Last data update: 2014.03.03

 R: Analysing Accelerometer Data Using Hidden Markov Models
HMMpa-packageR Documentation

Analysing Accelerometer Data Using Hidden Markov Models

Description

This package provides functions for analyzing accelerometer outpout data (known as a time-series of (impulse)-counts) to quantify length and intensity of physical activity.

Usually, so called activity ranges are used to classify an activity as “sedentary”, “moderate” and so on. Activity ranges are separated by certain thresholds (cut-off points). The choice of these cut-off points depends on different components like the subjects' age or the type of accelerometer device.

Cut-off point values and defined activity ranges are important input values of the following analyzing tools provided by this package:

1. Cut-off point method (assigns an activity range to a count given its total magintude). This traditional approach assigns an activity range to each count of the time-series independently of each other given its total magnitude.

2. HMM-based method (assigns an activity range to a count given its underlying PA-level). This approach uses a stochastic model (the hidden Markov model or HMM) to identify the (Markov dependent) time-series of physical activity states underlying the given time-series of accelerometer counts. In contrast to the cut-off point method, this approach assigns activity ranges to the estimated PA-levels corresponding to the hidden activity states, and not directly to the accelerometer counts.

Details

Package: HMMpa
Type: Package
Version: 1.0
Date: 2013-06-30
License: GPL-2 | GPL-3 [expanded from: GPL (= 2)]

The new procedure for analyzing accelerometer data can be roughly described as follows:
First, a hidden Markov model (HMM) is trained to estimate the number m of hidden physical activity states and the model specific parameters (delta, gamma, distribution_theta). Then, a user-sepcified decoding algorithm decodes the trainded HMM to classify each accelerometer count into the m hidden physical activity states. Finally, the estimated distribution mean values (PA-levels) corresponding to the hidden physical activity states are extracted and the accelerometer counts are assigned by the total magnitudes of their corresponding PA-levels to given physical activity ranges (e.g. "sedentary", "light", "moderate" and "vigorous") by the traditional cut-off point method.

Note

We thank Moritz Hanke for his help in realizing this package.

Author(s)

Vitali Witowski,
Dr. Ronja Foraita, Leibniz Institute for Prevention Research and Epidemiology (BIPS)

Maintainer: Dr. Ronja Foraita <foraita@bips.uni-bremen.de>

References

Baum, L., Petrie, T., Soules, G., Weiss, N. (1970). A maximization technique occurring in the statistical analysis of probabilistic functions of markov chains. The annals of mathematical statistics, vol. 41(1), 164–171.

Brachmann, B. (2011). Hidden-Markov-Modelle fuer Akzelerometerdaten. Diploma Thesis, University Bremen - Bremen Institute for Prevention Research and Social Medicine (BIPS).

Dempster, A., Laird, N., Rubin, D. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society. Series B (Methodological), vol. 39(1), 1–38.

Forney, G.D. (1973). The Viterbi algorithm. Proceeding of the IEE, vol. 61(3), 268–278.

Joe, H., Zhu, R. (2005). Generalized poisson distribution: the property of mixture of poisson and comparison with negative binomial distribution. Biometrical Journal, vol. 47(2):219–229.

MacDonald, I. L., Zucchini, W. (2009) Hidden Markov Models for Time Series: An Introduction Using R, Boca Raton: Chapman & Hall.

Viterbi, A.J. (1967). Error Bounds for concolutional codes and an asymptotically optimal decoding algorithm. Information Theory, IEEE Transactions on, vol. 13(2), 260–269.

Witowski, V. (2013). Hidden-Markov-Modelle fuer Zeitreihen - Analyse von Akzelerometerdaten der IDEFICS-Studie. Diploma Thesis, University Bremen - Leibniz Institute for Preventions Research and Epidemiology - BIPS GmbH

Examples


################################################################
###     Example 1  (traditional approach)    ################### 
###     Solution of the cut-off point method ################### 
################################################################

################################################################
### Fictitious activity counts #################################
################################################################

x <- c(1,16,19,34,22,6,3,5,6,3,4,1,4,3,5,7,9,8,11,11,
  14,16,13,11,11,10,12,19,23,25,24,23,20,21,22,22,18,7,
  5,3,4,3,2,3,4,5,4,2,1,3,4,5,4,5,3,5,6,4,3,6,4,8,9,12,
  9,14,17,15,25,23,25,35,29,36,34,36,29,41,42,39,40,43,
  37,36,20,20,21,22,23,26,27,28,25,28,24,21,25,21,20,21,
  11,18,19,20,21,13,19,18,20,7,18,8,15,17,16,13,10,4,9,
  7,8,10,9,11,9,11,10,12,12,5,13,4,6,6,13,8,9,10,13,13,
  11,10,5,3,3,4,9,6,8,3,5,3,2,2,1,3,5,11,2,3,5,6,9,8,5,
  2,5,3,4,6,4,8,15,12,16,20,18,23,18,19,24,23,24,21,26,
  36,38,37,39,45,42,41,37,38,38,35,37,35,31,32,30,20,39,
  40,33,32,35,34,36,34,32,33,27,28,25,22,17,18,16,10,9,
  5,12,7,8,8,9,19,21,24,20,23,19,17,18,17,22,11,12,3,9,
  10,4,5,13,3,5,6,3,5,4,2,5,1,2,4,4,3,2,1)  
    
    
traditional_cut_off_point_method <- cut_off_point_method(x=x, 
 	cut_points = c(5,15,23), 
 	names_activity_ranges = c("SED","LIG","MOD","VIG"), 
 	bout_lengths = c(1,1,2,4,5,10,11,20,21,60,61,260),
 	plotting = 1)
 	


################################################################ 
################################################################ 
###      Examples 2,3 and 4  (new approach)             ########
###      Solution of the HMM based cut-off point method ######## 
################################################################
###      Demonstrated both in three steps (Example 2)     ###### 
###      and condensed in one function (Examples 3 and 4) ######
################################################################

################################################################
### Example 2) Manually in three steps    ######################
################################################################

################################################################
### Fictitious activity counts #################################
################################################################
                                                                
x <- c(1,16,19,34,22,6,3,5,6,3,4,1,4,3,5,7,9,8,11,11,           
  14,16,13,11,11,10,12,19,23,25,24,23,20,21,22,22,18,7,         
  5,3,4,3,2,3,4,5,4,2,1,3,4,5,4,5,3,5,6,4,3,6,4,8,9,12,         
  9,14,17,15,25,23,25,35,29,36,34,36,29,41,42,39,40,43,         
  37,36,20,20,21,22,23,26,27,28,25,28,24,21,25,21,20,21,        
  11,18,19,20,21,13,19,18,20,7,18,8,15,17,16,13,10,4,9,         
  7,8,10,9,11,9,11,10,12,12,5,13,4,6,6,13,8,9,10,13,13,         
  11,10,5,3,3,4,9,6,8,3,5,3,2,2,1,3,5,11,2,3,5,6,9,8,5,         
  2,5,3,4,6,4,8,15,12,16,20,18,23,18,19,24,23,24,21,26,         
  36,38,37,39,45,42,41,37,38,38,35,37,35,31,32,30,20,39,        
  40,33,32,35,34,36,34,32,33,27,28,25,22,17,18,16,10,9,         
  5,12,7,8,8,9,19,21,24,20,23,19,17,18,17,22,11,12,3,9,         
  10,4,5,13,3,5,6,3,5,4,2,5,1,2,4,4,3,2,1)                      
     
################################################################
## Step 1: Training of a HMM ##################################
##         for the given time-series of counts ################ 
##         ####################################################
##         More precisely: training of a poisson ##############
##         distribution based hidden Markov model for #########
##         number of states m=2,...,6 #########################
##         and selection of the model with the most ########### 
##         plausible m ########################################
################################################################

## TIME CONSUMING
## Not run: 
m_trained_HMM <- HMM_training(x = x, 
 min_m = 2, 
 max_m = 6, 
 distribution_class = "pois")$trained_HMM_with_selected_m  
 	 
###############################################################
## Step 2: Decoding of the trained HMM for the given ##########
##         time-series of accelerometer counts to extract #####
##         hidden PA-levels ###################################
###############################################################
 
hidden_PA_levels <- HMM_decoding(x = x, 
 	 m = m_trained_HMM$m, 
 	 delta = m_trained_HMM$delta, 
 	 gamma = m_trained_HMM$gamma, 
 	 distribution_class = m_trained_HMM
 	 $distribution_class, 
 	 distribution_theta = m_trained_HMM$
 	 distribution_theta)$decoding_distr_means

############################################################### 
## Step 3: Assigning of user-sepcified activity ranges ########
##         to the accelerometer counts via the total ##########
##         magnitudes of their corresponding ##################
##         hidden PA-levels ###################################
##         ####################################################
##         In this example four activity ranges ###############
##         (named as "sedentary", "light", "moderate" #########
##         and "vigorous" physical activity) are ##############
##         separated by the three cut-points 5, 15 and 23) ####
################################################################
 
HMM_based_cut_off_point_method <- cut_off_point_method(x = x, 
 	 hidden_PA_levels = hidden_PA_levels, 
 	 cut_points = c(5,15,23), 
 	 names_activity_ranges = c("SED","LIG","MOD","VIG"), 
 	 bout_lengths = c(1,1,2,4,5,10,11,20,21,60,61,260),
 	 plotting=1)      				 

## End(Not run)



###############################################################
## Example 3) In a single function (Step 1-3 of Example 2  ####
##            combined in one function)                    ####
###############################################################
	
###############################################################
## Fictitious activity counts #################################
###############################################################
                                                                
x <- c(1,16,19,34,22,6,3,5,6,3,4,1,4,3,5,7,9,8,11,11,           
  14,16,13,11,11,10,12,19,23,25,24,23,20,21,22,22,18,7,         
  5,3,4,3,2,3,4,5,4,2,1,3,4,5,4,5,3,5,6,4,3,6,4,8,9,12,         
  9,14,17,15,25,23,25,35,29,36,34,36,29,41,42,39,40,43,         
  37,36,20,20,21,22,23,26,27,28,25,28,24,21,25,21,20,21,        
  11,18,19,20,21,13,19,18,20,7,18,8,15,17,16,13,10,4,9,         
  7,8,10,9,11,9,11,10,12,12,5,13,4,6,6,13,8,9,10,13,13,         
  11,10,5,3,3,4,9,6,8,3,5,3,2,2,1,3,5,11,2,3,5,6,9,8,5,         
  2,5,3,4,6,4,8,15,12,16,20,18,23,18,19,24,23,24,21,26,         
  36,38,37,39,45,42,41,37,38,38,35,37,35,31,32,30,20,39,        
  40,33,32,35,34,36,34,32,33,27,28,25,22,17,18,16,10,9,         
  5,12,7,8,8,9,19,21,24,20,23,19,17,18,17,22,11,12,3,9,         
  10,4,5,13,3,5,6,3,5,4,2,5,1,2,4,4,3,2,1)                      

###############################################################
## Use a (m=4 state) hidden Markov model based on the #########
## generalized poisson distribution to assign an      #########
## activity range to the counts                       #########
###############################################################
## In this example three activity ranges                   ####
## (named as "light", "moderate" and "vigorous" physical   ####
## activity) are separated by the two cut-points 15 and 23 ####
###############################################################

## TIME CONSUMING:
## Not run: 
HMM_based_cut_off_point_method <- HMM_based_method(x = x, 
 	 cut_points = c(15,23), 
 	 min_m = 4, 
 	 max_m = 4, 
 	 names_activity_ranges = c("LIG","MOD","VIG"), 
 	 distribution_class = "genpois", 
 	 training_method = "numerical",
 	 DNM_limit_accuracy = 0.05,
 	 DNM_max_iter = 10,
 	 bout_lengths = c(1,1,2,4,5,10,11,20,21,60,61,260),
 	 plotting = 1)

## End(Not run) 	 
 	 
 	 

###############################################################
## Example 4) In a single function (Step 1-3 of Example 2  ####
##            combined in one function)                    ####
##            (large and highly scatterd time-series)      ####
###############################################################

	 
################################################################
### Generate a large time-series of highly scattered counts ####
################################################################

x <- HMM_simulation(
 size = 1500, 
 m = 10,
 gamma = 0.93 * diag(10) + rep(0.07 / 10, times = 10),
 distribution_class = "norm", 
 distribution_theta = list(mean = c(10, 100, 200, 300, 450, 
 600, 700, 900, 1100, 1300, 1500), 
 sd=c(rep(100,times=10))), 
 obs_round=TRUE, 
 obs_non_neg=TRUE,
 plotting=5)$observations

################################################################
### Compare results of the tradional cut-point method ##########
### and the (6-state-normal-)HMM based method ##################
################################################################
		
traditional_cut_off_point_method <- cut_off_point_method(x=x, 
 	 cut_points = c(200,500,1000), 
 	 names_activity_ranges = c("SED","LIG","MOD","VIG"), 
 	 bout_lengths = c(1,1,2,4,5,10,11,20,21,60,61,260),
 	 plotting = 1)

## TIME CONSUMING:
## Not run: 
HMM_based_cut_off_point_method <- HMM_based_method(x=x,
	 max_scaled_x = 200, 
 	 cut_points = c(200,500,1000), 
 	 min_m = 6, 
 	 max_m = 6,
 	 BW_limit_accuracy = 0.5, 
 	 BW_max_iter = 10,
 	 names_activity_ranges = c("SED","LIG","MOD","VIG"), 
 	 distribution_class = "norm", 
 	 bout_lengths = c(1,1,2,4,5,10,11,20,21,60,61,260),
 	 plotting = 1)

## End(Not run)

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(HMMpa)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/HMMpa/HMMpa-package.Rd_%03d_medium.png", width=480, height=480)
> ### Name: HMMpa-package
> ### Title: Analysing Accelerometer Data Using Hidden Markov Models
> ### Aliases: HMMpa-package HMMpa
> ### Keywords: ts iteration
> 
> ### ** Examples
> 
> 
> ################################################################
> ###     Example 1  (traditional approach)    ################### 
> ###     Solution of the cut-off point method ################### 
> ################################################################
> 
> ################################################################
> ### Fictitious activity counts #################################
> ################################################################
> 
> x <- c(1,16,19,34,22,6,3,5,6,3,4,1,4,3,5,7,9,8,11,11,
+   14,16,13,11,11,10,12,19,23,25,24,23,20,21,22,22,18,7,
+   5,3,4,3,2,3,4,5,4,2,1,3,4,5,4,5,3,5,6,4,3,6,4,8,9,12,
+   9,14,17,15,25,23,25,35,29,36,34,36,29,41,42,39,40,43,
+   37,36,20,20,21,22,23,26,27,28,25,28,24,21,25,21,20,21,
+   11,18,19,20,21,13,19,18,20,7,18,8,15,17,16,13,10,4,9,
+   7,8,10,9,11,9,11,10,12,12,5,13,4,6,6,13,8,9,10,13,13,
+   11,10,5,3,3,4,9,6,8,3,5,3,2,2,1,3,5,11,2,3,5,6,9,8,5,
+   2,5,3,4,6,4,8,15,12,16,20,18,23,18,19,24,23,24,21,26,
+   36,38,37,39,45,42,41,37,38,38,35,37,35,31,32,30,20,39,
+   40,33,32,35,34,36,34,32,33,27,28,25,22,17,18,16,10,9,
+   5,12,7,8,8,9,19,21,24,20,23,19,17,18,17,22,11,12,3,9,
+   10,4,5,13,3,5,6,3,5,4,2,5,1,2,4,4,3,2,1)  
>     
>     
> traditional_cut_off_point_method <- cut_off_point_method(x=x, 
+  	cut_points = c(5,15,23), 
+  	names_activity_ranges = c("SED","LIG","MOD","VIG"), 
+  	bout_lengths = c(1,1,2,4,5,10,11,20,21,60,61,260),
+  	plotting = 1)
$activity_ranges
, , 1

     [lower boundary, upper boundary)
[1,]                0               5

, , 2

     [lower boundary, upper boundary)
[1,]                5              15

, , 3

     [lower boundary, upper boundary)
[1,]               15              23

, , 4

     [lower boundary, upper boundary)
[1,]               23             Inf


$classification
  [1] 1 3 3 4 3 2 1 2 2 1 1 1 1 1 2 2 2 2 2 2 2 3 2 2 2 2 2 3 4 4 4 4 3 3 3 3 3
 [38] 2 2 1 1 1 1 1 1 2 1 1 1 1 1 2 1 2 1 2 2 1 1 2 1 2 2 2 2 2 3 3 4 4 4 4 4 4
 [75] 4 4 4 4 4 4 4 4 4 4 3 3 3 3 4 4 4 4 4 4 4 3 4 3 3 3 2 3 3 3 3 2 3 3 3 2 3
[112] 2 3 3 3 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 1 1 2 2
[149] 2 1 2 1 1 1 1 1 2 2 1 1 2 2 2 2 2 1 2 1 1 2 1 2 3 2 3 3 3 4 3 3 4 4 4 3 4
[186] 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 3 3 3 3 2 2 2
[223] 2 2 2 2 2 3 3 4 3 4 3 3 3 3 3 2 2 1 2 2 1 2 2 1 2 2 1 2 1 1 2 1 1 1 1 1 1
[260] 1

$rel_freq_acitvity_range

      SED       LIG       MOD       VIG 
0.2038462 0.3500000 0.1961538 0.2500000 

$quantity_of_bouts
[1] 90

$abs_freq_bouts_el
       1    2 - 4   5 - 10  11 - 20  21 - 60 61 - 260 
      44       28       13        5        0        0 

>  	
> 
> 
> ################################################################ 
> ################################################################ 
> ###      Examples 2,3 and 4  (new approach)             ########
> ###      Solution of the HMM based cut-off point method ######## 
> ################################################################
> ###      Demonstrated both in three steps (Example 2)     ###### 
> ###      and condensed in one function (Examples 3 and 4) ######
> ################################################################
> 
> ################################################################
> ### Example 2) Manually in three steps    ######################
> ################################################################
> 
> ################################################################
> ### Fictitious activity counts #################################
> ################################################################
>                                                                 
> x <- c(1,16,19,34,22,6,3,5,6,3,4,1,4,3,5,7,9,8,11,11,           
+   14,16,13,11,11,10,12,19,23,25,24,23,20,21,22,22,18,7,         
+   5,3,4,3,2,3,4,5,4,2,1,3,4,5,4,5,3,5,6,4,3,6,4,8,9,12,         
+   9,14,17,15,25,23,25,35,29,36,34,36,29,41,42,39,40,43,         
+   37,36,20,20,21,22,23,26,27,28,25,28,24,21,25,21,20,21,        
+   11,18,19,20,21,13,19,18,20,7,18,8,15,17,16,13,10,4,9,         
+   7,8,10,9,11,9,11,10,12,12,5,13,4,6,6,13,8,9,10,13,13,         
+   11,10,5,3,3,4,9,6,8,3,5,3,2,2,1,3,5,11,2,3,5,6,9,8,5,         
+   2,5,3,4,6,4,8,15,12,16,20,18,23,18,19,24,23,24,21,26,         
+   36,38,37,39,45,42,41,37,38,38,35,37,35,31,32,30,20,39,        
+   40,33,32,35,34,36,34,32,33,27,28,25,22,17,18,16,10,9,         
+   5,12,7,8,8,9,19,21,24,20,23,19,17,18,17,22,11,12,3,9,         
+   10,4,5,13,3,5,6,3,5,4,2,5,1,2,4,4,3,2,1)                      
>      
> ################################################################
> ## Step 1: Training of a HMM ##################################
> ##         for the given time-series of counts ################ 
> ##         ####################################################
> ##         More precisely: training of a poisson ##############
> ##         distribution based hidden Markov model for #########
> ##         number of states m=2,...,6 #########################
> ##         and selection of the model with the most ########### 
> ##         plausible m ########################################
> ################################################################
> 
> ## TIME CONSUMING
> ## Not run: 
> ##D m_trained_HMM <- HMM_training(x = x, 
> ##D  min_m = 2, 
> ##D  max_m = 6, 
> ##D  distribution_class = "pois")$trained_HMM_with_selected_m  
> ##D  	 
> ##D ###############################################################
> ##D ## Step 2: Decoding of the trained HMM for the given ##########
> ##D ##         time-series of accelerometer counts to extract #####
> ##D ##         hidden PA-levels ###################################
> ##D ###############################################################
> ##D  
> ##D hidden_PA_levels <- HMM_decoding(x = x, 
> ##D  	 m = m_trained_HMM$m, 
> ##D  	 delta = m_trained_HMM$delta, 
> ##D  	 gamma = m_trained_HMM$gamma, 
> ##D  	 distribution_class = m_trained_HMM
> ##D  	 $distribution_class, 
> ##D  	 distribution_theta = m_trained_HMM$
> ##D  	 distribution_theta)$decoding_distr_means
> ##D 
> ##D ############################################################### 
> ##D ## Step 3: Assigning of user-sepcified activity ranges ########
> ##D ##         to the accelerometer counts via the total ##########
> ##D ##         magnitudes of their corresponding ##################
> ##D ##         hidden PA-levels ###################################
> ##D ##         ####################################################
> ##D ##         In this example four activity ranges ###############
> ##D ##         (named as "sedentary", "light", "moderate" #########
> ##D ##         and "vigorous" physical activity) are ##############
> ##D ##         separated by the three cut-points 5, 15 and 23) ####
> ##D ################################################################
> ##D  
> ##D HMM_based_cut_off_point_method <- cut_off_point_method(x = x, 
> ##D  	 hidden_PA_levels = hidden_PA_levels, 
> ##D  	 cut_points = c(5,15,23), 
> ##D  	 names_activity_ranges = c("SED","LIG","MOD","VIG"), 
> ##D  	 bout_lengths = c(1,1,2,4,5,10,11,20,21,60,61,260),
> ##D  	 plotting=1)      				 
> ## End(Not run)
> 
> 
> 
> ###############################################################
> ## Example 3) In a single function (Step 1-3 of Example 2  ####
> ##            combined in one function)                    ####
> ###############################################################
> 	
> ###############################################################
> ## Fictitious activity counts #################################
> ###############################################################
>                                                                 
> x <- c(1,16,19,34,22,6,3,5,6,3,4,1,4,3,5,7,9,8,11,11,           
+   14,16,13,11,11,10,12,19,23,25,24,23,20,21,22,22,18,7,         
+   5,3,4,3,2,3,4,5,4,2,1,3,4,5,4,5,3,5,6,4,3,6,4,8,9,12,         
+   9,14,17,15,25,23,25,35,29,36,34,36,29,41,42,39,40,43,         
+   37,36,20,20,21,22,23,26,27,28,25,28,24,21,25,21,20,21,        
+   11,18,19,20,21,13,19,18,20,7,18,8,15,17,16,13,10,4,9,         
+   7,8,10,9,11,9,11,10,12,12,5,13,4,6,6,13,8,9,10,13,13,         
+   11,10,5,3,3,4,9,6,8,3,5,3,2,2,1,3,5,11,2,3,5,6,9,8,5,         
+   2,5,3,4,6,4,8,15,12,16,20,18,23,18,19,24,23,24,21,26,         
+   36,38,37,39,45,42,41,37,38,38,35,37,35,31,32,30,20,39,        
+   40,33,32,35,34,36,34,32,33,27,28,25,22,17,18,16,10,9,         
+   5,12,7,8,8,9,19,21,24,20,23,19,17,18,17,22,11,12,3,9,         
+   10,4,5,13,3,5,6,3,5,4,2,5,1,2,4,4,3,2,1)                      
> 
> ###############################################################
> ## Use a (m=4 state) hidden Markov model based on the #########
> ## generalized poisson distribution to assign an      #########
> ## activity range to the counts                       #########
> ###############################################################
> ## In this example three activity ranges                   ####
> ## (named as "light", "moderate" and "vigorous" physical   ####
> ## activity) are separated by the two cut-points 15 and 23 ####
> ###############################################################
> 
> ## TIME CONSUMING:
> ## Not run: 
> ##D HMM_based_cut_off_point_method <- HMM_based_method(x = x, 
> ##D  	 cut_points = c(15,23), 
> ##D  	 min_m = 4, 
> ##D  	 max_m = 4, 
> ##D  	 names_activity_ranges = c("LIG","MOD","VIG"), 
> ##D  	 distribution_class = "genpois", 
> ##D  	 training_method = "numerical",
> ##D  	 DNM_limit_accuracy = 0.05,
> ##D  	 DNM_max_iter = 10,
> ##D  	 bout_lengths = c(1,1,2,4,5,10,11,20,21,60,61,260),
> ##D  	 plotting = 1)
> ## End(Not run) 	 
>  	 
>  	 
> 
> ###############################################################
> ## Example 4) In a single function (Step 1-3 of Example 2  ####
> ##            combined in one function)                    ####
> ##            (large and highly scatterd time-series)      ####
> ###############################################################
> 
> 	 
> ################################################################
> ### Generate a large time-series of highly scattered counts ####
> ################################################################
> 
> x <- HMM_simulation(
+  size = 1500, 
+  m = 10,
+  gamma = 0.93 * diag(10) + rep(0.07 / 10, times = 10),
+  distribution_class = "norm", 
+  distribution_theta = list(mean = c(10, 100, 200, 300, 450, 
+  600, 700, 900, 1100, 1300, 1500), 
+  sd=c(rep(100,times=10))), 
+  obs_round=TRUE, 
+  obs_non_neg=TRUE,
+  plotting=5)$observations
> 
> ################################################################
> ### Compare results of the tradional cut-point method ##########
> ### and the (6-state-normal-)HMM based method ##################
> ################################################################
> 		
> traditional_cut_off_point_method <- cut_off_point_method(x=x, 
+  	 cut_points = c(200,500,1000), 
+  	 names_activity_ranges = c("SED","LIG","MOD","VIG"), 
+  	 bout_lengths = c(1,1,2,4,5,10,11,20,21,60,61,260),
+  	 plotting = 1)
$activity_ranges
, , 1

     [lower boundary, upper boundary)
[1,]                0             200

, , 2

     [lower boundary, upper boundary)
[1,]              200             500

, , 3

     [lower boundary, upper boundary)
[1,]              500            1000

, , 4

     [lower boundary, upper boundary)
[1,]             1000             Inf


$classification
   [1] 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3
  [38] 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 3 4 3 4 4 4 4 3 4 3 4 3 4 4 4 4 4
  [75] 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 2 4 4 4 4 4 4 4 4 4 4
 [112] 4 4 4 4 4 4 4 4 4 4 3 3 4 3 2 3 2 3 3 3 2 1 1 1 1 1 2 2 2 1 2 1 1 1 1 1 1
 [149] 1 1 3 3 3 3 3 2 3 3 3 3 2 3 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 2 1 2
 [186] 1 1 1 1 1 1 1 1 2 1 1 2 2 4 4 1 1 1 1 1 1 1 1 1 3 3 3 2 2 3 3 2 3 2 3 2 3
 [223] 3 3 3 2 2 2 3 2 2 3 2 2 2 2 3 2 2 2 3 2 3 1 2 2 3 3 2 2 3 2 2 3 3 3 3 2 2
 [260] 3 2 2 2 2 2 3 3 2 3 4 3 3 3 3 3 3 4 3 4 3 3 3 3 3 3 3 3 4 3 3 3 4 4 3 3 3
 [297] 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 4 3 4 3 3 3 3 3 3
 [334] 3 3 4 3 3 3 3 4 3 3 3 4 3 4 3 2 3 2 2 2 2 2 3 2 2 2 2 2 3 2 3 2 2 2 3 2 2
 [371] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 2 3 3
 [408] 3 2 2 2 2 1 1 2 1 1 2 2 2 2 1 2 2 2 2 3 2 2 1 2 2 2 2 2 2 2 2 2 2 2 1 3 3
 [445] 3 3 3 2 2 3 2 2 3 3 2 2 2 2 2 3 2 3 2 2 3 3 2 3 2 2 2 3 3 2 2 2 3 3 2 3 3
 [482] 2 2 3 2 2 3 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 2 2 3 3 2 2 2 2
 [519] 2 2 2 2 2 2 2 2 2 3 3 2 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 1 2 2 2
 [556] 2 3 3 2 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 2 3 2 2 2 3 3 3 2 2 1 1 2 2 2 2 1 1
 [593] 1 1 1 1 3 3 3 4 3 3 1 1 2 3 2 3 4 4 4 4 4 4 4 4 4 2 3 3 2 2 2 2 2 1 3 3 3
 [630] 3 4 3 4 4 3 3 4 3 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3
 [667] 3 3 3 3 3 2 3 3 3 3 3 3 2 3 3 3 3 3 2 3 2 2 2 2 2 3 2 2 2 2 3 3 3 2 2 2 2
 [704] 3 3 2 2 2 2 2 2 2 3 2 2 2 2 2 2 3 2 3 2 2 2 2 3 3 3 2 3 2 3 3 3 2 3 2 3 2
 [741] 3 2 3 2 2 3 2 2 2 3 2 2 2 2 2 2 2 2 2 2 3 3 2 3 3 3 3 2 3 2 2 2 3 2 3 2 2
 [778] 3 2 3 2 2 3 3 3 2 2 3 2 2 2 3 2 3 2 3 2 2 2 2 2 3 2 2 2 2 2 3 2 2 1 2 1 2
 [815] 2 1 2 1 1 2 1 2 1 2 2 2 2 2 3 3 3 2 2 3 3 3 3 2 1 1 2 2 2 2 1 2 2 1 4 4 4
 [852] 4 4 4 4 4 1 1 2 2 1 1 2 2 1 1 2 1 2 1 1 1 1 2 2 2 1 1 2 1 1 1 1 1 1 1 1 1
 [889] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 1 2 1 2 2 1 1 1 1 1 1 1
 [926] 1 4 4 4 3 4 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 4 4 2 2 2 1 1 1 2 4 4 4 4 4 4 4
 [963] 3 2 2 2 2 2 2 2 2 3 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 3 2 3 2 2 3 3 3 2 2 3 2
[1000] 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 2 3 2 3 2 3 2 3 3 3
[1037] 3 3 4 3 3 3 3 3 2 3 3 3 2 2 3 2 2 2 2 3 3 3 3 3 3 1 1 1 2 1 1 1 1 1 1 1 1
[1074] 2 4 4 4 4 4 4 4 1 2 2 2 1 2 2 3 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2
[1111] 2 2 2 2 2 2 1 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1 1 1 2 1
[1148] 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3
[1185] 3 3 3 3 3 3 3 3 3 3 3 3 1 2 1 1 1 1 1 1 3 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3
[1222] 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
[1259] 3 3 3 3 3 1 2 1 2 2 2 1 2 2 1 2 1 2 1 2 1 1 2 2 2 2 2 1 1 2 1 1 2 2 1 2 2
[1296] 1 2 2 1 2 1 1 2 2 2 2 1 2 2 1 2 2 2 2 2 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1333] 1 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4
[1370] 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 1 1 2 1 1 1
[1407] 3 3 3 3 3 1 3 3 3 3 3 2 3 3 3 2 3 3 3 2 3 3 3 3 3 3 1 1 1 1 1 1 2 1 1 1 1
[1444] 1 3 4 4 4 4 4 4 4 4 4 2 3 2 2 3 3 3 3 3 3 3 3 3 2 3 2 3 3 2 3 3 3 4 4 4 4
[1481] 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 2 2

$rel_freq_acitvity_range

      SED       LIG       MOD       VIG 
0.2166667 0.2886667 0.4006667 0.0940000 

$quantity_of_bouts
[1] 463

$abs_freq_bouts_el
       1    2 - 4   5 - 10  11 - 20  21 - 60 61 - 260 
     231      144       62       19        7        0 

> 
> ## TIME CONSUMING:
> ## Not run: 
> ##D HMM_based_cut_off_point_method <- HMM_based_method(x=x,
> ##D 	 max_scaled_x = 200, 
> ##D  	 cut_points = c(200,500,1000), 
> ##D  	 min_m = 6, 
> ##D  	 max_m = 6,
> ##D  	 BW_limit_accuracy = 0.5, 
> ##D  	 BW_max_iter = 10,
> ##D  	 names_activity_ranges = c("SED","LIG","MOD","VIG"), 
> ##D  	 distribution_class = "norm", 
> ##D  	 bout_lengths = c(1,1,2,4,5,10,11,20,21,60,61,260),
> ##D  	 plotting = 1)
> ## End(Not run)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>


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