1. Introduction
Human activity recognition is the detection, understanding and recognition of human habitual or temporary behavior types, activity ways, and patterns. The recognition of human activities provides intelligent services for various application platforms, such as smart home [
1], healthcare [
2], patient care, exercise health, identity authentication, etc., and it has a wide application prospect.
Substantial research has been conducted in order to recognize human activities [
3]. In the aspect of motion data acquisition and recognition, there are mainly two ways that based on computer vision and various types of sensors [
4]. When compared to computer vision approaches, the various sensors have the advantage of small size, high sensitively, abundant information, and not being limited by the scene or time. Especially, for smartphone’s built-in sensor [
5], it does not require additional infrastructure, is universal, and it has better computational power. In addition, the accelerometer and gyroscope data can be collected from a smartphone.
Most of the existing sensor-based human activity recognition approaches often require steps, such as window division, feature extraction, model training, and activities recognition. Especially for feature extraction module, the existing researches are roughly divided into two categories: time and frequency domain features [
6] and automatically extracted features based on deep learning [
7,
8]. Chen et al. [
6] proposed a framework and performance analysis of human activity recognition system that is based on smartphone sensors, which accurately describe different human motion patterns by extracting seven features in the time-frequency domain and wavelet domain. Quaid et al. [
9] proposed a genetic algorithm using sensor data to solve complex feature selection and classification problems, by combining time and frequency domain features and acoustic signal characteristics (e.g., energy, zero crossing rate, etc.). Besides, from the perspective of medical services, the signal amplitude, average, standard deviation, maximum, and minimum values are extracted from the motion date after de-noising as eigenvalues, and then these statistical features are learnt and trained by linear support vector machine to realize human behavior recognition [
10]. Zhu et al. [
11] proposed a semi-supervised deep learning method, through the deep Long Short Term Memory (LSTM) to extract the features of local lazy items in the cyclic framework, and realized the six activities recognition. Zhang et al. [
12] combined attention mechanism with Convolutional Neural Networks (CNNs) to extract features. Meanwhile, there are some related literatures that combine the two methods for activity recognition. For example, literature [
5] has combined LSTM model-based with time and frequency domain features, and proposed a feature fusion framework to improve the performance of Human activity recognition (HAR) based on smartphone sensors. Also, Nguyen et al. [
13] used similar pose transform and discrete wavelet transform to extract time-frequency domain features, and then further utilize the bidirectional LSTM model to classify and recognize activities, thus improving the problem of different motions posture conversion.
There has been a widespread use of machine learning techniques in smartphone-based activity recognition [
3]. One of the most common approaches is to extract time and frequency domain features (i.e., mean, maximum, principal component analysis, etc.). However, the traditional statistical features usually have higher dimensions; thus, it increases the computational complexity. Additionally, this method often ignores the periodic and nonlinear characteristics of the activity, and it does not fully consider the potential dynamic features of the human activity. In addition, the idea of human activity recognition that is based on deep learning is to extract features from the raw sensor data through various neural network models. Comparing with the global information of time and frequency domain features, the motion feature information extracted by deep learning is difficult to understand and it has high computational complexity. Besides, although the machine learning techniques and deep learning methods have both achieved a higher recognition rate in the field of HAR, these approaches do not fully consider the underlying chaotic dynamics in activity time series (sensor data), and they also ignore the non-linear characteristics of human motion series [
14].
Nonlinear dynamical system studies the qualitative and quantitative changes of different motion states. Phase space reconstruction technology is a vital step in nonlinear dynamics analysis, which reconstructs a time series with chaotic features into a nonlinear dynamic system. Furthermore, there has been some works using dynamical system and chaos theory, along with machine learning techniques for human activity recognition [
3,
15,
16]. Saad et al. [
15] constructs a recognition framework for modeling and analyzing the nonlinear dynamics of human activities that are based on the chaos theory. Additionally, a four-dimensional eigenvector are built by parameters, such as Lyapunov exponent, embedding dimension, correlation integral and variance, the five activity classes are recognized and the recognition rate is 89.7%. Kawsar et al. [
17] develops an activity detection system where they use pressure sensor data from shoes along with accelerometers and gyroscope data from smart phone. Additionally, they exploit the time-delay embedding for detecting four activities (e.g., running, walking, sitting, and standing), and the classification accuracy achieves 100%. Whereas, they do not mention the number of participants in this study and also do not perform some widely tested activities (i.e., laying down, walking upstairs, and walking downstairs). The acceleration sensor data are used in order to build phase space reconstruction, and the principal component analysis is used to extract the nine maximum values as the eigenvalues form the phase space, and then the five activities are recognized by the support vector machine, and the recognition rate is 85% [
16]. Meantime, in the literature [
18], the acceleration signals are embedded into a six-dimensional pseudo phase space using the time-delay embedding. Subsequently, these activity observation series are classified into different motions by the geometric template matching algorithm, and the six basic activities from the UCI datasets are recognized. However, this paper does not analyze the activity time series from the chaotic features perspective. Additionally, an Electrocardiogram (ECG) signal (that is, a sensor signal) is reconstructed into phase space using the time-delay technique. The 21 geometric features through the trajectory from the phase space are extracted, and the four daily activities (i.e., rest, exercise, listening to music, and watching a video) are recognized by the support vector machine learning, and the accuracy rate is 97.7% [
19]. Based on the dynamic system and chaos theory, Md et al. [
3] proposed a human activity recognition system that is based on lightweight smartphone. They use acceleration sensor data from a smartphone to reconstruct the phase space, and Gaussian Mixture Models (GMM) is learnt from the dynamics system to classily human activities by the Maximum Likelihood Classifier (MLC). That is, the accuracy is 100% in the self-collected dataset, but, in the public dataset, it is 90%. However, this work provides another idea for human activity recognition, but does not perform experiments with other test activities, such as transition activity.
In the meantime, although there have been extensive works towards the HAR problem, most of them adopt the time and frequency domain feature, without exploiting the chaotic feature via Reconstructed Phase Space (RPS). Thus, in this work, we analyze the nonlinear dynamic features of the human activity from the dynamic system perspectives. In particular, we only leverage one-axis acceleration sensor data to capture the inherent dynamics of the human activity, and these sensor data are reconstructed in the phase space by time-delay embedding. Following that, a two-dimensional chaotic feature matrix is constructed, where the chaotic feature includes both the correlation dimension and largest Lyapunov exponent (LLE) of attractor trajectory in the RPS. Additionally, then, five classification algorithms are leveraged in order to classify and recognize the two different activity classes (e.g., basic and transitional activities).
In this work, we study the non-linear chaotic features-based human activity recognition. The distinctive features of this work are as follows:
We present a novel method for human activity recognition that is based on non-linear chaotic features. Because the time series with the chaotic feature can be reconstructed into a nonlinear dynamical system, this system studies the qualitative and quantitative changes of various human motion states.
The human activity acceleration sensor data can be described as a chaotic time series. As such, we attempt to reconstruct the activity time series in a phase space by time-delay embedding technology. In the meantime, in the process of reconstructing motions phase space, we leverage the C-C method and G-P algorithm in order to estimate the optimal delay time and embedding dimension, respectively.
We construct a two-dimensional chaotic feature matrix, where the chaotic feature is composed of the correlation dimension and LLE of attractor trajectory in the reconstruction phase space. Additionally, the chaotic feature is different from the time-frequency domain features and it can fully describe the human activity potential dynamic information.
The remainder of this paper is organized, as follows. In
Section 2, we overview the idea of HAR based on dynamic system and chaos theory. Additionally, we leverage the C-C method and G-P algorithm to solve the activity phase space reconstruction problem, respectively.
Section 3 discusses the details of the experiment result. We conclude this article in
Section 4.