Human gait decision was carried out with the help of similarity measure design. Gait signal was selected through hardware implementation including all in one sensor, control unit, and notebook with connector. Each gait signal was considered as high dimensional data. Therefore, high dimensional data analysis was considered via heuristic technique such as the similarity measure. Each human pattern such as walking, sitting, standing, and stepping up was obtained through experiment. By the results of the analysis, we also identified the overlapped and nonoverlapped data relation, and similarity measure analysis was also illustrated, and comparison with conventional similarity measure was also carried out. Hence, nonoverlapped data similarity analysis provided the clue to solve the similarity of high dimensional data. Considered high dimensional data analysis was designed with consideration of neighborhood information. Proposed similarity measure was applied to identify the behavior patterns of different persons, and different behaviours of the same person. Obtained analysis can be extended to organize health monitoring system for specially elderly persons.
Analysis on the human gait signal has been studied steadily by numerous researchers [
Generally, human gait signals consist of walking, sitting, standing, stepping up and down, and other usual behavior. Such a usual behavior would be done in house life, then it is quite easy for us to identify when we watch them in real situation. In order to develop a more massive monitoring system and healthcare system to analyze and identify behavior signal of each person, decision and classifying system for the gait signal is required. More specifically, decision whether he/she is doing in normal activities or not can be applied to the design of health care system. Therefore, obtained research output can be applied to the identification, healthcare, and other related fields. Additionally, more detail checking result even for the healthy people such as athletes can provide useful information whether he/she has suffered from other problems compared to the previous behavior.
To discriminate between different patterns, rational measure obtained from a statistical approach or heuristic approach is needed. By the point of statistical method, signal autocorrelation and cross correlation knowledge are useful because such formula provide us how much the signals are related with each other by the numeric value. Also, it is rather convenient to calculate due to the conventional software such as Matlab toolbox. However, it is not easy for high dimensional data to construct high dimensional correlation/covariance matrices. For heuristic approach, it needs preliminary processing for the signal, such as data redefinition and measure design based on the human thinking. Even the realization of measure based on heuristic idea is considered, ordinary measure for discrimination has to be considered such as distance. Fortunately, similarity measure design for the vague data has become a more interesting research topic; hence, numerous researchers have been focused on the similarity measure, entropy design problem for fuzzy set, and intuitionistic fuzzy set [
Similarity measure [
Then, distance between vectors can be organized by norms such as 1norm, Euclideannorm, and so forth. Similarity measure is also designed explicitly with the distance norm. Similarity measure design problem for highdimension needs more considerate approach. Conventionally, the similarity measure has been designed based on the distance measure between two considered data, that is, distance measure was considered information distance between two membership functions. In the similarity measure design with distance measure, measure structure should be related to the same support of the universe of discourse [
In the following section, preliminary results on the similarity measure on overlapped and nonoverlapped data were introduced. Proposed similarity measure was proved and applied to overlapped and nonoverlapped artificial data. In Section
In order to design similarity measure explicitly, usual measure such as Hamming distance was commonly used as distance measure between sets
A real function
For any set
Commutativity of (S1) is clear from (
For (S2),
(S3) is also easy to prove as follows:
Besides Theorem
For any set
Proofs are easy to be derived, and it was found in previous results [
Besides similarity measures of (
Overlapped data distribution.
(a) Data distribution between circle and diamond. (b) Data distribution between circle and diamond.
From (
Hence, it is required to design similarity measure for nonoverlapping data distribution. Consider the following similarity measure for nonoverlapped data such as Figures
For singletons or discrete data
(S1) and (S2) are clear. (S3) is also clear from definition as follows:
Similarity measure (
Next, calculate the similarity measure between circle and diamond with (
For Figure
For the calculation of Figure
Gait signals are collected with experiment unit; acquisition system (Figure
Data acquisition experiment.
Gait patterns are composed of walking, step up and step down for 20 persons. For each behavior, signals are measured with all in one sensor which integrated with three sensors (accelerator, magnetic, and Gyro sensors); each sensor represents three dimension direct signals. Four sensors are attached to waist, two legs, and head. Example of obtained gait signals is illustrated in the following Figure
Gait signal with all in one sensor.
Walking with acceleration sensor
Stair up with acceleration sensor
Walking with magnetic sensor
Stair up with magnetic sensor
Walking with Gyro sensor
Stair up with Gyro sensor
We get the signals from the control unit, and the signal is processed in a note book. Signal characteristics were considered peak value and magnitude distance between each gait signal. Next, by the application of the similarity measure, we get the calculation of each action such as walking, step up, and so on.
Research on big data analysis has been emphasized by research outcomes recently [
Biomedical data such as DNA sequence or Electroencephalography (EEG) data. It contains not only high dimension but also large number of channel data.
Recommendation systems and target marketing are important applications in the ecommerce area. Sets of customers/clients’ information analysis help to predict their action to purchase based on customers’ interest. It also includes a huge amount of data and high dimensional structure.
Industry application such as EV station scheduling problem needs geometrical information, city size, population, traffic flow, and others. Hence, number of station and station size constitute huge data and high dimension.
Direct data comparison is applicable to overlapped data with norm definition including Euclidean norm such as
Hence, analysis and comparison with each attribute provide explicit importance of each data. Similarity measure provides analysis between patterns, such as
Similarity measure between person to person is expressed as
Normalized similarity calculation results are illustrated in Table
Similarity measure comparison between patterns.
Similarity measure  Values 


0.344 

0.278 

0.550 
Results illustrate that the stair up and down shows higher similarity than the others. However, even similarity calculation result is higher than others; it is not much close to one, it just satisfies 0.55. Due to different directions stair up/down should have basic limit to close maximum similarity.
Table
Average similarity measure between individuals.
Similarity measure  Values 


0.624 

0.643 

0.712 
Similarity measure comparison between individuals (walking).
Similarity measure  1  2  3  4  5  6  7 

18  19  20  

1  1  0.511  0.621  0.420  0.462  0.581  0.617  0.581  0.470  0.623  
2  0.511  1  0.592  0.590  0.490  0.632  0.543  0.603  0.619  0.577  
3  0.621  0.592  1  0.510  0.611  0.640  0.599  0.710  0.566  0.582  
4  0.420  0.590  0.510  1  0.701  0.653  0.589 

0.612  0.629  0.585  
5  0.462  0.490  0.611  0.701  1  0.599  0.603  0.489  0.581  0.620  
6  0.581  0.632  0.640  0.653  0.599  1  0.576  0.499  0.545  0.629  
7  0.617  0.543  0.599  0.589  0.603  0.576  1  0.710  0.627  0.634  

0.590  0.611  0.589  


0.429  0.570  0.630  
0.559  0.628  0.549  
18  0.581  0.603  0.710  0.612  0.489  0.499  0.710  0.590  0.429  0.559  1  0.345  0.626 
19  0.470  0.619  0.566  0.629  0.581  0.545  0.627  0.611  0.570  0.628  0.345  1  0.556 
20  0.623  0.577  0.582  0.585  0.620  0.629  0.634  0.589  0.630  0.549  0.626  0.556  1 
Similar results for stair up and down are obtained.
Gait signal identification was carried out through similarity measure design. Gait signal was obtained via data acquisition system including mobile station, all in one sensor attached to the head, waist, and two legs. In order to discriminate the gait signal with respect to different behaviors and individuals, similarity measure design was considered. Similarity measure was considered with the distance measure. For data distribution, overlapped and nonoverlapped distribution were considered, and similarity measure was applied to calculate the similarity. However, the conventional similarity measure was shown that it was not available to calculate the similarity on nonoverlapped data. To overcome such a drawback, the similarity measure was considered with data information of neighbor. Closeness between neighbor data provides a measure of similarity among data sets; hence, the similarity measure was calculated. Calculation proposed two different artificial data, and the proposed similarity measure was useful to identify nonoverlapped data distribution. It is meaningful that similarity measure design can be extended to high dimensional data processing because gait signal was considered as a high dimensional data. With data acquisition system, 20 person gait signals were collected through experiments. Different gaits, walking, stair up, and stair down signals were obtained, and similarity measure was applied. By calculation, similarity between stair up and stair down showed higher similarity than others. Individual similarity for a different gait signal was also obtained.
Gait signal analysis can be used for behavior decision system development; it is also naturally extended to health care system, especially to elderly people. Additionally, it is also useful for athlete to provide useful information if he/she is suffering from different actions compared to previous behavior.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported in part by a Grant from the Research Development Fund of XJTLU (RDF 110203).