clustersfound by our algorithm on Olivetti <strong>and</strong> Columbia (resp. 19123