Phantom: Prediction of Human Motion with Distributed Body Sensors - Prediction and Classification of Respiratory Motion - page 55

3.5.3 Comparison of Grouping Methods
with Other Techniques

To find out the best grouping numbers, we have evaluated several clustering
algorithms: k-means [ 33 ], spectral clustering [ 37 , 38 ], nonparametric Bayesian
inference [ 55 ], and EM algorithm [ 30 ]. To determine the quality of group number
hypothesis, we would like to show established metrics, i.e., Akaike's Information
Criterion (AIC) that provides a measure of model quality by simulating a statistical
model for model selection [ 56 ]. For this selection, we assume that the model errors
are normally and independently distributed and that the variance of the model
errors is unknown but equal for them all.
Let n be the number of training observations. The formula AIC can be
expressed as a simple function of the residual sum of squares (RSS), i.e.,
AIC ¼ 2k þ n ln RSS = n ð ½ , where k and RSS are the number of parameters in the

statistical model and the residual sum of squares ( P i ¼ 1 e i , e i : estimated residuals
for a candidate model), respectively (see Sect. 2.2 in [ 56 ]). Given any estimated
models, the model with the minimum value of AIC is the one to be preferred.
We set the number of training observations to n = 1,000 for all the datasets.
Table 3.3 shows the comparison of grouping number methods with AIC values.
We can notice that all of the methods except the spectral clustering method have
selected the identical grouping numbers: G = 3 for Chest datasets, G = 3 for
Head datasets, and G = 4 for Upper Body. Please note that all the grouping
number methods have the minimum AIC values for Chest (G = 3) and Upper
Body (G = 4) datasets. In Head datasets, there exists inconsistency among the

Table 3.3 Comparison of grouping number methods with AIC values

k-means Spectral clustering Nonparametric Bayesian EM algorithm

Chest G = 2 7444 7411 7346 7404

G = 3 7393 6328 6942 7379

G = 4 7608 6356 7523 7603

G = 5 7824 6977 7383 7550

G = 6 7674 7365 7662 7680

G = 7 7761 7177 7514 7497

Head G = 2 6272 6272 6284 6256

G = 3 6222 6314 5847 6220

G = 4 6783 6509 6500 6770

G = 5 6677 6455 6337 6305

G = 6 6427 6512 6325 6529

G = 7 6711 6471 6402 6530

Upper
body

G = 2 10874 10885 10760 10827

G = 3 11043 10967 10645 10780

G = 4 10809 10874 10617 10448

G = 5 10962 10928 10757 10928

G = 6 10941 10987 10938 10987

G = 7 11127 10901 10876 10861