Biomed. Eng.-Biomed. Tech. 2015; aop
Abed Khorasani, Mohammad Reza Daliri* and Mohammad Pooyan
Recognition of amyotrophic lateral sclerosis disease using factorial hidden Markov model DOI 10.1515/bmt-2014-0089 Received August 24, 2014; accepted June 1, 2015
Abstract: Amyotrophic lateral sclerosis (ALS) is a common disease among neurological disorders that can change the pattern of gait in human. One of the effective methods for recognition and analysis of gait patterns in ALS patients is utilizing stride interval time series. With proper preprocessing for removing unwanted artifacts from the raw stride interval times and then extracting meaningful features from these data, the factorial hidden Markov model (FHMM) was used to distinguish ALS patients from healthy subjects. The results of classification accuracy evaluated using the leave-one-out (LOO) cross-validation algorithm showed that the FHMM method provides better recognition of ALS and healthy subjects compared to standard HMM. Moreover, comparing our method with a state-of-the art method named least square support vector machine (LS-SVM) showed the efficiency of the FHMM in distinguishing ALS subjects from healthy ones. Keywords: amyotrophic lateral sclerosis; factorial hidden Markov model; gait classification; movement disorders.
Introduction Amyotrophic lateral sclerosis (ALS) is a progressive and, in some cases, fatal disease, which is caused by the deterioration of motor neurons. These types of neurons located in the central nervous system (CNS) play an important role in
*Corresponding author: Mohammad Reza Daliri, Faculty of Electrical Engineering, Department of Biomedical Engineering, Iran University of Science and Technology (IUST), Narmak, 16846-13114 Tehran, Iran, Phone: +98-21-73225738, Fax: +98-2173225777, E-mail: [email protected] Abed Khorasani: Faculty of Electrical Engineering, Department of Biomedical Engineering, Iran University of Science and Technology (IUST), Narmak, 16846-13114 Tehran, Iran Mohammad Pooyan: Faculty of Electrical Engineering, Department of Biomedical Engineering, Shahed University, Tehran, Iran
the control of volunteer movements in humans [20]. Both atrophy and weakness of muscles are the main symptoms of ALS. ALS progression can be resulted in the lack of volunteer movements, and so, the disability to normal walking can be commonly seen in many cases. Hence, the investigation of walking parameters may help for both better perception of motor control mechanism and also diagnosing neurological diseases such as ALS in its early stages [16]. In the recent years, the automatic methods have been introduced for biomedical diagnosis of different diseases such as Alzheimer, lung cancer, breast cancer, and Parkinson [4, 5, 7, 8, 21, 28]. Furthermore, the recent studies have been focused on using the computer-based methods for recognition and measurement of gait parameters [1, 13, 15, 17, 18, 23]. In addition to the aforementioned studies, the analysis of stride-to-stride variability can be used for the gait analysis in the ALS patients. In Ref. [26], it is shown that in the normal subjects, the stride-to-stride time changes in the arbitrary and complex way. Furthermore, in Ref. [14], it is shown that the stride-to-stride time during walking in the persons suffering from neurological diseases alters with a complex pattern. Although the analysis of stride variability have been done and investigated in these studies, introducing a novel method with the ability of characterizing the gait variability has remained an open problem. In Ref. [2], a linear model was proposed for analyzing the gait patterns in the neurodegenerative diseases. The results showed that this model can be used to extract important features corresponding to gait patterns and so to diagnose the neurodegenerative diseases. In Ref. [10], to recognize the neurodegenerative diseases based on the gait patterns, three different features were extracted from the double support interval, stance interval, and swing interval. Then, a neural network-based method was used to distinguish subjects surfing from the neurodegenerative diseases from the healthy ones. Furthermore, in a similar study, by extracting different features from the times series of double support interval, stance interval, and swing interval, the support vector machines algorithm was used for the diagnosis of neurodegenerative diseases [6]. In Ref. [29], the probability density function (PDF) corresponding to the stride interval time of the left foot in
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2 A. Khorasani et al.: Recognition of ALS using FHMM
the ALS subjects was estimated in the first phase. Then, two different features were calculated from this PDF. The results showed that these two features were significantly different in ALS in comparison to healthy ones, and so, a proper classifier could distinguish the gait patterns of ALS subjects from the healthy ones. In Ref. [30], in order to analyze the stride-to-stride gait variability in ALS subjects compared with healthy ones, two features were extracted from the gait data of these subjects in terms of stride interval times. Then, these features were used to classify the gait data, and a new method was proposed to distinguish the ALS persons from the healthy ones. Although the performance of the proposed method in terms of percent of true classification rate has been acceptable, in this study, a new extension of the HMM method is proposed for separating the healthy persons from the ALS ones. Furthermore, in this study, we tried to extract the simple features representing the stride variability from the raw gait data as the input of our proposed classifier. The HMM method has been widely used in medical applications for the classification of time series data such as EEG and ECG [3, 31]. In these works, the HMM models have been used for recognition and diagnosis of the patients suffering from neurological and cardiac diseases. These applications motivated us to use the HMM method for the analysis of the gait in the ALS patients. Furthermore, the HMM methods have been used in different studies for gait recognitions of humans from image sequences of persons [19, 24]. In Ref. [22], the HMM method was used to separate the subjects suffering from Parkinson’s disease from the healthy ones based on the raw gait data. In this article, a new framework of the HMM method named the factorial hidden Markov model (FHMM) has been used to classify the stride interval time series related to ALS and healthy subjects. This paper is organized based on the following sections. In the Materials and methods section, the materials and methods including data description, feature extraction, and classification are reviewed. In the Results section, the result of the gait data classification is represented. Finally, the discussion and conclusion are presented.
(http://www.physionet.org) [25]. The dataset includes the gait data from 16 healthy and 13 ALS subjects. The mean (standard deviation) age of ALS patients and healthy subjects who participated in the aforementioned study were 55.6 (12.8) and 39.3 (18.5), respectively. In order to extract the gait information, force sensors were located in the foot’s shoe of each subject. Then, the stride interval time representing the time from the contact of a foot to the ground to the following contact of the same foot was extracted from these data. In order to remove the unwanted artifacts in the beginning of the movements, the first 20s of the stride time signals were removed. Based on the experimental setup described in Ref. [14], subjects were requested to walk through a hallway during the recording of the gait signals. Because of the limited length of the hallway for walking, the subjects had to turn around at the end of the hallway, and this produced large peaks at the extracted gait signals. To remove the outliers, the samples with 3 SDs larger or less than the median value were substituted with the mean value of the related gait signals [12].
Pattern recognition The general structure of the proposed model for classification of stride interval times is depicted in Figure 1. After preprocessing of gait data and removing outliers from them, the related features that represent the most important information about data should be extracted from the raw preprocessed gait data. In the next step, these features are used as the inputs of classifiers to distinguish the gait data of ALS subjects from the healthy ones.
FHMM method The general structure of standard HMM model is depicted in Figure 2A. As can be seen, a standard HMM model is composed of two separate layers including the hidden state and observation layers. In a standard HMM, each state in time depends on only its previous state. Furthermore, the observation in each time depends only on its current state. In each time, the HMM system has one state, and the
Preprocessing Raw stride interval time series
Removing outliers Feature extraction
Classification HMM method
Materials and methods
Classification result
Gait data description
ALS
The gait data provided by Hausdorff et al. were used in this study [14, 15]. These data can be accessed via the physionet web page
Healthy
Figure 1: The general structure of the algorithm for distinguishing ALS patients from healthy subjects.
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A. Khorasani et al.: Recognition of ALS using FHMM 3
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Figure 2: The structure of two HMM model. (A) A typical structure of standard HMM. (B) A typical structure of a FHMM with three layers. transition between states is defined based on the related probability. Furthermore, the connections between each state and observations are defined based on the associated probability. For further information about the HMM, refer to Ref. [27]. There are other frameworks of HMM such as the FHMM, which has a more complex structure than the standard HMM and can be used to obtain better performance. This method was introduced by Ghahramani et al. for the first time for the modeling of stochastic random processes [11]. The FHMM has a complex structure that is composed of different layers. As can be seen in Figure 2B, there is no connection between the hidden layers, and so each layer is independent from the other layers. Moreover, the observation layer depends on the current state of all the hidden layers. So, in the FHMM, each state variable is composed of a combination of states, and by considering the M hidden layers, we have now a new state structure named “meta-state” in the following form: St = St( 1) ,…,St( M )
(1)
Here, St, St(M) represent the “meta-state”, the state of the mth layer at a time, respectively. In the simple form of FMMM, for each layer, the same number of states can be considered. For example, for a FHMM with M layers, a structure with M k*k is required. By this definition, the FHMM structure can be considered as a standard HMM with a KM*KM transition matrix. Moreover, by considering the previous assumption that each “meta-state” is independent from other state variables, the conditional probability of states results to the following form: P( St | St -1 ) = ∏ m= 1 P( St(-1m ) | St(-1m ) ) M
(2)
For the calculation of this probability, the Ghahramani et al. method has been used in the current study [11]. According to their work, this probability can be modeled using a Gaussian PDF with a common mean and covariance. Equation 3 shows this PDF: ⎧ 1 M M m| S ( m| S ) P( Yt | St ) = exp ⎨- ( Yt -∑ m= 1 µ t ) t C -1 ( Yt -∑ m= 1 µ t ) ⎩ 2 m| S
(3)
where µ t represents the mean of layer M, and C represents its covariance. In order to estimate the parameters of the FHMM model, the expectation maximization (EM) algorithm can be used. These parameters are the mean and covariance of all states in each layer, the transition and the prior probability matrices. The details about this method are given in Ref. [11].
In this section, the results of the analysis of the gait data to distinguish between healthy and ALS subjects are introduced. In Figure 3, two examples of the raw stride interval time signal corresponding to an ALS patient and a healthy subject are shown. As can be seen in Figure 3A, two apparent features that show the difference between ALS and healthy subjects can be identified. Furthermore, as can be seen in Figure 3B, this difference is not completely significant for the raw gait data of all the subjects. However, the case shown in Figure 3B is rather rare in the gait dataset. First, the average of the stride time during walking in the ALS subject is much higher than the average of the stride time in the healthy subject. Second, the variance of the stride times in the ALS patient is higher than the variance of the stride times in the healthy subject. According to Table 1, the Wilcoxon rank sum test shows that the average and variance of the stride interval times in the ALS subjects have been significantly different from those in healthy subjects (p
Abed Khorasani, Mohammad Reza Daliri* and Mohammad Pooyan
Recognition of amyotrophic lateral sclerosis disease using factorial hidden Markov model DOI 10.1515/bmt-2014-0089 Received August 24, 2014; accepted June 1, 2015
Abstract: Amyotrophic lateral sclerosis (ALS) is a common disease among neurological disorders that can change the pattern of gait in human. One of the effective methods for recognition and analysis of gait patterns in ALS patients is utilizing stride interval time series. With proper preprocessing for removing unwanted artifacts from the raw stride interval times and then extracting meaningful features from these data, the factorial hidden Markov model (FHMM) was used to distinguish ALS patients from healthy subjects. The results of classification accuracy evaluated using the leave-one-out (LOO) cross-validation algorithm showed that the FHMM method provides better recognition of ALS and healthy subjects compared to standard HMM. Moreover, comparing our method with a state-of-the art method named least square support vector machine (LS-SVM) showed the efficiency of the FHMM in distinguishing ALS subjects from healthy ones. Keywords: amyotrophic lateral sclerosis; factorial hidden Markov model; gait classification; movement disorders.
Introduction Amyotrophic lateral sclerosis (ALS) is a progressive and, in some cases, fatal disease, which is caused by the deterioration of motor neurons. These types of neurons located in the central nervous system (CNS) play an important role in
*Corresponding author: Mohammad Reza Daliri, Faculty of Electrical Engineering, Department of Biomedical Engineering, Iran University of Science and Technology (IUST), Narmak, 16846-13114 Tehran, Iran, Phone: +98-21-73225738, Fax: +98-2173225777, E-mail: [email protected] Abed Khorasani: Faculty of Electrical Engineering, Department of Biomedical Engineering, Iran University of Science and Technology (IUST), Narmak, 16846-13114 Tehran, Iran Mohammad Pooyan: Faculty of Electrical Engineering, Department of Biomedical Engineering, Shahed University, Tehran, Iran
the control of volunteer movements in humans [20]. Both atrophy and weakness of muscles are the main symptoms of ALS. ALS progression can be resulted in the lack of volunteer movements, and so, the disability to normal walking can be commonly seen in many cases. Hence, the investigation of walking parameters may help for both better perception of motor control mechanism and also diagnosing neurological diseases such as ALS in its early stages [16]. In the recent years, the automatic methods have been introduced for biomedical diagnosis of different diseases such as Alzheimer, lung cancer, breast cancer, and Parkinson [4, 5, 7, 8, 21, 28]. Furthermore, the recent studies have been focused on using the computer-based methods for recognition and measurement of gait parameters [1, 13, 15, 17, 18, 23]. In addition to the aforementioned studies, the analysis of stride-to-stride variability can be used for the gait analysis in the ALS patients. In Ref. [26], it is shown that in the normal subjects, the stride-to-stride time changes in the arbitrary and complex way. Furthermore, in Ref. [14], it is shown that the stride-to-stride time during walking in the persons suffering from neurological diseases alters with a complex pattern. Although the analysis of stride variability have been done and investigated in these studies, introducing a novel method with the ability of characterizing the gait variability has remained an open problem. In Ref. [2], a linear model was proposed for analyzing the gait patterns in the neurodegenerative diseases. The results showed that this model can be used to extract important features corresponding to gait patterns and so to diagnose the neurodegenerative diseases. In Ref. [10], to recognize the neurodegenerative diseases based on the gait patterns, three different features were extracted from the double support interval, stance interval, and swing interval. Then, a neural network-based method was used to distinguish subjects surfing from the neurodegenerative diseases from the healthy ones. Furthermore, in a similar study, by extracting different features from the times series of double support interval, stance interval, and swing interval, the support vector machines algorithm was used for the diagnosis of neurodegenerative diseases [6]. In Ref. [29], the probability density function (PDF) corresponding to the stride interval time of the left foot in
Brought to you by | Kungliga Tekniska Högskolan Authenticated Download Date | 9/17/15 8:13 AM
2 A. Khorasani et al.: Recognition of ALS using FHMM
the ALS subjects was estimated in the first phase. Then, two different features were calculated from this PDF. The results showed that these two features were significantly different in ALS in comparison to healthy ones, and so, a proper classifier could distinguish the gait patterns of ALS subjects from the healthy ones. In Ref. [30], in order to analyze the stride-to-stride gait variability in ALS subjects compared with healthy ones, two features were extracted from the gait data of these subjects in terms of stride interval times. Then, these features were used to classify the gait data, and a new method was proposed to distinguish the ALS persons from the healthy ones. Although the performance of the proposed method in terms of percent of true classification rate has been acceptable, in this study, a new extension of the HMM method is proposed for separating the healthy persons from the ALS ones. Furthermore, in this study, we tried to extract the simple features representing the stride variability from the raw gait data as the input of our proposed classifier. The HMM method has been widely used in medical applications for the classification of time series data such as EEG and ECG [3, 31]. In these works, the HMM models have been used for recognition and diagnosis of the patients suffering from neurological and cardiac diseases. These applications motivated us to use the HMM method for the analysis of the gait in the ALS patients. Furthermore, the HMM methods have been used in different studies for gait recognitions of humans from image sequences of persons [19, 24]. In Ref. [22], the HMM method was used to separate the subjects suffering from Parkinson’s disease from the healthy ones based on the raw gait data. In this article, a new framework of the HMM method named the factorial hidden Markov model (FHMM) has been used to classify the stride interval time series related to ALS and healthy subjects. This paper is organized based on the following sections. In the Materials and methods section, the materials and methods including data description, feature extraction, and classification are reviewed. In the Results section, the result of the gait data classification is represented. Finally, the discussion and conclusion are presented.
(http://www.physionet.org) [25]. The dataset includes the gait data from 16 healthy and 13 ALS subjects. The mean (standard deviation) age of ALS patients and healthy subjects who participated in the aforementioned study were 55.6 (12.8) and 39.3 (18.5), respectively. In order to extract the gait information, force sensors were located in the foot’s shoe of each subject. Then, the stride interval time representing the time from the contact of a foot to the ground to the following contact of the same foot was extracted from these data. In order to remove the unwanted artifacts in the beginning of the movements, the first 20s of the stride time signals were removed. Based on the experimental setup described in Ref. [14], subjects were requested to walk through a hallway during the recording of the gait signals. Because of the limited length of the hallway for walking, the subjects had to turn around at the end of the hallway, and this produced large peaks at the extracted gait signals. To remove the outliers, the samples with 3 SDs larger or less than the median value were substituted with the mean value of the related gait signals [12].
Pattern recognition The general structure of the proposed model for classification of stride interval times is depicted in Figure 1. After preprocessing of gait data and removing outliers from them, the related features that represent the most important information about data should be extracted from the raw preprocessed gait data. In the next step, these features are used as the inputs of classifiers to distinguish the gait data of ALS subjects from the healthy ones.
FHMM method The general structure of standard HMM model is depicted in Figure 2A. As can be seen, a standard HMM model is composed of two separate layers including the hidden state and observation layers. In a standard HMM, each state in time depends on only its previous state. Furthermore, the observation in each time depends only on its current state. In each time, the HMM system has one state, and the
Preprocessing Raw stride interval time series
Removing outliers Feature extraction
Classification HMM method
Materials and methods
Classification result
Gait data description
ALS
The gait data provided by Hausdorff et al. were used in this study [14, 15]. These data can be accessed via the physionet web page
Healthy
Figure 1: The general structure of the algorithm for distinguishing ALS patients from healthy subjects.
Brought to you by | Kungliga Tekniska Högskolan Authenticated Download Date | 9/17/15 8:13 AM
A. Khorasani et al.: Recognition of ALS using FHMM 3
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Figure 2: The structure of two HMM model. (A) A typical structure of standard HMM. (B) A typical structure of a FHMM with three layers. transition between states is defined based on the related probability. Furthermore, the connections between each state and observations are defined based on the associated probability. For further information about the HMM, refer to Ref. [27]. There are other frameworks of HMM such as the FHMM, which has a more complex structure than the standard HMM and can be used to obtain better performance. This method was introduced by Ghahramani et al. for the first time for the modeling of stochastic random processes [11]. The FHMM has a complex structure that is composed of different layers. As can be seen in Figure 2B, there is no connection between the hidden layers, and so each layer is independent from the other layers. Moreover, the observation layer depends on the current state of all the hidden layers. So, in the FHMM, each state variable is composed of a combination of states, and by considering the M hidden layers, we have now a new state structure named “meta-state” in the following form: St = St( 1) ,…,St( M )
(1)
Here, St, St(M) represent the “meta-state”, the state of the mth layer at a time, respectively. In the simple form of FMMM, for each layer, the same number of states can be considered. For example, for a FHMM with M layers, a structure with M k*k is required. By this definition, the FHMM structure can be considered as a standard HMM with a KM*KM transition matrix. Moreover, by considering the previous assumption that each “meta-state” is independent from other state variables, the conditional probability of states results to the following form: P( St | St -1 ) = ∏ m= 1 P( St(-1m ) | St(-1m ) ) M
(2)
For the calculation of this probability, the Ghahramani et al. method has been used in the current study [11]. According to their work, this probability can be modeled using a Gaussian PDF with a common mean and covariance. Equation 3 shows this PDF: ⎧ 1 M M m| S ( m| S ) P( Yt | St ) = exp ⎨- ( Yt -∑ m= 1 µ t ) t C -1 ( Yt -∑ m= 1 µ t ) ⎩ 2 m| S
(3)
where µ t represents the mean of layer M, and C represents its covariance. In order to estimate the parameters of the FHMM model, the expectation maximization (EM) algorithm can be used. These parameters are the mean and covariance of all states in each layer, the transition and the prior probability matrices. The details about this method are given in Ref. [11].
In this section, the results of the analysis of the gait data to distinguish between healthy and ALS subjects are introduced. In Figure 3, two examples of the raw stride interval time signal corresponding to an ALS patient and a healthy subject are shown. As can be seen in Figure 3A, two apparent features that show the difference between ALS and healthy subjects can be identified. Furthermore, as can be seen in Figure 3B, this difference is not completely significant for the raw gait data of all the subjects. However, the case shown in Figure 3B is rather rare in the gait dataset. First, the average of the stride time during walking in the ALS subject is much higher than the average of the stride time in the healthy subject. Second, the variance of the stride times in the ALS patient is higher than the variance of the stride times in the healthy subject. According to Table 1, the Wilcoxon rank sum test shows that the average and variance of the stride interval times in the ALS subjects have been significantly different from those in healthy subjects (p
