**4.3.2 Outlier analysis in orbital stability**

Because of the errors of computing, maybe there are few outliers in the features of orbital stability. For an example, the last 3 cycles of the displacement of right hip (p10) at vertical is shown in Fig. 25. There is an outlier in the last cycle, the left maximum point should be found instead of the right maximum point.

There are a variety of outlier detection approaches from several areas, including statistics, machine learning, and data mining. A kind of proximity-based outlier detection approach, called distance to k-nearest neighbor, is used to find the outliers in orbital stability. This approach is more general and more easily applied than statistical approached, since it is easier to determine a meaningful proximity measure for a data set than to determine its statistics distribution.

Fig. 24. Last 3 cycles of the displacement of right hip (p10) at vertical

Fig. 25 shows the outliers in the displacement of right hip (p10). The points with a circle are the outlier point. The outlier score of an object is given by the distance to its k-nearest neighbor, using a value of k = 5.

Fig. 25. Outliers in the displacement of right hip

#### **4.3.3 Effects of aging on orbital stability**

After analysis all subjects between 20 to 70 years old, the item results of orbital stability are shown in Fig. 26. The position stability *FS(P),* segment stability *FS(S),* joint stability *FS(J)* and the whole orbital stability are in shown in Fig. 27. It is observed that, although each of orbital variability does not increase strictly with age, the variability of orbital features increases with age generally. As persons grow old, the orbital stability is becoming weakly.

Fig. 26. Each item of orbital stability with age

Because of the errors of computing, maybe there are few outliers in the features of orbital stability. For an example, the last 3 cycles of the displacement of right hip (p10) at vertical is shown in Fig. 25. There is an outlier in the last cycle, the left maximum point should be

There are a variety of outlier detection approaches from several areas, including statistics, machine learning, and data mining. A kind of proximity-based outlier detection approach, called distance to k-nearest neighbor, is used to find the outliers in orbital stability. This approach is more general and more easily applied than statistical approached, since it is easier to determine a meaningful proximity measure for a data set than to determine its

\* \* \* \*

Fig. 25 shows the outliers in the displacement of right hip (p10). The points with a circle are the outlier point. The outlier score of an object is given by the distance to its k-nearest

After analysis all subjects between 20 to 70 years old, the item results of orbital stability are shown in Fig. 26. The position stability *FS(P),* segment stability *FS(S),* joint stability *FS(J)* and the whole orbital stability are in shown in Fig. 27. It is observed that, although each of orbital variability does not increase strictly with age, the variability of orbital features increases with age generally. As persons grow old, the orbital stability is

Fig. 24. Last 3 cycles of the displacement of right hip (p10) at vertical

**4.3.2 Outlier analysis in orbital stability** 

found instead of the right maximum point.

statistics distribution.

neighbor, using a value of k = 5.

Fig. 25. Outliers in the displacement of right hip

**4.3.3 Effects of aging on orbital stability** 

becoming weakly.

Fig. 27. Position stability, segment stability and joint stability, and orbital stability with age

#### **4.4 Dynamic stability based on dynamic time warping (DTW)**

Dynamic stability is the main reason for leading to falls for people, especially for elders. This section discusses age influence on dynamic stability based on dynamic time warping.

Human Walking Analysis, Evaluation and Classification Based on Motion Capture System 383

<sup>1</sup> ( ,) () *m*

where *m* is the number of subjects in the same age class, *lk* is the average leg length of subjects in the same age class, *Dj(Si)* is similarity value of the selected feature *i* by Equation (14), is a single stability value of the same feature *i* in the same age class *Ak*, and *k* is the

According to Equation (14), similarity value of all selected features in the same age group

1 ( ) ( ,) *p k ki i FA SA S* 

This figure tells us that if all dynamic features are employed to do statistics on such kind of stability, the dynamic stability is decreasing with ageing except the twenties. It seems that

The previous section did statistic on all 57 dynamic stability. To reduce the computational complexity, and more importantly, to get more important and contributing features, this paper did feature selection on those 57 dynamic features. On the one hand, it could simplify the method of data acquisition; On the other hand, it is more persuasive by analyzing those

This section ties to find the best features reflecting the relationship between age and walking stability among those 57 ones, which include 257-1 different kinds of feature combination. A classic method of feature selection, which is the cooperation of adaptive genetic algorithm

In order to avoid that better solutions with high fitness disappear in a standard genetic algorithm although the algorithm is accommodated again and again. This paper proposed a formulation to adjust crossover probability (*pc*) between average fitness and maximum

where *p* is the number of features, in this case, *p* is equal to 32, and *k* is equal to 5.

Fig. 29 shows trend on the change of dynamic stability.

Fig. 29. Statistic on stability of all dynamic features

**4.5 Feature selection on dynamic stability** 

and support vector machine, was used to do it.

**4.5.1 Improved crossover operation** 

fitness, as shown in Equation (17).

all of those features are desirable.

selected features.

number of age class.

was calculated by age.

*SA S D S m l*

*k i j i k j*

1

(15)

(16)
