In this paper, Viterbi algorithm based on a hidden Markov model is applied to recognize activity sequences from observed sensors events. Alternative features selections of time feature values of sensors events and activity length size feature values are tested, respectively, and then the results of activity sequences recognition performances of Viterbi algorithm are evaluated. The results show that the selection of larger time feature values of sensor events and/or smaller activity length size feature values will generate relatively better results on the activity sequences recognition performances.

1. Research Article
Influence of time and length size feature selections for human activity
sequences recognition
Hongqing Fang a,n
, Long Chen a
, Raghavendiran Srinivasan b
a
College of Energy & Electrical Engineering, Hohai University, Jiangsu 211100, PR China
b
School of Electrical Engineering & Computer Science, Washington State University, WA 99163, USA
a r t i c l e i n f o
Article history:
Received 6 January 2013
Received in revised form
17 August 2013
Accepted 4 September 2013
Available online 25 September 2013
Keywords:
Activity recognition
Feature selections
Hidden Markov model
Viterbi algorithm
Smart home
a b s t r a c t
In this paper, Viterbi algorithm based on a hidden Markov model is applied to recognize activity
sequences from observed sensors events. Alternative features selections of time feature values of sensors
events and activity length size feature values are tested, respectively, and then the results of activity
sequences recognition performances of Viterbi algorithm are evaluated. The results show that the
selection of larger time feature values of sensor events and/or smaller activity length size feature values
will generate relatively better results on the activity sequences recognition performances.
& 2013 ISA. Published by Elsevier Ltd. All rights reserved.
1. Introduction
The smart homes [1–16] provide continuous monitoring cap-
ability that conventional methodologies lack. Being able to auto-
mate the activity recognition from human motion patterns using
unobtrusive sensors or other devices can be useful in monitoring
older adults in their homes and keeping track of their activities of
daily livings (ADLs) and behavioral changes [13–23]. The Center for
Advanced Studies in Adaptive Systems (CASAS) smart home
project is a multi-disciplinary research project at Washington
State University, focused on the creation of an intelligent
home environment. The approach is to view the smart home as
an intelligent agent that perceives its environment through the
use of sensors, and can act upon the environment through the use
of actuators. The research goals of the CASAS smart home project
are to enhance and improve quality of life, prolong stay at
home with technology-enabled assistance, minimize the cost of
maintaining the home and maximize the comfort of its inhabitants
[8–10].
To implement the goal of the CASAS smart home project, a
primary challenge is to design an algorithm that labels the activity
performed by an inhabitant in a smart environment from the sensor
data collected by the environment during the activity. Medical
professionals also believe that one of the best ways to detect
emerging medical conditions before they become serious is to look
for changes in the ADLs. Recently, human activity discovery and
recognition has gained a lot of interest due to its enormous potential
in context aware computing systems, including smart home envir-
onments. To recognize residents' activities and their daily routines
can greatly help in providing automation, security, and more
importance in remote health monitoring of elder or people with
disabilities. The main objective of human activity recognition in
smart home environments is to find interesting patterns of behavior
from sensor data and to recognize such patterns. Researchers have
commonly tested the machine learning algorithms such as
knowledge-driven approach (KDA) [13], evolutionary ensembles
model (EEM) [14], support vector machine (SVM) [15], Dempster–
Shafer theory of evidence (D–S) [16], naïve Bayes (NB) classifier,
Markov model (MM), hidden Markov model (HMM) and conditional
random fields (CRF) [17–30], etc., for human activity (pattern)
recognition in smart home environments. Even though the datasets
include a large number of sensor events sequences generated by a
various activities, the results appear in these papers are mainly the
evaluation and comparison of the total activity recognition accuracy
rate generated by different machine learning algorithms. Another
shortcoming is that any activity annotated in dataset has various
features. Usually, these features values are selected in one method in
all tests. However, the influences of these feature values to human
activity recognition performance are seldom addressed in previous
works. Moreover, it is also necessary to recognize which activities
generate sensor events sequences.
Contents lists available at ScienceDirect
journal homepage: www.elsevier.com/locate/isatrans
ISA Transactions
0019-0578/$ - see front matter & 2013 ISA. Published by Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.isatra.2013.09.001
n
Corresponding author. Tel.: þ86 18061705168.
E-mail addresses: fanghongqing@sohu.com, fanghongqing@gmail.com
(H. Fang).
ISA Transactions 53 (2014) 134–140

2. In this paper, Viterbi algorithm is a dynamic programming
algorithm for finding the most likely sequence of hidden states
that results in a sequence of observed events, especially in the
context of Markov information sources [31,32] and hidden Markov
models [24,25,28–30,33]. Therefore, Viterbi algorithm is applied to
recognize activities sequences from observed sensors events
sequences. And then, alternative features selections are tested
[34–36], and finally the results of activities sequences recognition
performance measures of Viterbi algorithm with different time
feature values of sensor events and activity length size feature
values are evaluated.
The rest of the paper is organized as follows. Section 2 briefly
describes the smart apartment testbed installed in the Washington
State University campus and also the data collection procedures.
Section 3 describes Viterbi algorithm applied to represent and
recognize human activities sequences. Section 4 presents the
results of the influence of time and activity length size feature
values to activities sequences recognitions performances. Section 5
summarizes the main contributions.
2. Smart apartment testbed and data collection
The smart apartment testbed is located on Washington State
University campus and is maintained as part of the ongoing CASAS
smart home project [8–10,18,24–30]. As shown in Fig. 1, the smart
apartment testbed includes three bedrooms, one bathroom, a
kitchen, and a living/dining room. The smart apartment is equipped
with motion sensors distributed approximately 1 m apart through-
out the space on the ceilings. In addition, other sensors installed
provide ambient temperature readings and custom-built analog
sensors provide readings for hot water, cold water, and stove burner
use. Voice over IP using Asterisk software captures phone usage and
contact switch sensors to monitor usage of key items including
a cooking pot, a medicine container, and the phone book. Lastly,
Insteon power controls and switches are used to monitor and control
the lighting in the space. Sensors data are captured using a sensor
network that was designed in-house and stored in a SQL database.
The middleware uses a XMPP-based publish-subscribe protocol as a
lightweight platform and language-independent method to push
data to client tools with minimal overhead and maximal flexibility.
After collecting data from the smart apartment testbed, the sensors
events are annotated for ADLs. A large number of sensors events are
generated everyday.
The data gathered by CASAS smart home is represented by the
following parameters, which specify the number of features that
are used to describe the sensors events. The default number of
features is 5. The default interpretation of the five features is:
(1) Sensor ID, which is an integer value in the range of 0 to the
number of logical sensor values.
(2) Time of day, which is the input time of the sensor event but is
discretized to an integer value. The default value is 5, which
means the time ranges of one entire day are 0–5, 6–10, 11–15,
16–20, and 21–24. The value of this feature is adjustable.
(3) Day of week, which the input date of the sensor event is
converted into a value in the range of 0–6 that represents the
day of the week on which the sensor event occurred.
(4) Previous activity, which is an integer value that represents the
activity that occurred before the current activity.
(5) Activity length, which represents the length of the current
activity measured in number of sensors events. The value of
this feature is to calculate the value of length size threshold,
and the default value is 3, which means the length size of each
activity is distinguished by 3 thresholds: {small, medium,
large}. The value of this feature is adjustable.
The generalized syntax of the dataset is given below.
Date Time SensorID SensorValue 〈label〉
An example of the dataset of Night_wandering activity is
{
2009-06-10 03:20:59.08 M006 ON Night_wandering begin
2009-06-10 03:25:19.05 M012 ON
2009-06-10 03:25:19.08 M011 ON
2009-06-10 03:25:24.05 M011 OFF
2009-06-10 03:25:24.07 M012 OFF Night_wandering end
}
This example shows one sensors sequence corresponds to the
Night_wandering activity with concrete Date, Time, SensorID,
SensorValue as well as activity label parameters [18–30].
3. Viterbi algorithm applied for activity sequences recognition
An HMM is a statistical model in which the underlying model is a
stochastic process that is not observable (i.e., hidden) and is assumed
to be a Markov process which can be observed through another set
of stochastic processes that produce the sequence of observed
symbols [33]. The current state depends on a finite history of previous
states. Actually, in this research, the current state depends only on the
previous state. An HMM models a system using a finite set of states.
A hidden state is used to represent each of the separate activities.
Each observable and hidden state is associated with a multidimen-
sional probability distribution over a set of parameters. The parameters
for the model are the features values described in the previous section.
Transitions between states are governed by transition probabilities.
An HMM assigns probability values over a potentially infinite number
of sequences. But as the probabilities values must sum to one, the
distribution described by HMM is constrained. The conditional prob-
ability distribution of any hidden state depends only on the value of
the preceding hidden state. Similarly, the value of an observable state
depends only on the value of the current hidden state.
Consider a system that has N distinct states, fs1; s2; ⋯; sNg, and
the actual state at time t is qt ¼ si; 1rirN , then each state has
M distinct observation symbols, which can be denoted as
fv1; v2; ⋯; vMg. In the theory of HMM, the observable variable
ot ¼ vk; 1rk rM at time t depends only on the hidden state
variable si at that time.Fig. 1. The smart apartment testbed.
H. Fang et al. / ISA Transactions 53 (2014) 134–140 135

3. An HMM utilizes three probability distributions, the first is a
probability distribution over initial states
πi ¼ Pðq1 ¼ siÞ ð1Þ
Second, the state transition probability distribution represents
the probability of transitioning from state i to state j, which has the
form of
aij ¼ Pðqt ¼ sjjqt À1 ¼ siÞ; 1ri; jrN ð2Þ
Third, the observation probability distribution indicates the
probability that the state j would generate observation ot ¼ vk
bjðkÞ ¼ Pðot ¼ vkjqt ¼ sjÞ; 1rjrN; 1rkrM ð3Þ
These distributions are estimated based on the relative fre-
quencies of visited states and state transitions observed in the
training data.
In this case, the Viterbi algorithm can be applied to identify this
sequence of hidden states, which compute the most likely
sequence of hidden states that correspond to a sequence of
observable sensors events.
The aim of Viterbi algorithm are to find the single best state
sequence, fqn
1; qn
2; ⋯; qn
T g, for a given observation sequence,
fo1; o2; ⋯; oT g. The best score, i.e., the highest probability, along a
single path at time t is define as
δtðiÞ ¼ max
q1;q2;⋯;qt À 1
Pðq1q2⋯qt ¼ si; o1o2⋯otÞ ð4Þ
δtðiÞ accounts for the first t observations and end in state si, and
it can be solved inductively as
δt þ1ðjÞ ¼ ½ max
1r ir N
δtðiÞUaijŠUbjðot þ 1Þ ð5Þ
where 1rjrN and 1rtrT À1.
The initialization is
δ1ðiÞ ¼ πi Ubiðo1Þ; 1rirN ð6Þ
In each recursion of Eq. (5), the label of a hidden state which in
Eq. (4) is returned by
l
n
t ¼ arg max ½δtðiÞŠ
1r ir N
ð7Þ
Once the procedure is done, the best hidden state label
sequence can be obtained as fl
n
1; l
n
2; ⋯; l
n
T g, which corresponds to
the best hidden state sequence fqn
1; qn
2; ⋯; qn
T g.
To implement Viterbi algorithm, each activity is treated as a
hidden state. Since a total of m activities are labeled in the dataset
to be recognized, Viterbi algorithm includes m hidden states. Each
hidden state denotes one of the m modeled activities. Next, each
sensor is treated as an observable state, because of each used
sensor is observable in the dataset.
Viterbi algorithm processes the sensors events sequence as a
continuous stream, and then return the activity label (hidden
node) with the highest probability, which corresponds to the most
recent sensor event. However, since one sensor event may have
different probabilities corresponding to different hidden states
(activities), therefore, the recognition accuracy is not definitely
100%.
In this research, Viterbi algorithm uses the relative frequencies
of features values and the activity labels for the sample train-
ing data to learn a mapping from a data point description to a
classification label. It determines activity labels probabilistically
based on the number of sensor event of various kinds that occu-
rred during the activity. All activities are represented by various
features including the number of occurring times of sensor ID,
time of day, day of week, previous activity and activity length.
Actually, Viterbi algorithm uses three probability distributions:
the distribution over initial states πi, the state transition prob-
ability distribution aij, and the observation distribution bjðkÞ. These
probability distributions are estimated based on the relative
frequencies of visited states and state transitions observed in the
training data. Given a set of training data, Viterbi algorithm uses
the sensors values as parameters of a hidden Markov model. Given
an input sequence of sensors events observations, the goal is to
find the most likely sequence of hidden states, or activities, which
could have generated the observed event sequence, following the
calculation in Eq. (7). Furthermore, the training data are used to
learn the transition probabilities between states for the corre-
sponding activity model and to learn probability distributions for
the features values of each state in the model. For this, the prior
probability (i.e., the start probability) of every state can be
calculated based on the collected data. The prior probability
represents the belief about which state of HMM is in when the
first sensor event is seen. For a state (i.e., activity) A, it is calculated
as the ratio of instances for which the activity label is A. The
transition probability which represents the change of the state in
the underlying hidden Markov model, can also be calculated. For
any two states A and B, the probability of transitioning from state A
to state B is calculated as the ratio of instances having activity label
A followed by activity label B, to the total number of instances. The
transition probability signifies the likelihood of transitioning from
a given state to any other state in the model and captures the
temporal relationship between the states. Furthermore, the emis-
sion probability represents the likelihood of observing a particular
sensor event for a given activity. This is calculated by finding the
frequency of every sensor event as observed for each activity [29].
4. Tests results
4.1. Training activities
A total of 10 activities were performed in the CASAS smart
apartment by two volunteers to provide physical training data for
the Viterbi algorithm. These activities include both basic and more
complex ADLs that are found in clinical questionnaires. These
activities are:
(1) Bed_to_toilet (activity 0, A0): transition between bed and
toilet in the nighttime.
(2) Breakfast (activity 1, A1): the residents have breakfast.
(3) Bed (activity 2, A2): the activity of sleeping in bed.
(4) C_work (activity 3, A3): the activity of residents work in the
office space.
(5) Dinner (activity 4, A4): the residents have dinner.
(6) Laundry (activity 5, A5): the residents clean clothes using the
laundry machine.
(7) Leave_home (activity 6, A6): the activity of the resident
leaves the smart home.
(8) Lunch (activity 7, A7): the residents have lunch.
(9) Night_wandering (activity 8, A8): the activity of the residents
wanders during nighttime sleep.
(10) R_medicine (activity 9, A9): the activity of the residents takes
medicine.
The data have been collected in the CASAS smart apartment
testbed for 55 days, which resulting in total 600 instances of these
activities and 647, 485 collected motion sensors events. The 3-fold
cross validation is applied in this research.
4.2. Selections of time feature values
In this case, the activity length size feature value is defined as
the default value 3. This means that three activity length size
ranges are used. However, the time feature values are compared
H. Fang et al. / ISA Transactions 53 (2014) 134–140136

4. for different numbers of ranges including 1, 2, 3, 4, 5, 6, 8, 12 and
24, respectively.
Table 1 shows that Viterbi algorithm has the best hidden states
sequence average recognition accuracy rate when time feature
value is 24 for activities 0, 2, 3, 4, and 8, i.e., the proportion is 50%
of all activities. When time feature value is 12, the best results are
generated of activities 1, 6 and 9, and the proportion is 30%. Also,
activity 7 has the best result when time feature value is 6. The only
one exception is activity 5, for which the best result is generated
when time feature value is 3.
Again, it can be seen from Table 2 that 30% of all the activities, i.
e., activities 2, 5 and 8, have the best hidden states sequence
recognition success rate when time feature value is 24. Activities 0,
3 and 9 have the best results if time feature value is 12, which is of
the same proportion. Further, activity 6 has the best result when
time feature value is 8; activity 1 has the best result when time
feature value is 6; activity 7 has the best result when time feature
value is 4; and activity 4 has the best result when time feature
value is 2.
Similarly, Table 3 shows that activities 0, 1, 4, 7 and 8 have the
lowest hidden states sequence recognition failure rates with a
time feature value of 24, and the proportion is 50%. The best time
feature value for activity 6 is 12, and for activity 9 is 8. Activities
2 and 5 have the same best time feature value of 6. Activity 3 has
the best time feature value of 1.
One important point to be noted is that more than one optimal
results shown in Tables 1–3 are not generated under only one
specific time feature value, which means that Viterbi algorithm
generate the same optimal results under different time feature
values. However, in these tests, only the maximal optimal time
feature value for each activity is listed above. Even though, it
shows that most of the activities have better results with a
relatively higher time feature value. The reasons can be explained
from the statistical data shown in Table 4, which shows the hour-
by-hour sensors events proportion of the 10 activities. Since one
day has 24 h, therefore, if time feature value is defined as 24,
which means 24 separate time zones are defined, hour-by-hour.
Actually, Table 4 also reflects that the living habits of the residents
or ADLs have strong relationship with time of the residents in
CASAS smart home, e.g., for activity 0 (bed-to-toilet), 17.75%
sensors events occur in the time zone of (0:00–1:00), 29.12%
sensors events occur in the time zone of (2:00–3:00), and there
are no sensors events occur in the time zone of (8:00–22:00). A
relatively larger time feature value means more precise time zone
resolution, which generates relatively better results.
4.3. Selections of activity length size feature values
In this case, time feature value is defined with a larger value as
24, and activity length size feature value is defined from 2 to 45,
respectively.
Fig. 2 shows the trends of the hidden states sequence average
recognition accuracy rates of activities 0–9 generated by Viterbi
algorithm with the increasing of activity length size feature values.
In this test, it shows that activity 0 yields an optimal result with
activity length size feature value of 16; the optimal length feature
value for activity 1 is 4; activities 2 and 5 have the same optimal
activity length size feature value of 3; activities 3 and 9 have the
same optimal activity length size feature value of 5; the optimal
activity length size feature value for activity 4 is 23; for activity 6,
it is 43;for activity 7, it is 6; and for activity 8, it is 10. Therefore, a
proportion of 70% of all activities have relatively small optimal
activity length size feature values, which are not more than 10.
Fig. 3 shows the trends of the hidden states sequence recogni-
tion success rate of activities 0–9 generated by Viterbi algorithm
with increasing of length feature values. It can be found that the
proportion is 50% of all activities which have relatively smaller
optimal activity length size feature values, specifically less than 10.
Concretely, activities 1 and 7 have the same optimal activity
length size feature value of 2; activities 3 and 9 have the same
optimal activity length size feature value of 5; activity 5 has the
optimal activity length size feature value of 3; activity 2 has the
optimal activity length size feature value of 18; activities 0 and
4 have the same optimal activity length size feature value of 23;
activity 8 has the optimal activity length size feature value
of 28 and activity 6 has the optimal activity length size feature
value of 41.
Fig. 4 shows the trends of the hidden states sequence recogni-
tion failure rate of activities 0–9 generated by Viterbi algorithm
with increasing of activity length size feature values. Actually, it is
better to have a lower failure rate in this test. Again, it can be seen
that, most of the activities have a relatively smaller optimal
activity length size feature value, specifically less than 10. The
overall proportion is 70%. Activities 4 and 5 have the same optimal
Table 1
Results for hidden states sequence average accuracy rate by Viterbi algorithm.
Activities Time feature selections
1 2 3 4 5 6 8 12 24
0 0.267 0.264 0.264 0.288 0.341 0.347 0.406 0.368 0.463
1 0.287 0.267 0.767 0.356 0.569 0.767 0.850 0.797 0.823
2 0.774 0.755 0.760 0.811 0.893 0.887 0.835 0.882 0.902
3 0.300 0.286 0.244 0.277 0.255 0.263 0.276 0.282 0.350
4 0.790 0.780 0.573 0.856 0.718 0.667 0.795 0.811 0.886
5 0.447 0.423 0.455 0.443 0.402 0.420 0.357 0.163 0.351
6 0.810 0.799 0.798 0.837 0.827 0.791 0.842 0.805 0.764
7 0.239 0.570 0.685 0.587 0.578 0.685 0.556 0.576 0.678
8 0.403 0.423 0.432 0.538 0.649 0.613 0.650 0.675 0.689
9 0.649 0.736 0.733 0.760 0.716 0.741 0.780 0.776 0.736
Table 2
Results for hidden states sequence success rate by Viterbi algorithm.
Activities Time feature selections
1 2 3 4 5 6 8 12 24
0 0.167 0.133 0.133 0.167 0.167 0.167 0.200 0.200 0.167
1 0.021 0.021 0.500 0.021 0.375 0.500 0.375 0.375 0.354
2 0.575 0.546 0.536 0.623 0.691 0.594 0.618 0.667 0.739
3 0.152 0.152 0.109 0.109 0.152 0.109 0.130 0.174 0.130
4 0 0.095 0 0 0 0 0 0 0.071
5 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0 0.1
6 0.580 0.536 0.623 0.638 0.652 0.609 0.681 0.580 0.551
7 0 0.108 0.081 0.108 0 0.081 0 0 0
8 0.239 0.284 0.284 0.358 0.493 0.418 0.448 0.4786 0.552
9 0.477 0.523 0.5 0.455 0.523 0.546 0.546 0.568 0.523
Table 3
Results for hidden states sequence failure rate by Viterbi algorithm.
Activities Time feature selections
1 2 3 4 5 6 8 12 24
0 0.700 0.700 0.700 0.667 0.600 0.600 0.533 0.600 0.467
1 0.063 0.042 0.042 0.042 0.042 0.042 0.042 0.042 0.042
2 0.159 0.174 0.169 0.121 0.063 0.048 0.097 0.053 0.053
3 0.413 0.478 0.522 0.478 0.500 0.544 0.522 0.544 0.457
4 0 0 0 0 0 0 0 0 0
5 0.400 0.400 0.400 0.400 0.500 0.400 0.500 0.800 0.600
6 0.058 0.058 0.101 0.058 0.058 0.101 0.058 0.058 0.130
7 0.432 0.135 0.135 0.135 0.162 0.135 0.135 0.162 0.135
8 0.254 0.313 0.299 0.254 0.090 0.105 0.090 0.090 0.090
9 0.273 0.159 0.159 0.091 0.182 0.159 0.091 0.114 0.159
H. Fang et al. / ISA Transactions 53 (2014) 134–140 137

5. activity length size feature value of 2; activities 3 and 9 have the
same optimal activity length size feature value of 5; activity 1 has
the optimal activity length size feature value of 4; activity 7 has
the optimal activity length size feature value of 6; activity 8
has the optimal activity length size feature value of 8; activity
0 has the optimal activity length size feature value of 11; activity
2 has the optimal activity length size feature value of 22 and
activity 6 has the optimal activity length size feature value of 43.
Again, it should be noted that the optimal results shown in
Figs. 2–4 are not generated by only one specific length feature
value, which means that the Viterbi algorithm generates same
optimal results under different activity length size feature values.
Actually, only the minimum optimal activity length size feature
value for each activity is given in this discussion. However, the
results show that, it is better to define a small activity length size
feature value to get a relatively better result. The reasons can be
explained from the statistical data shown in Table 5, which shows
the average (mean), standard variance (std), maximal (max) and
minimum (min) sensors events length size of each activity. It can
be found that different activities have different statistical data of
sensors events length size, e.g., activity 6 has an average sensors
events length size of 6, in contrast, activity 4 has an average
sensors events length size of 534, etc. A relatively larger activity
length size feature value results in smaller length threshold value,
which will generate more length features. Since the probability of
feature given a specific activity is the product of the probabilities
of each sub-feature given this activity [29], more length features
will generate a smaller probability of feature given this activity.
Therefore, a larger length size feature value generates relatively
worse results.
Table 4
Hour-by-hour sensors events proportion of these activities.
Time zones Activities
0 1 2 3 4 5 6 7 8 9
0:00–1:00 0.1775 0.0182 0.0 0.0 0.0 0.0 0.0 0.0 0.0696 0.0
1:00–2:00 0.0881 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1468 0.0
2:00–3:00 0.2912 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0615 0.0
3:00–4:00 0.1916 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.2458 0.0
4:00–5:00 0.0319 0.0 0.0054 0.0 0.0 0.0 0.0 0.0 0.1752 0.0
5:00–6:00 0.0 0.0 0.0238 0.0064 0.0 0.0 0.0 0.0 0.0699 0.0159
6:00–7:00 0.0 0.0889 0.2212 0.073 0.0 0.0 0.0 0.0 0.0233 0.2739
7:00–8:00 0.0217 0.4825 0.2294 0.1065 0.0 0.0247 0.0372 0.0 0.0149 0.5219
8:00–9:00 0.0 0.2879 0.0707 0.0606 0.0 0.0 0.0665 0.0 0.0 0.1106
9:00–10:00 0.0 0.1225 0.0555 0.0493 0.0 0.0431 0.1037 0.0 0.0 0.0777
10:00–11:00 0.0 0.0 0.0023 0.1001 0.0 0.2034 0.2447 0.0019 0.0 0.0
11:00–12:00 0.0 0.0 0.0 0.0034 0.0 0.0 0.0878 0.3542 0.0 0.0
12:00–13:00 0.0 0.0 0.0 0.0444 0.0 0.1356 0.0878 0.6043 0.0 0.0
13:00–14:00 0.0 0.0 0.0 0.003 0.0 0.0 0.0346 0.0396 0.0 0.0
14:00–15:00 0.0 0.0 0.0 0.0463 0.0 0.3112 0.0691 0.0 0.0 0.0
15:00–16:00 0.0 0.0 0.0 0.0433 0.0 0.0647 0.0612 0.0 0.0 0.0
16:00–17:00 0.0 0.0 0.0 0.0602 0.0 0.1109 0.0505 0.0 0.0 0.0
17:00–18:00 0.0 0.0 0.0 0.0015 0.23 0.0 0.1064 0.0 0.0 0.0
18:00–19:00 0.0 0.0 0.0 0.0154 0.6955 0.0 0.0239 0.0 0.0 0.0
19:00–20:00 0.0 0.0 0.0036 0.2084 0.0667 0.1063 0.0266 0.0 0.0 0.0
20:00–21:00 0.0 0.0 0.2782 0.1178 0.0078 0.0 0.0 0.0 0.0 0.0
21:00–22:00 0.0 0.0 0.0972 0.0606 0.0 0.0 0.0 0.0 0.0685 0.0
22:00–23:00 0.0562 0.0 0.0119 0.0 0.0 0.0 0.0 0.0 0.0798 0.0
23:00–0:00 0.1418 0.0 9.05e-04 0.0 0.0 0.0 0.0 0.0 0.0448 0.0
Fig. 2. The trends of hidden states sequence average recognition accuracy rate of activities 0–9 generated by Viterbi algorithm.
H. Fang et al. / ISA Transactions 53 (2014) 134–140138

6. 5. Conclusions
This paper applies Viterbi algorithm based on a hidden Markov
model to represent and recognize activities sequences. Since any
activity annotated in dataset has various features, therefore, it is
necessary to select suitable features values to obtain better activities
sequences recognition performances. The alternative features values
selections have been tested and the recognition accuracy perfor-
mances of Viterbi algorithm have been evaluated. From the results, it
can be concluded that the selections of larger time feature values of
sensor events and/or smaller activity length size feature values will
generate relatively better results on the activities sequences
recognition performance measures of Viterbi algorithm. According
to these results, the features values for better activity recognition
performance can be determined. In future work, the methods of
automatically selecting features values will be studied.
Acknowledgment
This work was partially supported by Qing Lan Project, Jiangsu
Province, China, and the data were collected from the smart home
testbed located on the Washington State University campus.
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