The New and Computationally Efficient MIL-SOM Algorithm: Potential Benefits for Visualization and Analysis of a Large-Scale High-Dimensional Clinically Acquired Geographic Data

Table 2

Training parameters of standard SOM and MIL-SOM algorithms for experimental datasets.

Data points	Standard SOM	MIL-SOM	Standard SOM		MIL-SOM
	Elapsed time (s)	Elapsed time (s)	Qe	Te	Qe	Te
Childhood asthma data *
2000	5.406	1.016	2081	0.052	1064	0.019
4000	8.016	1.625	1780	0.032	1103	0.035
6000	10.75	2.094	1637	0.028	961	0.036
8000	12.75	2.797	1502	0.029	887	0.031
10000	18.547	3.922	1309	0.031	828	0.037
Adult asthma data *
1000	3.25	0.922	813	0.034	571	0.021
2000	5.61	1.094	635	0.007	467	0.039
3000	7.109	1.297	612	0.018	434	0.04
4000	7.875	1.563	537	0.015	416	0.031
4910	7.5	1.641	507	0.019	403	0.043
Randomly generated data *
2000	5.625	1.141	0.379	0.065	0.345	0.107
4000	7.813	1.516	0.374	0.059	0.338	0.127
6000	10.344	2.016	0.365	0.057	0.336	0.147
8000	12.672	2.828	0.347	0.065	0.322	0.141
10000	19.765	3.703	0.336	0.062	0.318	0.136
Blood lead levels data **
5000	12.435	2.018	2897.2	0.0032	2271.2	0.0094
10000	34.435	4.808	2110.7	0.0047	1947	0.0185
15000	40.134	7.748	2018.1	0.0074	1969.5	0.022
20000	33.193	10.418	1980.5	0.0057	1877.4	0.0214
24691	101.035	16.276	1826.8	0.0083	1712.9	0.0211

*Note. There was great improvement in map quality in terms of the quantization errors (Qe) for MIL-SOM for real-world datasets, but standard SOM appears to do better with the topological errors (Te), especially for the random dataset that is noisy. The initial neighborhood radii for the rough training phase and fine-tuning phase were set as max(m size)/4=5 and max(m size)/4)/4=1.25, respectively, until the fine-tuning radius reached 1, where max is the maximum value of the map size matrix. For all the datasets, the map size was (20 20), so max was 20. Some minor adjustments were initially made during the MIL-SOM training with respect to the specifications of map size, neighborhood radius, and the length of training to fine tune the training SOM parameters [40].
**Training parameters for the new training dataset—blood lead levels (BLLs). The results further confirm the trends reported in an earlier report [40].