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dppb05 / nerf_c

Implementation of the NERF algorithm in C.
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Adequacy function using wrong distance matrix #1

Closed dppb05 closed 7 years ago

dppb05 commented 7 years ago

nerf.c Adequacy function should use global_dmatrix instead of dmatrix.

dppb05 commented 7 years ago

It is still unsure whether the objective function should indeed use the global_dmatrix, which is the relational matrix after the beta-transform was applied. [1] does not use the objective function as stop criterion although it suggests that it minimizes the same objective function as the OFCM algorithm.

[2] and [3] re-arrange the original RFCM, which NERF is based on, objective function, through some mathematical manipulation and suggest that the NERF uses the same objective function.

1 - Hathaway, Richard J., and James C. Bezdek. "NERF c-means: Non-Euclidean relational fuzzy clustering." Pattern recognition 27.3 (1994): 429-437. 2 - Hathaway, Richard J., John W. Davenport, and James C. Bezdek. "Relational duals of the c-means clustering algorithms." Pattern recognition 22.2 (1989): 205-212. 3 - Frigui, Hichem, Cheul Hwang, and Frank Chung-Hoon Rhee. "Clustering and aggregation of relational data with applications to image database categorization." Pattern Recognition 40.11 (2007): 3053-3068.

dppb05 commented 7 years ago

I believe it would not matter whether global_dmatrix or dmatrix is used, since the Adequacy value is used mainly (if not solely) as a stop criterion and, for a given iteration, it compares the current with the previous value, which means that the matrix used is a constant in this case.

Although, for the sake of consistency, I have come to the conclusion that the global_dmatrix should be used, since the relational matrix must be euclidean [1] and global_dmatrix is the dmatrix after the beta-transform is applied which causes the non-euclidean dmatrix to be euclidean.

1 - Hathaway, Richard J., John W. Davenport, and James C. Bezdek. "Relational duals of the c-means clustering algorithms." Pattern recognition 22.2 (1989): 205-212.