Replace Floyd-Warshall with simpler approach #1
Conversation
Since the only possible distance between two neighboring cells is 1 and there is no such thing as unreachable node then there is no need in Floyd-Warshall. We know the shape of the grid and we can just calculate position of each node. Then we count number of steps needed to get to that node from each other node. This reduces complexity from O(n^3) to O(n^2). In my case of SOM with side 25 (625 nodes) that was an improvement from 4 minutes to 18 seconds (total algorithm time).
This is not true in general. The algorithm is designed to allow arbitrary networks as the "grid" for the SOM (e.g. if the user provides the grids. This is especially useful for evolving-grid SOM variants, but also includes higher dimensional rectilinear grids, etc.. Since the minimum-distances calculation doesn't happen very often (once, for non-evolving grids), this doesn't seem that important, but it might be worth converting the Floyd-Warshall algorithm to Cython eventually. On 19 August 2016 3:57:17 AM AEST, Ilya Kuzovkin [email protected] wrote:
Sent from my Android device with K-9 Mail. Please excuse my brevity. |
…scikit-learn#7838) * initial commit for return_std * initial commit for return_std * adding tests, examples, ARD predict_std * adding tests, examples, ARD predict_std * a smidge more documentation * a smidge more documentation * Missed a few PEP8 issues * Changing predict_std to return_std #1 * Changing predict_std to return_std scikit-learn#2 * Changing predict_std to return_std scikit-learn#3 * Changing predict_std to return_std final * adding better plots via polynomial regression * trying to fix flake error * fix to ARD plotting issue * fixing some flakes * Two blank lines part 1 * Two blank lines part 2 * More newlines! * Even more newlines * adding info to the doc string for the two plot files * Rephrasing "polynomial" for Bayesian Ridge Regression * Updating "polynomia" for ARD * Adding more formal references * Another asked-for improvement to doc string. * Fixing flake8 errors * Cleaning up the tests a smidge. * A few more flakes * requested fixes from Andy * Mini bug fix * Final pep8 fix * pep8 fix round 2 * Fix beta_ to alpha_ in the comments
2 participants
Since the only possible distance between two neighboring cells is 1 and there is no such thing as unreachable node then there is no need in Floyd-Warshall. We know the shape of the grid and we can just calculate position of each node. Then we count number of steps needed to get to that node from each other node. This reduces complexity from O(n^3) to O(n^2). In my case of SOM with side 25 (625 nodes) that was an improvement from 4 minutes to 18 seconds (total algorithm time).