Examples provided are the standard Mnist-digits and Mnist-fashion.
The coreset points, with their weights attached are clustered by our simplistic kmedoid algorithm.
The cost of clustering with these centers is then compared with the cost of clustering the whole original data obtained
with the crate kmedoids using the parallel par_fastermap.
The computation times, in seconds, given are system time elapsed and total cpu times (to account for parallelism)
The size of the coreset was set 0.11 * the number of data points. We asked 10 clusters.
We give the cost of clustering the coreset and the cost (of dispatching a posteriori the whole original data to the medoids position obtained via coreset clustering.
As the results are random we give they are given in the form (mean +-standard deviation) obtained on a sample of 20 computations.
The timings takes into account the computing of the distance matrix (fully multithreaded).
| mnist | cost | time(sys) s | time(cpu) s |
|---|---|---|---|
| digits | 1.789 10^6 | 55 | 1660 |
| fashion | 2.181 10^6 | 53 | 1460 |
| mnist | cost (coreset) | cost (whole data) | time(sys) s | time(cpu) s |
|---|---|---|---|---|
| digits | (1.864 +- 0.025) 10^6 | (1.873 +- 0.022) 10^6 | 1 | 14 |
| fashion | (2.250 +- 0.041) 10^6 | (2.255 +- 0.043) 10^6 | 1 | 14 |
The results are, on the average at less than 5% above the reference cost obtained by par_fastermap, and consistently within 8% at 2 std deviations.
| mnist | cost (coreset) | cost (whole data) | time(sys) s | time(cpu) s |
|---|---|---|---|---|
| digits | (1.868 +- 0.021) 10^6 | (1.876 +- 0.021) 10^6 | 1.1 | 16 |
| fashion | (2.230 +- 0.026) 10^6 | (2.239 +- 0.022) 10^6 | 1.1 | 16 |
The results are slightly better in the fashion case with 2.6% of overestimation of the cost compared with par_fastermap. The results are, on the average less than 5% above the reference cost obtained by par_fastermap, and within 8% at 3 std deviations.