Phantom: Prediction of Human Motion with Distributed Body Sensors - Prediction and Classification of Respiratory Motion - page 53

Given in Fig. 3.8 , we can notice that the higher the group number, the bigger the
iteration number; and the more even the group distribution probabilities of a
sample training data, the smaller the iteration number.

(2) Calculation of the Difference (D) of the Consecutive lLg-likelihood
with Non-collaborative Grouping

The objective of this Chapter is to find an optimal cluster number (G*) with the
consecutive log-likelihood functions ( 3.3 ) based on EM process. Figure 3.9 below
shows the difference (D(G)) of the consecutive log-likelihood functions, described
in Eq. ( 3.3 ). For example, when G = 2, we calculate all the log-likelihood functions
of EM operations, and then select the minimum as a representing value in Fig. 3.9 .
We iterate the same procedure with different group number (G = 2, …, 7) in the
three kinds of the motion data. We expect to find out, as described in Sect. 3.2.2 , the
minimum of D(G).
Given the results in Fig. 3.9 , we may select the group number G* for the three
datasets: 2, 4, or 6 for Chest; 2 or 3 for Head; and 2, 4, 5, or 6 for Upper Body. As the
group numbers are increased, the differences start to become drastically greater.
However, we cannot identify the least minimum number; for example, it is hard
to choose among 2, 4, 5, or 6 for Upper Body. Therefore, in the next experiment,
we will recalculate the difference (D ADT (G)) of the consecutive log-likelihood with
collaborative grouping.

(3) Calculation of the Difference (D) of the Consecutive Log-likelihood
with Collaborative Grouping

The objective of this Chapter is to find an optimal cluster number (G*) using
log-likelihood function with the adaptive posterior probability ( 3.8 ). Based on the
initial hyper-parameter (b y )( 3.4 ), we can calculate the adaptive (ADT) posterior
probability p ADT (y | z j ) and iterate E-step ( 3.6 ) and M-step ( 3.7 ) with a specific
group number (G).

Fig. 3.9 The difference
(D(G)) with non-
collaborative grouping

3000

Chest
Head
Upper Body

2500

2000

1500

1000

500

0

1 2 3 4 5 6 7

Group Number (G)