Sentence examples for minimal span function from inspiring English sources

We highlight the good performance of PQR sort for minimizing minimal span function for both the studied coefficients.

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.

If the objective is to optimize minimal span function (with simple matching or Jaccard coefficient), we identified three sub-cases: – For 100 × 100 matrices with noise ratio 0.1, the PQR sort returns the best results.

If the objective is to optimize minimal span function (with simple matching or Jaccard coefficient), we identified three sub-cases:  If the objective is to optimize the anti-Robinson function with Jaccard coefficient, Sugiyama returns the best reordering for both matrices.

In some situations, there is a clear winner in both criteria, for example, the PQR sort provides the best values for the minimal span function with simple matching coefficient in 100 × 100 matrices of the Rectnoise experiment, in the shortest execution time.

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'.

Given this, the evaluation software calculates the minimal span loss function and the anti-Robinson loss function AR(i) of the similarity matrices for evaluating the reordered matrix according to the selected coefficients.

Minimal span loss function is a sum of the coefficients of neighbor columns (or rows); lower values of this function represent a good matrix permutation in terms of local structures.

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.

The optimal span is the minimal span that best fits the polynomial function of the loess normalization.