Cheap vibramycin, In this continuing series, we explore the NMath Stats functions for performing cluster analysis in .NET. (For previous posts, Vibramycin chlamydia, see here.) The sample data set we're using classifies 89 single malt scotch whiskies on a five-point scale (0-4) for 12 flavor characteristics. To visualize the data set and clusterings, we make use of the free Microsoft Chart Controls for .NET, vibramycin for cats, which provide a basic set of charts. Vibramycin hyclate, In this post, we'll cluster the scotches based on "similarity" in the original 12-dimensional flavor space using k-means clustering. The k-means clustering method assigns data points into k groups such that the sum of squares from points to the computed cluster centers is minimized, vibramycin medication. In NMath Stats, class KMeansClustering performs k-means clustering, cheap vibramycin.

The algorithm used is that of Hartigan and Wong (1979):

• For each point, Vibramycin doxycycline, move it to another cluster if that would lower the sum of squares from points to the computed cluster centers.


• If a point is moved, immediately update the cluster centers of the two affected clusters.


• Repeat until no points are moved, or the specified maximum number of iterations is reached.

A KMeansClustering instance is constructed from a matrix or a dataframe containing numeric data, vibramycin tablets. Each row in the data set represents an object to be clustered. Vibramycin doxycycline hyclate, The Cluster() method clusters the data into the specified number of clusters. The method accepts either k, the number of clusters, vibramycin syrup, or a matrix of initial cluster centers:

• If k is given, a set of distinct rows in the data matrix are chosen as the initial centers using the algorithm specified by a KMeanClustering.Start enumerated value. By default, rows are chosen at random.


• If a matrix of initial cluster centers is given, comprare vibramycin online, k is inferred from the number of rows.

For example, Vibramycin dose, this C# code clusters the scotch data (loaded into a dataframe in Part I) into four clusters:

KMeansClustering km = new KMeansClustering(df);

int k = 4;

km.Cluster(k, KMeansClustering.Start.QuickCluster);

K-means clustering requires a set of starting cluster centers to initiate the iterative algorithm. By default, vibramycin chlamydia, rows are chosen at random from the given data. Vibramycin suspension, Here we employ the QuickCluster algorithm, similar to the SPSS QuickCluster function, for choosing the starting centers, doxycycline vibramycin. (The QuickCluster algorithm proceeeds as follows: If the distance between row r and its closest center is greater than the distance between the two closest centers (m, Order vibramycin, n), then r replaces m or n, whichever is closest to r, generic vibramycin. Otherwise, if the distance between row r and its closest center (q) is greater than the distance between q and its closest center, then row r replaces q.)

The Clusters property returns a ClusterSet object, which represents a collection of objects assigned to a finite number of clusters, cheap vibramycin. The following C# code prints out the members of each cluster:

ClusterSet cs = km.Clusters;

for (int i = 0; i < cs.NumberOfClusters; i++)

{

     Console.WriteLine("Cluster {0} contains:", Vibramycin dosage, i);

     int[] members = cs.Cluster(i);

     for (int j = 0; j < members.Length; j++)

     {

          Console.Write("{0} ", df.RowKeys[members[j]]);

     }

     Console.WriteLine("\n");

}

The output looks like this:

Cluster 0 contains:

Aberfeldy Aberlour Ardmore Auchroisk Balmenach Belvenie

BenNevis Benriach Benrinnes Benromach BlairAthol Craigallechie

Dailuaine Dalmore Deanston Edradour GlenKeith GlenOrd

Glendronach Glendullan Glenfarclas Glenlivet Glenrothes

Glenturret Knochando Linkwood Longmorn Macallan Mortlach

OldFettercairn RoyalLochnagar Scapa Strathisla

Cluster 1 contains:

Ardbeg Caol Ila Clynelish Lagavulin Laphroig Talisker
Cluster 2 contains:

AnCnoc Auchentoshan Aultmore Bladnoch Bunnahabhain

Cardhu Craigganmore Dalwhinnie Dufftown GlenElgin GlenGrant

GlenMoray GlenSpey Glenallachie Glenfiddich Glengoyne

Glenkinchie Glenlossie Inchgower Loch Lomond Mannochmore

Miltonduff Speyburn Speyside Strathmill Tamdhu Tamnavulin

Tobermory Tomintoul Tomore Tullibardine
Cluster 3 contains:

ArranIsleOf Balblair Bowmore Bruichladdich GlenDeveronMacduff

GlenGarioch GlenScotia Glenmorangie Highland Park Isle of Jura

Oban OldPulteney RoyalBrackla Springbank Teaninich Tomatin

To help visualize these clusters, we can once again plot the scotches in the plane formed by the first two principal components (see Part I), vibramycin uses, which collectively account for ~50% of the variance, Vibramycin uses, coloring the points based on cluster assignment.

Remember that although we've used dimension reduction (principal component analysis, in this case) to visualize the clustering, vibramycin suspension, the clustering itself was performed based on similarity in the original 12-dimensional flavor space, Vibramycin drug, not based on distance in this plane. Nonetheless, the clusters look pretty reasonable, vibramycin hyclate.

K-means clustering is very efficient for large data sets, Vibramycin syrup, but does require you to know the number of clusters, k, in advance, vibramycin chlamydia. Cheap vibramycin, Also, you have no control of the similarity metric used to cluster the objects (within-cluster sum of squares). In the next post in this series, Vibramycin doxycycline, we'll look at hierarchical cluster analysis, which constructs the entire hierarchical cluster tree, and allows you to specify the distance and linkage functions to use.

Ken

References

Hartigan, J.A. and Wong, M.A. (1979). A k-means clustering algorithm, cheap vibramycin. Algorithm AS136, Appl. Stat. 28, pp. 100–108.

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Tags: clustering, clustering .NET, clustering C#, k-means, k-means .NET, k-means C#

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