1 Introduction

Embedded systems are designed to do some specific tasks. Examples of embedded systems are accelerometers, GPS, thermostats, digital cameras, medical equipments, etc. There has been extensive research on timing analysis [32, 33], energy efficiency [28, 29, 37, 39, 42, 45], reliability issues [38, 44], security issues [34–36], and software synthesis problems [43] on embedded systems. One current trend of an embedded application is to connect embedded systems to a network or internet to allow the embedded systems be controlled remotely, or to allow the data collected from embedded systems be analyzed remotely. Various types of embedded devices such as RFID, GPS, accelerometers are now connected to the Internet (called Internet of Things or Cyber-Physical Systems) to achieve intelligent identification, tracking, and monitoring to help improve the quality of life of people.

According to the health report in Canada [25], approximately 30 % of people over 65 years of age living in the community fall each year. Falls are the major cause of injury related to hospitalization among the elderly population. Injuries from falls include broken or fractured bones, and soft tissue damage, etc. Falls are also the major cause of injury deaths. Fall detection is thus an important application. An accelerometer attached to a human body can gather real-time body motion data. The development of wireless sensor network technologies makes it possible to transmit the motion data to a remote analysis center without affecting human motion (no wires needed). Movement detection and activity recognition have been applied for various applications such as interactive entertainment, and fall detection for elderly people [6, 7, 27]. This paper studies methods to recognize human movement activities using advanced intelligent methods or machine learning algorithms.

Movement detection is an emerging technique among various pattern recognition problems [3, 12, 30, 31]. There are a lot of previous works proposed for human movement detection [1–5, 40]. Some of them used one waist mounted triaxial accelerometer [1], and some of them used several biaxial accelerometers mounted on different parts of the body [2]. Chen [3] built a real-time motion monitoring system based on two waist mounted Mica2 motes. Dai et al. [27] implemented a fall detection prototype system based on mobile phone platform. Zhang et al. [46] designed an unobtrusive wireless sensor network for nighttime falls detection.

Machine learning algorithms or simple threshold comparison methods are used to classify the activities from the data acquired from sensors. The activity classification methods in [3, 27, 41] are threshold-based methods. Machine learning techniques are widely for activity classification. Karantonis et al. [1] constructed a real time decision tree based human movement classification system with the data acquired from one single, waist-mounted triaxial accelerometer unit. Chen et al. [13] employed a fuzzy basis function classifier for human activity detection. Yang [8] applied the neural network classifier for activity recognition. Huang et al. [5] first applied an ant colony clustering algorithm to estimate and classify the body posture and then used hidden Markov models for human motion recognition. Ward et al. [9] also used hidden Markov models to recognize continuous human activities such as sawing, hammering, drilling, etc. Ravi et al. [10] evaluated the performances of activity recognition on four different machine learning algorithms: support vector machine, decision tree, K nearest neighbor and naive Bayes. Bao and Intille [2] compared several machine learning classifiers for activity recognition with the data acquired from five biaxial accelerometers worn on different parts of the body.

As there are large amount of real-time raw data received from accelerometers and there are noises associated with these data, the machine learning based classifier algorithms usually do not work directly on the raw motion data. Instead, feature extraction is performed first. Feature representation is an important procedure in pattern recognition. It includes feature extraction, feature selection, and feature reduction. Previous studies on activity detection are mostly based on three kinds of features:

  1. (1)

    the triaxial acceleration data [1],

  2. (2)

    the fusion of acceleration data [2, 8, 10–13] such as mean, correlation between axes, energy, and standard deviation,

  3. (3)

    features selected by selection and reduction methods such as feature subset selection based on common principal component analysis [8, 11], and linear discriminate analysis [11, 13].

How to extract and select good features to better represent a pattern is critical problem for pattern recognition and will directly affect the recognition rate. In this paper, we use singular value decomposition (SVD) [15, 16] to construct the enriched feature for human movement detecting.

Singular value decomposition is a well-developed method for extracting the dominant features of large data sets and for reducing the dimensionality of the data by projecting the original high dimensional space onto low semantic dimensional space. It is a mathematical concept used in most of the Latent Semantic Indexing (LSI) methods. LSI was originally proposed as an information retrieval method [17] to construct the semantic relationship. It can also be used for pattern classification [18]. Compared to other feature reduction methods, such as principal component analysis and linear discriminate analysis, SVD takes advantage of the consideration of relationships between features to establish underlying semantic means. It generates an enriched feature space with a small number of features to represent the whole feature space, which can not only reduce the dimensionality, but also improve the performance.

The motivation of our work is to detect and monitor the individual activity and provide valuable information of people’s health status and daily life. It is very useful for remote health care, especially for elderly people.

The overview of the system is shown in Fig. 1. In the data acquisition step, the accelerometers in the two ADXL202 mobile motes [3] read the signal stream resulted from the human movement, and the motes send the data to the processing computer. The raw triaxial acceleration data will go through the preprocessing stage and form sliding windows with 20 % overlap. Feature extraction method is performed on the signal sequence windows to generate the fusion feature such as mean, correlation of axes. Feature reconstruction is then used to enrich the feature by adapting the singular value decomposition technique. The enriched features will be used by the movement classification algorithms such as K-Nearest Neighbor (KNN) and neural network for human movement recognition.

Fig. 1
figure 1

The overview of the system

Full size image

The rest of the paper is organized as follows. Section 2 describes two different machine learning algorithms, which are used in our system for movement activity recognition. Section 3 describes the data acquisition and feature reconstruction process. Section 4 describes the experiments design, results comparison, and analysis. The conclusions are given in Sect. 5.

2 Machine learning algorithms

A major focus of machine learning research is to automatically learn to recognize complex patterns and make intelligent decisions based on experiments or samples. Based on whether the desired outcome for the training input data is given to the machine learning algorithm, there are mainly four types of machine learning algorithms, that is, supervised learning, unsupervised learning, semisupervized learning, and reinforcement learning. Based on different learning paradigms, there are many different kinds of machine learning algorithms such as decision tree learning, Bayesian networks, support vector machines, k-nearest neighbor, and artificial neural networks. The applications for machine learning include computer vision [19, 20], natural language processing [18, 22, 26], search engines [21], medical diagnosis [23], and pattern recognition [24]. In this paper, we use two commonly used machine learning algorithms: K Nearest Neighbor algorithm (KNN) and Back Propagation Neural Network (BPNN) algorithm, for our activity recognition problem.

2.1 K nearest neighbor algorithm

The K Nearest Neighbor algorithm (KNN) is a method for classifying objects based on the closest training examples in the feature space. It is one of the most fundamental and simple algorithms for classification problems. The KNN for classification can be briefly described as follows.

Given a sample S to be classified, KNN finds the k samples (or neighbors) in the training data that are closest to S. If most of these neighbors belong to class A, then S is assigned to class A. The KNN algorithm can be viewed as a voting system in which neighbors vote for classes.

The major steps of the KNN algorithm can be summarized as follows:

  1. (1)

    Construct a training matrix D, which includes x samples and f features, with each row corresponding to a training sample, and each column representing a feature.

  2. (2)

    For each training sample x that belongs to D, compute the corresponding feature weight of feature vector d x .

  3. (3)

    For each test sample y, compute the corresponding feature weight of feature vector d y .

  4. (4)

    Calculate the cosine similarity (or distance) between the test sample and each training sample S x =cosSim(d y ,d x ).

  5. (5)

    Sort samples in D by decreasing order of the value of S x .

  6. (6)

    Let N be the first k samples in D.

  7. (7)

    Return the majority class of samples in N.

2.2 Back propagation neural network algorithms

The Back Propagation Neural Network (BPNN) algorithm is the most popular of the neural network applications. The topology structure of the standard BPNN algorithm is shown in Fig. 2.

Fig. 2
figure 2

Three layer neural networks

Full size image

The BPNN for classification can be briefly described as: Given a sample S to be classified, the network will calculate the corresponding output for the certain input sample according to the neural network algorithm. The network will compare the actual output with the desired output for each class. If the actual output for input pattern S is the closest to the desired output for class A, then S should be assigned to class A.

Different from the KNN method, there is a training process in neural network. The neural network training process is to adjust the weights of the networks. The major steps of the BPNN training algorithm can be summarized as follows:

  1. (1)

    For each training sample, calculate the actual output value in hidden layer and output layer.

  2. (2)

    Compute the system error using mean absolute error (MAE) function.

  3. (3)

    Back-propagate the difference between the actual output value and the desired output value from output layer to hidden layer.

  4. (4)

    Back-propagate the difference between the actual output value and the desired output value from hidden layer to input layer.

  5. (5)

    Compute the change of the weight between the hidden layer and the output layer.

  6. (6)

    Compute the change of the weight between the input layer and the hidden layer.

  7. (7)

    Compute the change of bias in the hidden layer and in the input layer.

  8. (8)

    Stop training when no changes have been made on the network.

The BPNN classification steps are as follows:

  1. (1)

    For each test sample, calculate the actual output value by multiplying the input features with the final updated weights between two layers.

  2. (2)

    Compare the actual output value of the test samples with desired output value for each class.

  3. (3)

    Assign the test sample to the class in which the corresponding actual output value of the test sample is closest to the desired output value of the class.

Next, we will describe the data used by the two machine learning methods for movement activity classification.

3 Data acquisition and feature reconstruction

3.1 Data acquisition

In our system, the acceleration data are acquired from the accelerometers embedded in the Mica2 motes, which are attached to the central back of the human waist. The accelerometer data includes gravitational acceleration (GA) component and dynamic acceleration (DA) component. In real world, for every object, GA is caused by the force of gravity. DA is due to the force applied to the object. It could be internal force or external force. The internal force is caused by the object itself, such as human body movement or exercise. So, the DA component is used to distinguish activity due to the body movement. The signals in each axis can be represented as [3]:

$$\begin{aligned} x&=x_{\mathrm{DA}}+x_{\mathrm{GA}} \end{aligned}$$
(1)
$$\begin{aligned} y&=y_{\mathrm{DA}}+y_{\mathrm{GA}} \end{aligned}$$
(2)
$$\begin{aligned} z&=z_{\mathrm{DA}}+z_{\mathrm{GA}} \end{aligned}$$
(3)

Because the movement signals form continuous sequence, we divide the sequence data into windows with the interval of 1 s [12]. One window includes 10 triaxial data points. For every 0.1 s, we obtain a group of triaxial x, y, z data. The triaxial accelerometer is captured as the original data and will be used to extract features.

3.2 Feature extraction

Using only the original triaxial accelerometer data cannot easily discriminate various types of movement well. Some previous works explored fusion features from the three axes of the accelerometer [13, 14]. In this paper, we also extract the features in time domain and frequency domain from each window of the triaxial acceleration data using the same method as introduced in [13]. The time domain features include: (1) mean value of the acceleration data (x,y,z) over a window, (2) correlation between axes (x,y), (y,z), (z,x), (3) interquartile range, (4) mean absolute deviation, (5) root mean square, (6) standard deviation, and (7) variance. The frequency domain feature (8) energy, is calculated as the sum of the magnitudes of squared discrete fast Fourier transform (FFT) components of the signal in a window.

So far, we have extracted 8 features for each axes, and 24 features for x,y,z axes. We also introduce another two features [1] to be part of the feature space:

(1) Signal magnitude area (SMA) is defined as

$$ \mathit{SMA}=1/t\biggl(\int_{0}^{t}\bigl|x(t)\bigr|\,dt+\int_{0}^{t}\bigl|y(t)\bigr|\,dt+\int_{0}^{t}|z(t)|\,dt\biggr) $$
(4)

where x t , y t , z t are components of the x, y, z axis for the samples. SMA can be used to determine whether human’s movement is dynamic or static during a time period.

(2) Signal magnitude vector (SVM) is defined as

$$ \mathit{SVM}=\sqrt{x_{i}^{2}+y_{i}^{2}+z_{i}^{2}} $$
(5)

where x i , y i , z i are the ith sample of the x, y, z axis signals. SVM can be used to determine whether human falls or not during a time period.

We get totally 26 features from the original acceleration data after feature extraction. The feature vector for sample i can be represented as

$$ F_{i}=\{M_{x}, M_{y}, M_{z}, \mathit{Cor}_{x}, \mathit{Cor}_{y}, \mathit{Cor}_{z}\ldots \mathit{SMA}, \mathit{SVM}\} $$
(6)

3.3 Feature reconstruction

In linear algebra, Singular value decomposition (SVD) is a factorization of a matrix. It has many applications in signal processing and information retrieval. Singular value decomposition (SVD) is a semantic indexing method attempting to capture the underling relationship among the features, which is helpful for discriminating the classes. It is also a good dimension reduction technique as shown below.

The training data with m samples and n features for each sample can represent as a matrix A(m×n). Then the matrix decomposed into three different matrixes as Fig. 3.

Fig. 3
figure 3

The diagram of singular value decomposition

Full size image

The feature reconstruction using SVD technique can be described as follows:

  1. (1)

    Construct a training matrix A(m×n) which includes x samples and y features, with each row corresponding to a training sample, and each column representing a feature.

  2. (2)

    Apply the SVD technique on matrix A as shown in Fig. 3.

  3. (3)

    Reduce the dimensionality by taking the first K columns and rows as shown in Fig. 3 marked by red point.

  4. (4)

    Feature reconstruction according to the formula F new=F old×U k , where F new is the feature space after feature reconstruction, F old is the original feature space, and U k is the first k columns of U matrix.

4 Experiments design and results

To evaluate the performance of the algorithms on the movement and fall detection, a set of experiments have been designed to test the recognition rate. Mica2 Motes [26] are used in our system. Two motes are used for building the triaxial mobile node and are attached to the tester’s back of waist. And the other motes are placed in the room. Five adults took part in the test. We test 3 rounds with 20 samples for each round. All the tests are evaluated in the indoor environment based on the activities of standing, sitting, lying, walking, running, and fall.

Two sets of experiments have been designed to test our classifier. Set 1 distinguishes the active and inactive manner. Inactive manner stands for the static activity and active manner stands for the dynamic activity. For example, doing some tasks while sitting on the chair is classified as active sitting, and sitting on the chair in still is classified as inactive sitting. Experiment set 2 does not distinguish the active and inactive manner. The sitting activity in this set of experiments includes both active and inactive sitting. The experimental results are shown in the following tables.

Table 1 gives the recognition results based on nine movement types which distinguish the active and inactive manner. The results show that the neural network learning algorithm works better than the KNN algorithm.

Table 1 1: Movement classification result when distinguishing the active and inactive manner
Full size table

Table 2 gives the recognition results based on six types of movements without distinguishing the active and inactive manner. The results show that the recognition rate on the six movement types in experiment set 2 is much higher than that of the nine movement types in experiment set 1. The results in experiment set 2 also show that the neural network learning algorithm works better than the KNN algorithm.

Table 2 2: Movement classification result without distinguishing the active and inactive manner
Full size table

The first set of experiments needs to distinguish the active and inactive manner, which makes the patterns more complex, thus causes more misclassification. This explains that the recognition rate in set 1 is not as accurate as that in set 2. Therefore, the discrimination ability of the KNN and BPNN algorithm to classify movement types in set 1 is less than that in set 2.

A proper number of dimension can obtain a good result since SVD captures the most important information as well as establish the semantic relationship between features. Figure 4 shows the application of SVD on the first set of experiments, where the dimensions vary from 3 to 25. The original feature space (when SVD is not applied) has the dimensionality of 26. We test how the performance varies when the dimensionality is decreased. When the reduction of the dimensionality is small, we find that the performance (the recognition rate) increases when the dimension decreases. This is because some noisy information is removed when reducing the dimensions. However, when dimension becomes too small, the recognition rate becomes lower. This is because a small feature space resulted from SVD may cause important information loss, and thus lead to bad performance.

Fig. 4
figure 4

Apply SVD on experiment set 1

Full size image

From the Fig. 4, we found that the best performance of KNN is obtained when the dimensions are 12, reduced more than half. The best performance of BPNN is obtained when the dimensions are 8, reduced more than 2/3.

Figure 5, shows the application of SVD on the second set of experiments, where the dimensions also vary from 3 to 25. In Fig. 5, The best performance of 0.955 for KNN is obtained when the dimensions are 13, reduced around half. The best performance of 0.986 for BPNN is obtained when the dimensions are 9, reduced almost 2/3. The average recognition rate for experiment 1 and 2 with different features and different algorithms are shown in Table 3. The introduction of SVD improves the average recognition rate in the first set of experiment from 0.870 to 0.894 for KNN and 0.927 to 0.944 for BPNN. The introduction of SVD improves the average recognition rate of the second experiment from 0.941 to 0.955 for KNN and 0.983 to 0.986 for BPNN.

Fig. 5
figure 5

Apply SVD on experiment set 2

Full size image
Table 3 Performance comparison
Full size table

5 Conclusions

Recognizing human movement activity types is especially useful for elderly people and has gained a lot of attention. In this paper, we present a framework for human activity recognition using machine learning algorithms. Singular value decomposition technique has been adapted to generate a set of enriched features based on the acceleration data collected from wireless sensor network. Experiments conducted on different setting achieve different performances. The first set of experiments distinguishes the active and inactive manner; the activity patterns are thus complex and have a higher rate of misclassification. The second set of experiments does not distinguish the active and inactive manners, and the misclassification rate is lower. The introduction of SVD in the experiments has reduced the dimensions of features, which not only leads to lower computation cost, but also improves the recognition rate.