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In the particular case of single linkage clustering, a minimal spanning tree is constructed that provably minimizes this sum [ 21].
They are the Minimal Spanning Tree (MST) [30] and the Planar Maximally Filtered Graph (PMFG) [7].
The minimal spanning tree algorithm could be run on the nodes involving a multicast connection.
The minimal spanning tree is made for a Steiner tree with the minimum hop count.
The iteration continues until all the cycles are eliminated to obtain the resultant minimal spanning tree.
The minimal spanning tree problem is a popular problem of discrete optimization.
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We highlight the good performance of PQR sort for minimizing minimal span function for both the studied coefficients.
We found that PQR sort is an interesting method for minimizing minimal span loss functions based on Jaccard or simple matching coefficients, specially for a given pattern called Rectnoise with a noise ratio of 0.01 or 0.02 and a matrix size of 100 × 100 or 1,000 × 1,000.
We highlight that PQR sort provides good results if we want to minimize the minimal span loss function (and, therefore, to reveal local structures) calculated over similarity matrices whose coefficient is Jaccard or simple matching, specially for the Rectnoise pattern with noise ratio 0.01 or 0.02, as summarized in Subsection 'Summary of PQR sort contributions'.
If we aim to optimize the minimal span function (with any of the studied coefficients): If we aim to optimize the minimal span function (with any of the studied coefficients): – PQR sort provides the fastest and best results for 100 × 100 matrices; – PQR sort also returns the fastest and best results for 1,000 × 1,000 matrices whose noise ratio is 0.01 or 0.02.
The authors also refer to anti-Robinson and minimal span loss functions as available criteria for evaluating row and column permutations of these similarity matrices and, consequently, for evaluating the permutation of the data matrix itself.
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