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<group> |
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<p><b>VLFeat</b> offers a hierarchical version of integer k-means, which |
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recursively applies <code>vl_ikmeans</code> to compute finer and finer |
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partitions. For more details see |
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<a href="%pathto:root;api/hikmeans_8h.html">Hierarchical Integer |
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k-means API reference</a> and the <a href="%pathto:tut.ikm;">Integer |
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k-means tutorial</a>. |
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</p> |
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<ul> |
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<li><a href="%pathto:tut.hikm.usage;">Usage</a></li> |
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<li><a href="%pathto:tut.hikm.tree;">Tree structure</a></li> |
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<li><a href="%pathto:tut.hikm.elkan;">Elkan</a></li> |
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</ul> |
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<h1 id="tut.hikm.usage">Usage</h1> |
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<p>First, we generate some random data to cluster in <code>[0,255]^2</code>:</p> |
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<pre> |
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data = uint8(rand(2,10000) * 255) ; |
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datat = uint8(rand(2,100000)* 255) ; |
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</pre> |
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<p>To cluster this data, we simply use <code>vl_hikmeans</code>:</p> |
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<pre> |
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K = 3 ; |
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nleaves = 100 ; |
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[tree,A] = vl_hikmeans(data,K,nleaves) ; |
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</pre> |
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<p>Here <code>nleaves</code> is the desired number of leaf |
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clusters. The algorithm terminates when there are at least |
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<code>nleaves</code> nodes, creating a tree with <code>depth = |
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floor(log(K nleaves))</code></p> |
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<p>To assign labels to the new data, we use <code>vl_hikmeanspush</code>:</p> |
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<pre> |
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AT = vl_hikmeanspush(tree,datat) ; |
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</pre> |
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<div class="figure"> |
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<image src="%pathto:root;demo/hikmeans-tree.jpg"/> |
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<image src="%pathto:root;demo/hikmeans-clusters.jpg"/> |
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<div class="caption"> |
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<span class="content"> |
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<b>Hierarchical integer K-means.</b> Left: A depiction of the |
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recursive clusters. Each node is a cluster center. The root note is |
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not depicted (its center would be the mean of the dataset). Right: |
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Clusters are represented as different colors (here are more than 100 |
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clusters, but only three colors are used). |
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</span> |
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</div> |
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</div> |
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<h1 id="tut.hikm.tree">Tree structure</h1> |
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<p>The output <code>tree</code> is a MATLAB structure representing the tree of |
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clusters:</p> |
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<pre> |
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> tree |
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tree = |
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K: 3 |
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depth: 5 |
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centers: [2x3 int32] |
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sub: [1x3 struct] |
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</pre> |
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<p>The field <code>centers</code> is the matrix of the cluster centers at the |
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root node. If the depth of the tree is larger than 1, then the field |
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<code>sub</code> is a structure array with one entry for each cluster. Each |
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element is in turn a tree:</p> |
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<pre> |
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> tree.sub |
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ans = |
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1x3 struct array with fields: |
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centers |
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sub |
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</pre> |
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<p>with a field <code>centers</code> for its clusters and a field |
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<code>sub</code> for its children. When there are no children, this |
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field is equal to the empty matrix</p> |
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<pre> |
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> tree.sub(1).sub(1).sub(1).sub(1) |
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ans = |
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centers: [2x3 int32] |
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sub: [] |
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</pre> |
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<h1 id="tut.hikm.elkan">Elkan</h1> |
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<p>VLFeat supports two different implementations of k-means. While they |
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produce identical output, the Elkan method is sometimes faster. |
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The <code>method</code> parameters controls which method is used. Consider the case when <code>K=10</code> and our data is now 128 dimensional (e.g. SIFT descriptors):</p> |
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<pre> |
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K=10; |
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nleaves = 1000; |
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data = uint8(rand(128,10000) * 255); |
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tic; |
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[tree,A] = vl_hikmeans(data,K,nleaves,'method', 'lloyd') ; % default |
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t_lloyd = toc |
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tic; |
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[tree,A] = vl_hikmeans(data,K,nleaves,'method', 'elkan') ; |
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t_elkan = toc |
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t_lloyd = |
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8.0743 |
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t_elkan = |
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3.0427 |
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</pre> |
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</group> |
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