Fix right candidate selection for large cluster refinement #20
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AHeise
reviewed
Sep 26, 2019
| @@ -139,7 +139,7 @@ private static double scoreClustering(final byte[] partitions, final double[][] | |||
| .mapToObj(i -> { | |||
| // reverse of Gaussian | |||
| int leftIndex = (int) (Math.sqrt(i + 0.25) - 0.5); | |||
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First error, it should be: int leftIndex = (int) (Math.sqrt(2 * i + 0.25) - 0.5);
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Explanation: Gaussian formula is i = n * (n + 1) / 2, with n is leftIndex
To solve: 0 = n^2 + n - 2 * i
AHeise
reviewed
Sep 26, 2019
| @@ -139,7 +139,7 @@ private static double scoreClustering(final byte[] partitions, final double[][] | |||
| .mapToObj(i -> { | |||
| // reverse of Gaussian | |||
| int leftIndex = (int) (Math.sqrt(i + 0.25) - 0.5); | |||
| int rightIndex = i - getNumEdges(leftIndex) + leftIndex; | |||
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Second error, it should just be int rightIndex = i - getNumEdges(leftIndex);
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Explanation: leftIndex and rightIndex should take all possible values where leftIndex > rightIndex and leftIndex < numNodes and rightIndex < numNodes.
i is a random edge < numEdges
leftIndex is the largest node, such that leftIndex * (leftIndex + 1) / 2 <= i
rightIndex is then the remainder.
Examples:
| i | leftIndex | rightIndex |
|---|---|---|
| 0 | 0 | 0 |
| 1 | 1 | 0 |
| 2 | 1 | 1 |
| 3 | 2 | 0 |
| 4 | 2 | 1 |
| 5 | 2 | 2 |
| 6 | 3 | 0 |
| 7 | 3 | 1 |
| 8 | 3 | 2 |
| 9 | 3 | 3 |
| 10 | 4 | 0 |
| 11 | 4 | 1 |
| 12 | 4 | 2 |
| 13 | 4 | 3 |
| 14 | 4 | 4 |
| 15 | 5 | 0 |
| 16 | 5 | 1 |
| 17 | 5 | 2 |
| 18 | 5 | 3 |
| 19 | 5 | 4 |
| 20 | 5 | 5 |
| 21 | 6 | 0 |
| 22 | 6 | 1 |
| 23 | 6 | 2 |
| 24 | 6 | 3 |
| 25 | 6 | 4 |
| 26 | 6 | 5 |
| 27 | 6 | 6 |
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After reverse-engineering the algorithm and trying to understand the equation for computing the right candidate, we came to the conclusion the index need to be halved. Before it was causing issues due to IndexOutOfBoundsExceptions for larger clusters.
Now the equation seems to be sound, at least a quick check with Wolfram Alpha prooves that we cannot run out of bounds anymore.
@AHeise Can you give it a short review, if we haven't broken something unintentionally?