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Date: Wed, 12 Apr 2017 00:13:41 +0000 (UTC)
From: "Rob Tompkins (JIRA)" <jira@apache.org>
To: issues@commons.apache.org
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Subject: [jira] [Updated] (MATH-1378) KMeansPlusPlusClusterer optimize
 seeding procedure, by computing sum of squared distances outside the loop.
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archived-at: Wed, 12 Apr 2017 00:13:52 -0000


     [ https://issues.apache.org/jira/browse/MATH-1378?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]

Rob Tompkins updated MATH-1378:
-------------------------------
    Fix Version/s: 4.0

> KMeansPlusPlusClusterer optimize seeding procedure, by computing sum of squared distances outside the loop.
> -----------------------------------------------------------------------------------------------------------
>
>                 Key: MATH-1378
>                 URL: https://issues.apache.org/jira/browse/MATH-1378
>             Project: Commons Math
>          Issue Type: Improvement
>            Reporter: Artem Barger
>            Assignee: Artem Barger
>             Fix For: 4.0
>
>         Attachments: MATH-1378.patch
>
>
> Currently in KMeansPlusPlusClusterer class,  function which implements initial clusters seeding *chooseInitialCenters*, has following computation executed inside the while loop cycle:
> {code}
>         while (resultSet.size() < k) {
>             // Sum up the squared distances for the points in pointList not
>             // already taken.
>             double distSqSum = 0.0;
>             for (int i = 0; i < numPoints; i++) {
>                 if (!taken[i]) {
>                     distSqSum += minDistSquared[i];
>                 }
>             }
> // Rest skipped for simplicity
> {code}
> While computation of this sum could be produced once outside the loop and latter adjusted according to the values of minimum distances to the centers set. E.g.:
> {code}
>         // Sum up the squared distances for the points in pointList not
>         // already taken.
>         double distSqSum = 0.0;
>         // There is no need to compute sum of squared distances within the "while" loop
>         // we can compute initial value ones and maintain deltas in the loop.
>         for (int i = 0; i < numPoints; i++) {
>             if (!taken[i]) {
>                 distSqSum += minDistSquared[i];
>             }
>         }
>         while (resultSet.size() < k) {
>             // Add one new data point as a center. Each point x is chosen with
>             // probability proportional to D(x)2
>             final double r = random.nextDouble() * distSqSum;
>             // The index of the next point to be added to the resultSet.
>             int nextPointIndex = -1;
>             // Sum through the squared min distances again, stopping when
>             // sum >= r.
>             double sum = 0.0;
>             for (int i = 0; i < numPoints; i++) {
>                 if (!taken[i]) {
>                     sum += minDistSquared[i];
>                     if (sum >= r) {
>                         nextPointIndex = i;
>                         break;
>                     }
>                 }
>             }
>             // If it's not set to >= 0, the point wasn't found in the previous
>             // for loop, probably because distances are extremely small.  Just pick
>             // the last available point.
>             if (nextPointIndex == -1) {
>                 for (int i = numPoints - 1; i >= 0; i--) {
>                     if (!taken[i]) {
>                         nextPointIndex = i;
>                         break;
>                     }
>                 }
>             }
>             // We found one.
>             if (nextPointIndex >= 0) {
>                 final T p = pointList.get(nextPointIndex);
>                 resultSet.add(new CentroidCluster<T> (p));
>                 // Mark it as taken.
>                 taken[nextPointIndex] = true;
>                 if (resultSet.size() < k) {
>                     // Now update elements of minDistSquared.  We only have to compute
>                     // the distance to the new center to do this.
>                     for (int j = 0; j < numPoints; j++) {
>                         // Only have to worry about the points still not taken.
>                         if (!taken[j]) {
>                             double d = distance(p, pointList.get(j));
>                             // Subtracting the old value.
>                             distSqSum -= minDistSquared[j];
>                             // Update minimum distance.
>                             minDistSquared[j] = FastMath.min(d*d, minDistSquared[j]);
>                             // Adjust the overall sum of squared distances.
>                             distSqSum += minDistSquared[j];
>                         }
>                     }
>                 }
>             } else {
>                 // None found --
>                 // Break from the while loop to prevent
>                 // an infinite loop.
>                 break;
>             }
>         }
> {code}


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