Pervasive and Mobile Computing 57 (2019) 1–13

Contents lists available at ScienceDirect

Pervasive and Mobile Computing
journal homepage: www.elsevier.com/locate/pmc

Cross-position activity recognition with stratified transfer
learning∗

Yiqiang Chen a,b , , Jindong Wang a,b , Meiyu Huang c , Han Yu daBeijing Key Lab of Mobile Computing and Pervasive Devices, Institute of Computing Technology, Chinese Academy of
Sciences, Chinab
University of Chinese Academy of Sciences, Chinac
Qian Xuesen Lab of Space Technology, China Academy of Space Technology, Chinad
School of Computer Science and Engineering, Nanyang Technological University, Singapore

articleinfo

Article history:
Available online 17 April 2019
Keywords:
Activity recognition
Transfer learning
Domain adaptation
Pervasive computing

a b s t r a c t
Human activity recognition (HAR) aims to recognize the activities of daily living by
utilizing the sensors attached to different body parts. HAR relies on the machinelearning models trained using sufficient activity data. However, when the labels froma certain body position (i.e. target domain) are missing, how to leverage the data fromother positions (i.e. source domain) to help recognize the activities of this position?
This problem can be divided into two steps. Firstly, when there are several source
domains available, it is often difficult to select the most similar source domain to
the target domain. Secondly, with the selected source domain, we need to performaccurate knowledge transfer between domains in order to recognize the activities on
the target domain. Existing methods only learn the global distance between domains
while ignoring the local property. In this paper, we propose a Stratified Transfer Learning(STL) framework to perform both source domain selection and activity transfer. STL isbased on our proposed Stratified distance to capture the local property of domains. STL
consists of two components: 1) Stratified Domain Selection (STL-SDS), which can selectthe most similar source domain to the target domain; and 2) Stratified Activity Transfer(STL-SAT), which is able to perform accurate knowledge transfer. Extensive experimentson three public activity recognition datasets demonstrate the superiority of STL.
© 2019 Elsevier B.V. All rights reserved.

1. Introduction
Human activity recognition (HAR) aims to seek high-level knowledge from the low-level sensor inputs. For example,
we can detect if a person is walking or running using the on-body sensors such as the smartphone or the wristband.
Activities are of great importance to a person’s health status. When a person is performing some activities, each of his
body parts has certain activity patterns. Thus, sensors can be attached on some body positions to collect activity data
which can be used to build machine learning models in order to recognize their activities. The combination of sensor
signals from different body positions can be used to reflect meaningful knowledge such as a person’s detailed healthconditions [1] and working states [2]. However, it is nontrivial to design wearing styles for a wearable device. On the one
hand, it is not bearable to equip all the body positions with sensors which makes the activities not natural. Therefore,∗ Corresponding author at: Beijing Key Lab of Mobile Computing and Pervasive Devices, Institute of Computing Technology, Chinese Academy of
Sciences, China.
E-mail address: yqchen@ict.ac.cn (Y. Chen).
https://doi.org/10.1016/j.pmcj.2019.04.004
1574-1192/© 2019 Elsevier B.V. All rights reserved.

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Fig. 1. An example of cross-position activity recognition. How to leverage the well-labeled activity data on other body parts (the blue dots) toacquire the labels of the pentacle part given that their signal distributions are different?

we can only attach sensors on limited body positions. On the other hand, it is impossible to perform HAR if the labels
on some body parts are missing, since the activity patterns on specific body positions are significant to capture certain
information.
Fig. 1 illustrates this situation. Assume this person is suffering from Small Vessel Disease (SVD) [3], which is a severe
brain disease heavily related to activities. However, we cannot equip his all body with sensors to acquire the labels since
this will make his activities unnatural. We can only label the activities on certain body parts in reality. If the doctor wants
to see his activity information on the arm (the red pentacle, we call it the target domain), which only contains sensor
readings instead of labels, how to utilize the information on other parts (such as torso or leg, we call them the source
domains) to help obtain the labels on the target domain? This is referred to as the cross-position activity recognition (CPAR).
The problem of CPAR is extremely challenging. Firstly, we do not know which body part is the most similar to thetarget position since the sensor signals are not independent, but highly correlated because of the shared body structuresand functions. If we use all the body parts as the source domain, there is likely to be negative transfer [4] because somebody parts may be dissimilar. Secondly, we only have the raw activity data on the target domain without the actual
activity labels, making it infeasible to measure the similarities between different body positions. Thirdly, even when weknow the similar body parts to the target domain, it is still difficult to build a good machine learning model using boththe source and the target domains. The reason is that signals from different domains are following different distributions,which means there are distribution discrepancies between them. However, traditional machine learning models are built
by assuming that all signals follow the same distribution. Fourthly, when it comes to multiple persons, the sensor readings
are more different compared to different body parts on one person. This makes the problem more challenging.
To tackle the above challenges, several transfer learning methods have been proposed [5]. The key is to learn andreduce the distribution divergence (distance) between two domains. With the distance, we can perform source domain
selection as well as knowledge transfer. Based on this principle, existing methods can be summarized into two categories:
exploiting the correlations between features [6,7], or transforming both the source and the target domains into a newshared feature space [8–10].
Existing approaches tend to reduce the global distance by projecting all samples in both domains into a single subspace.
However, they fail to consider the local property within classes [11]. The global distance may result in loss of domain
local property such as the source label information and the similarities within the same class. Therefore, it will generate anegative impact on the source selection as well as the transfer learning process. It is necessary to exploit the local property
of classes to overcome the limitation of global distance learning.
In this paper, we propose a Stratified Transfer Learning (STL) framework to tackle the challenges of both source
domain selection and knowledge transfer in CPAR. The term stratified comes from the notion of splitting at different levels
and then combining. We adopt the well-established assumption that data samples within the same class should lay on
the same subspace, even if they come from different domains [12]. Thus, stratified refers to the procedure of transforming
features into distinct subspaces. This has motivated us to propose the concept of Stratified distance (SD) in comparison to
traditional Global distance (GD). STL has two components regarding the challenges in CPAR: a Stratified Domain Selection(STL-SDS) algorithm to select the most similar source domain to the target domain, and a Stratified Activity Transfer (STLSAT) method to perform activity knowledge transfer between different body parts. Both STL-SDS and STL-SAT are able toexploit the local property of domains, thus they can achieve promising results in CPAR. Comprehensive experiments on 4
large public activity recognition datasets (i.e. OPPORTUNITY, PAMAP2, UCI DSADS, and MHEALTH) demonstrate that STLSDS is better than the existing global distance used in selecting source domains. STL-SAT outperforms five state-of-the-art
methods with a significant improvement of 6.3% in classification accuracy with improved F 1 score.
This paper is a substantial extended version of our PerCom paper [13]. To summarize, the contributions are as follows:(1) We propose the Stratified Transfer Learning (STL) framework for source domain selection and knowledge transfer
in CPAR. STL is the first attempt to exploit the Stratified distance (SD) in order to capture the local property between
domains. SD is a general distance that can be applied to different transfer learning applications.

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3(2) We propose two novel algorithms: (1) Stratified Domain Selection (STL-SDS) algorithm to accurately select the mostsimilar source domain to the target domain, and (2) Stratified Activity Transfer (STL-SAT) method to perform knowledgetransfer for cross-position activity recognition.
(3) We extensively investigate the performance of STL on four public HAR datasets, indicating its effectiveness incross-domain HAR applications.
2. Related work
2.1. Activity recognition
Human Activity recognition has been a popular research topic in pervasive computing [14] for its competence inlearning profound high-level knowledge about human activity from raw sensor inputs.
Conventional machine learning approaches have made tremendous progress on HAR by adopting machine learningalgorithms such as similarity-based approach [15,16], active learning [17], crowdsourcing [18], and other semi-supervised
methods [19,20]. Those methods typically treat HAR as a standard time series classification problem. And they tend tosolve it by subsequently performing preprocessing procedures, feature extraction, model building, and activity inference.
However, they all assume that the training and test data are with the same distribution. As for CDAR where the training
and the test data are from different feature distributions, those conventional methods are prune to under-fitting since
their generalization ability will be undermined [4].
2.2. Transfer learning
According to the literature survey [4], transfer learning can be categorized into 3 types: instance-based, parameterbased, and feature-based methods. Our framework belongs to the feature based category, which brings the features ofsource and target domain into the same subspace where the data distributions can be the same. STL differs from existing
feature-based methods in the following aspects:
Exploit the correlations between features. [6] proposed structural correspondence learning (SCL) to generatively
learn the relation of features. [7] applied a feature-level transfer model to learn the dependence between domains, thentrained a domain-adapted classifier. Instead of modeling the relationship of domain features, SAT transforms the domain
data into a new subspace, which does not depend on the domain knowledge.
Transform domains into new feature space. [21] proposed maximum mean discrepancy embedding (MMDE) to learn
latent features in the reproducing kernel Hilbert space (RKHS). MMDE requires solving a semidefinite programming (SDP)
problem, which is computationally prohibitive. [8] extended MMDE by Transfer Component Analysis (TCA), whichlearns a kernel in RKHS. [22] adopted a similar idea. [23] learns target predictive function with a low variance. [24]sampled the domain features by viewing the data in a Grassmann manifold to obtain subspaces. [9] exploited thelow-dimensional structure to integrate the domains according to geodesic flow kernel (GFK). Long et al. proposed
joint distribution adaptation (JDA) based on minimizing joint distribution between domains, while SAT focuses on themarginal distribution. [10] proposed transfer kernel learning (TKL), which learned a domain-invariant kernel in RKHS. [25]studied the conditional transfer components between domains. Methods in this literature tend to learn some common
representations in the new feature space, then a global domain shift can be achieved. However, the difference between
individual classes is ignored.
2.3. Transfer learning based activity recognition
Among existing work on transfer learning based HAR [5], Zhao et al. proposed a transfer learning method TransEMDT[26] using decision trees, but it ignored the intra-class similarity within classes. [27] proposed the TransAct framework,
which is a boosting-based method and ignores the feature transformation procedure. Thus it is not feasible in most activity
cases. Feuz et al. [28] proposed a heterogeneous transfer learning method for HAR, but it only learns a global domain shift.
A more recent work of Wang et al. [29] performs activity recognition using deep transfer learning, which also focused on
the global distance between domains. To the best of our knowledge, STL is the first attempt towards learning a stratified
distance to capture the local property of domains.
3. Stratified transfer learning
In this section, we introduce the Stratified Transfer Learning (STL) framework for cross-position activity recognition.

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Fig. 2. Traditional global distance (GD) and proposed stratified distance (SD).

3.1. Problem definition
The goal of cross-position activity recognition (CPAR) is to predict the activities of one body part (i.e. the target
domain) using existing labeled data from another body part (i.e. the source domain). Formally speaking, we can usenn
Ds = {(xsi , ysi )}i=s 1 to denote the labeled source domain, and Dt = {(xtj , ytj )}j=t 1 denotes the target domain. Note that ytj
is missing, i.e. it is the goal of CPAR. In CPAR, we assume the sensor modalities and the activity categories are equal in
all body parts, thus the feature space X s = X t and label space Ys = Yt . Here, d denotes the feature dimension. We use
C to denote the total categories of both domains. The different data distributions on different body parts means that themarginal and conditional distributions between domains are different. Therefore, P(xs ) ̸ = P(xt ), and Q (ys |xs ) ̸ = Q (yt |xt ).
3.2. Motivation
The key to successful transfer is to utilize the similarity between the source and the target domain [4]. It is notdifficult to directly measure the similarity between domains using existing distance functions. For instance, we can adopt
the Euclidean distance or the Kullback–Leibler divergence [30] to calculate the probability distance between domains.
Unfortunately, these computing approaches are only calculating the global distance between domains since they areapplied to the whole domain. The global distance may result in loss of domain local property such as the source label
information and the similarities within the same class. Therefore, it will generate a negative impact on the source selection
as well as activity transfer.
In order to capture the local property of domains, we adopt the assumption [12]: the data samples from the same classshould lay on the same subspace, even if they belong to different domains. By following this assumption, we propose thestratified distance to capture the local property of domains. The stratified distance refers to the class-wise distance between
(1)
(5)
(1)
(5)
two different domains. For example, if there are 5 classes in two domains: Ds = (Ds , . . . , Ds ) and Dt = (Dt , . . . , Dt ),then the stratified distance (SD) should be calculated as:
5

SD =

1∑
5

(i)

Dist(Ds(i) , Dt ),

(1)

i=1

where Dist(·) denotes some distance function such as the Euclidean distance. As a comparison, the global distance (GD)
can be represented as:
GD = Dist(Ds , Dt ).

(2)

Fig. 2 briefly illustrates the results of global and our stratified distance using two classes of the same target domain [13].
It indicates that SD could not only help to learn good classification function, but helps to obtain tighter within-classdistance.
3.3. The STL framework
In this paper, we propose Stratified Transfer Learning (STL) framework to address both of these two challenges. Firstly,
STL uses a popular majority voting technique to acquire the labels for the target domain. Secondly, STL exploits an effective
distance measure called Maximum Mean Discrepancy (MMD) to calculate the SD distance and perform Intra-class transfer.
Finally, STL could perform source domain selection and activity transfer based on the calculated distance. Fig. 3 illustrates
the main idea of the STL framework.
3.3.1. Majority voting
We can easily obtain the pseudo labels for the target domain based on a weak classier such as 1-nearest-neighbor(1NN) trained on the source domain by following existing methods [31]. However, since there is a large distribution
discrepancy between two domains, a simple 1NN classifier may not work well. Therefore, we propose to use the majority
voting technique to exploit the knowledge from the crowd [32]. The idea is that one certain classifier may be less reliable,

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5

Fig. 3. Main idea of the Stratified Transfer Learning (STL) framework. There are two steps: (1) Stratified Domain Selection (STL-SDS), which canselect the most similar source domains to the target domains. (2) Stratified Activity Transfer (STL-SAT), which can perform activity recognition on
the target domain based on transfer learning.

so we assemble several different classifiers to obtain more reliable pseudo labels. To this end, STL makes use of some baseclassifiers learned on Ds to collaboratively learn the labels for Dt .
Let Aj (j = 1, 2, . . . , n2 ) denotes the final result of majority voting on xtj , and ft (j) denotes the prediction of the jth
sample by the tth classifier ft (·), then:majority(ft (j), t)

if majority holds−1otherwise

{
Aj =

(3)

where t ∈ {1, 2, . . .} denotes the index of the classifier.
The majority voting technique generally ensembles all the classifiers learned in the source domain. The condition‘‘majority holds’’ refers to any potential scheme that helps to generate a better solution such as simple voting and weighted
voting. Specifically, Aj could be defined as (a) if most classifiers have the same results on a sample, we take its label, else
we label it ‘−1’; (b) same as (a) with voting weights to classifiers; (c) the stacking of some base classifiers. In theory, theclassifiers can be of any type.
Formally, we call the samples with pseudo labels in the target domain Candidates, which is denoted as Xcan . For thosesamples with label ‘−1’, we call them Residuals and denote as Xres . Using majority voting, STL can generate reliable pseudolabels for the target domain.
3.3.2. Intra-class transfer
In this step, STL exploits the local property of domains to further transform each class of the source and target domains
into the same subspace. Since the properties within each class are more similar, the Intra-class transfer technique will
guarantee that the transformed domains have the minimal distance. In this step, we only consider the candidates fromthe target domain for their reliable pseudo labels.
Initially, Ds and Xcan are divided into C groups according to their (pseudo) labels, where C is the total number of classes.
Then, feature transformation is performed within each class of both domains. Finally, the results of distinct subspaces are
merged.
In order to achieve intra-class transfer, we need to calculate the distance between each class. Since the target domain
has no labels, we use the pseudo labels from majority voting. For the candidates and the source domain, we calculate
their intra-class distance using the stratified distance:
C

SD =
(c)

1∑
C

Dist(Ds(c) , X(c)can ),

(4)

c =1
(c)

where Ds and Xcan denote the samples from class c in the source and candidates, respectively.
This distance can easily be calculated using existing metrics such as Euclidean distance and Kullback–Leibler (KL)divergence [30]. However, the Euclidean distance and KL divergence are too general for activity recognition problem,
which ignores the label information of the source domain. Moreover, the KL divergence needs to first estimate theprobability of both domains, which is trivial and not suitable since the target domain has no labels. Therefore, we needto calculate the similarity between domains while considering the label information on the source domain.
In order to calculate the function Dist(·) in Eq. (1), we adopt Maximum Mean Discrepancy (MMD) [33] as themeasurement. MMD is a nonparametric method to measure the divergence between two distinct distributions and it has
been widely applied to many transfer learning methods [8,10]. The MMD distance between two domains can be formally6

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computed as:


2




∑ 1 ∑1 ∑st 
D(Ds , Xcan ) =φ (xi ) − (c)φ (xj ) ,
 (c)
n

nt t (c)c =1  s xs ∈D (c)x ∈Xcan
s
C

i

j

(5)

H

(c)
where H denotes reproducing kernel Hilbert space (RKHS). ns

(c)

(c)

(c)

= |Ds |, nt = |Xcan |. Here φ (·) denotes some feature map
to map the original samples to RKHS. The reason we do not use the original data is that the features are often distorted
in the original feature space, and it can be more efficient to perform knowledge transfer in RKHS [8].
Therefore, given a predefined mapping function φ (·), we can compute the intra-class distance between two domains.
Remark. The majority voting and intra-class transfer are common steps in STL. In the next sections, we will elaborate
on how to use the STL framework to perform source domain selection and activity transfer.
3.4. Stratified domain selection
In this paper, based on the STL framework, we propose the Stratified Domain Selection (STL-SDS) algorithm to select themost similar domains to the target. Based on the proposed Stratified distance, STL-SDS well exploits the local property ofdifferent domains as well as the supervised information on the source domain.
We adopt a greedy technique in STL-SDS. We know that the most similar body part to the target is the one with themost similar structure and body functions. Therefore, we use the distance to reflect their similarity. We calculate thestratified distance according to Eq. (5) between each source domain and the target domain and select the one with theminimal distance.
Unfortunately, it is non-trivial to solve Eq. (5) directly since the mapping function φ (·) is to be determined. Simply
use a certain function will ruin the local property of domains. Thus, we turn to some kernel methods. We define a kernel
matrix K ∈ R(n1 +n2 )×(n1 +n2 ) , which can be constructed by the inner product of the mapping:
Kij = ⟨φ (xsi ), φ (xtj )⟩ = φ (xsi )⊤ φ (xtj ),(6)where xsi and xtj are samples from either Ds or Xcan .
Therefore, we can easily calculate this equation without losing the local property by giving φ (·) a certain implementation. In our work, we use the Radical Basis Function (RBF), which can be defined as:(
K (xsi,xtj )= exp −

∥xsi − xtj ∥22
2σ 2

)
,

(7)

where σ is the kernel bandwidth. The procedure of STL-SDS is in Algorithm 1.
Algorithm 1 STL-SDS: Stratified Domain Selection
Input: A list of source domains Ds1 , · · · , DsK , target domain Dt .
Output: The source domain that has the minimal distance to Dt .
1: Initialize a source domain set S = {};2: Perform majority voting on Dt to acquire Xcan ;3: Obtain the pseudo labels yt for Dt ;4: for i = 1 to K do
5:Compute the distance SDi between Dsi and Xcan using Eq. (5);6:Add SDi to S;
7: end for
8: return Index j of source domain that SDj = min{S }.
3.5. Stratified activity transfer
After source domain selection, we can obtain the most similar body part to the target domain. The next step is to design
an accurate transfer learning algorithm to perform activity transfer. In this paper, we propose a Stratified Activity Transfer(STL-SAT) method for activity recognition. STL-SAT is also based on our stratified distance, and it can simultaneouslytransform the individual classes of the source and target domains into the same subspaces by exploiting the local propertyof domains. After feature learning, STL can learn the labels for the candidates. Finally, STL-SAT will perform a second
annotation to obtain the labels for the residuals. The process of STL-SAT can be seen in Fig. 4.
The feature transformation is also based on the intra-class transfer technique in Eq. (5). However, different from STLSDS where we use a certain mapping function such as RBF for feature mapping, we learn this mapping φ (·) in this step.

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7

Fig. 4. Main idea of Stratified Activity Transfer (STL-SAT). There are three steps: (1) Candidates generating to generate pseudo labels for the target
domain; (2) Perform intra-class transfer between source domain and candidates; (3) Perform activity transfer using the transferred data.

The reason is that STL-SDS only needs one particular feature map to avoid the feature distortion, while STL-SAT will findthe optimal feature map with the minimal domain distance.
The learning of this feature map also starts with Eq. (5). For efficient learning, we introduce a feature transformation
matrix W ∈ R(n1 +n2 )×m to transform the samples of both domains from the original space to the RKHS. Here m ≪ d denotes
the dimension after feature transformation. Thus, learning φ (·) is equal to learning the matrix W. Then, via kernel tricks,
Eq. (5) can be formulated as a trace optimization problem:
min
W

C
∑

tr(W⊤ KLc KW) + λtr(W⊤ W)

(8)

c =1

⊤

s.t. W KHKW = I∑CThere are two terms in the objective function of Eq. (8). The first term ( c =1 tr(W⊤ KLc KW)) denotes the MMD distanceof each class between source and target domain, and the second one (λtr(W⊤ W)) denotes the regularization term toensure the problem is well-defined with λ the trade-off parameter. The constraint in Eq. (8) is used to guarantee that thetransformed data (W⊤ K) will still preserve some structure property of the original data. Ins +nt is the identical matrix, and
H = Ins +nt − 1/(ns + nt )11⊤ is the centering matrix. For notational brevity, we will drop the subscript for Ins +nt in thesequel. Lc is the intra-class MMD matrix:

⎧
1
⎪
2
⎪
⎪
⎪ (n(c)
s )
⎪
⎪
1
⎪
⎪
⎨ (c) 2(c)xi , xj ∈ Ds(c)xi , xj ∈ Xcan

(nt )(Lc )ij ={⎪⎪⎪− (c)1 (c)
⎪
⎪
ns nt
⎪
⎪
⎪
⎩

(c)

(c)

(c)

(c)

xi ∈ Ds , xj ∈ Xcan

(9)xi ∈ Xcan , xj ∈ Ds0otherwise

Learning algorithm: Acquiring the solution of Eq. (8) is non-trivial. To this end, we adopt Lagrange method as mostof the existing work did [8,10,13,34]. We denote Φ the Lagrange multiplier, then the Lagrange function can be derived as(
L = tr W⊤ K

C∑)
Lc K⊤ W

+ λtr(W⊤ W)

c =1

(

⊤

⊤

+ tr (I − W KHK W)Φ

(10)

)

Setting the derivative ∂ L/∂ W = 0, Eq. (10) can be finally formalized as an generalized eigen-decomposition problem

(
K

C
∑

)
Lc K + λI W = KHK⊤ WΦ
⊤

(11)

c =1

Eq. (11) can be easily solved as a generalized eigen-decomposition problem and take the m smallest eigenvectors toconstruct W. W can transform both domains into the same subspace with minimum domain distance while preserving
their properties. Since the knowledge transfer pertains to each class, we call this step intra-class transfer, and that iswhere the name stratified originates from. After this step, the source and target domains belonging to the same class aretransformed into the same subspaces.
After solving the above optimization problem, it is easy to get more reliable predictions (ŷcan ) of the candidates.
Specifically, we train a standard classifier using {[W⊤ K]1:n1 ,: , ys } and apply prediction on [W⊤ K]n1 +1:n2 ,: . Finally, the labelsof residuals can be obtained by training classifier on instances {Xcan , ŷcan }. The labels of candidates can be correspondingly
close to the ground truth by annotating twice since the domains are now in the same subspace after intra-class transfer.
The procedure of STL-SAT is in Algorithm 2.

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Algorithm 2 STL-SAT: Stratified Activity Transfer
Input: Source domain Ds , target domain Dt , dimension m.
Output: The labels for the target domain: {yt }.
Majority voting on Dt using Eq. (3) to get {Xcan , ỹcan } and Xres ;2: Construct kernel matrix K according to Eq. (6) using Xsrc and Xcan , and compute the intra-class MMD matrix Lc using
Eq. (9);repeat4:
Solve the eigen-decomposition problem in Eq. (11) and take the m smallest eigen-vectors to obtain thetransformation matrix W;
Transform the same classes of Xs and Xcan into the same subspaces using W, and then merge them;
6:
Perform second annotation to get {ŷcan } and {ŷres };Construct K and compute intra-class MMD matrix Lc using Eq. (9);8: until Convergence
return {yt }.
Table 1
Statistical information of three public datasets for activity recognition.
DatasetPersonActivity

SamplePosition

OPP
PAMAP
DSADS
MHEALTH

4
9
8
10

4
18
19
12

701K
284M
114M
66M

Back (B), Right Upper Arm (RUA), Right Left Arm (RLA), Left Upper Arm (LUA), Left Lower Arm (LLA)
Hand (H), Chest(C), Ankle (A)Torso (T), Right Arm (RA), Left Arm (LA), Right Leg (RL), Left Leg (LL)
Chest (C), Right Wrist (RW) and Left Ankle (LAn)

4. Experiments
In this section, we evaluate the performances of STL framework (STL-SDS and STL-SAT) via extensive experiments on
public HAR datasets.
4.1. Datasets and preprocessing
Four large public datasets are adopted in experiments. Table 1 provides a brief introduction to them. In the following,
we briefly introduce those datasets, and more information can be found in their original papers. OPPORTUNITY dataset(OPP) [35] is composed of 4 subjects executing different levels of activities with sensors tied to more than 5 body parts.
PAMAP2 dataset (PAMAP) [36] is collected by 9 subjects performing 18 activities with sensors on 3 body parts. UCI
daily and sports dataset (DSADS) [37] consists of 19 activities collected from 8 subjects wearing body-worn sensors on 5
body parts. MHEALTH [38] is composed of 10 subjects performing 12 kinds of activities. Accelerometer, gyroscope, andmagnetometer are all used in these datasets.
In our experiments, we use the data from all three sensors in each body part since√ most information can be retainedin this way. For one sensor, we combine the data from 3 axes together using a = x2 + y2 + z 2 . Then, we exploit thesliding window technique to extract features (window length is 5s). The feature extraction procedure is mainly executed
according to existing work [39]. In total, 27 features from both time and frequency domains are extracted for a single
sensor. Since there are three sensors (i.e. accelerometer, gyroscope, and magnetometer) on one body part, we extracted
81 features from one position.
In order to better exploit these three datasets, we perform two aspects of cross-position activity recognition: Within
Dataset and Cross dataset. Within Dataset refers to perform CPAR inside a particular dataset. For instance, we can learn
the labels for the Right Arm (RA) of the DSADS dataset by using labeled data from the other four body parts. In contrast,
Cross dataset uses the labeled body parts from another different dataset as the source domains. In our experiments, we
use DSADS and OPP datasets for Within dataset since they contain more body parts than PAMAP. We use all classes foreach dataset in this aspect. For Cross Dataset, we use the body parts from DSADS and OPP as the target domain, and use
body parts from PAMAP as the source domain since there are more samples in PAMAP than other two datasets (Table 1).
Note that there are different activities in three datasets. Thus we extract 4 common classes: Walking, Sitting, Lying, andStanding.
4.2. Evaluation of stratified domain selection
We perform source domain selection using the proposed STL-SDS (i.e. the stratified distance (SD)) algorithm on boththe Within Dataset and Cross Dataset aspects. The comparison method is the global distance (GD) using the MMD. It is
worth noting that there is no effective evaluation metric for this domain selection problem. We can never quantitatively
know the actual distance between two activity domains. Thus, we evaluate the similarity based on classification accuracy

Y. Chen, J. Wang, M. Huang et al. / Pervasive and Mobile Computing 57 (2019) 1–13

9Fig. 5. (a) The comparison between global and stratified distance for domain selection. (b) Classification accuracy of different methods of each person
on RA → LA task.
Table 2Comparison of Global (G) and Stratified (S) distance on source domain selection. The symbol item denotes that the item is not consistent withthe ground truth.
Target dataset

DSADS

Target position

T

RA

LA

RL

LL

B

RUA

RLA

LUA

LLA

Truth

RA

LA

RA

LL

RL

LUA

RLA

RUA

B

LUA

GD

LA

T

T

LL

RL

LUA

LLA

RUA

LLA

RUA

Cross dataset

Cross dataset

OPP

SD

LA

LA

T

LL

RL

LUA

RLA

RUA

LLA

RUA

Truth

Chest

Ankle

Chest

Hand

Hand

Chest

Chest

Chest

Chest

Chest

GD

Chest

Chest

Chest

Chest

Chest

Chest

Ankle

Ankle

Ankle

Ankle

SD

Chest

Ankle

Chest

Hand

Chest

Chest

Chest

Ankle

Chest

Chest

LUA

LLA

–

Table 3
Accuracy (%) of Global (GD) and Stratified (SD) distance on domain selection.
Target dataset

DSADS

Target position

T

Target as source
Within dataset

Cross dataset

OPP
RA

LA

RL

LL

B

Average
RUA

RLA

87.6

83.4

84.8

87.9

88.4

37

37.3

36.7

34.8

38.3

61.6

Truth

35.0

69.5

66.9

69.9

77.3

30.9

33.2

32.1

24.6

27.8

46.7

GD

31.5

34.1

36.0

69.9

77.3

30.9

20.3

32.1

22.7

19.6

37.4

SD

31.5

69.5

36.0

69.9

77.3

30.9

33.2

32.1

22.7

19.6

42.2

Truth

23.8

25.0

24.8

25.0

25.0

50.1

50.0

49.9

50.0

50.0

37.4

GD

23.8

0.6

24.8

2.7

2.0

50.1

24.5

24.5

47.3

23.6

22.4

SD

23.8

25.0

24.8

25.0

2.0

50.1

50.0

24.5

50.0

50.0

32.5

using the same classifier following existing work [29]. For instance, for source domains A and B and target domain C, we
respectively train a linear SVM classifier using A or B and apply prediction on C. The accuracy acts as the ground truth
for domain similarity: higher accuracy means shorter distance. Then, the source domain with the highest accuracy is theright source for the target domain. Therefore, we can obtain the ‘ground truth’ for the source domain selection.
Fig. 5(a) shows the average source domain selection accuracy of the global and stratified distance. It is obvious that our
proposed SD distance achieves better performance than the traditional global distance. Note that in both Within Dataset
and Cross Dataset scenarios, SD distance outperforms GD. Furthermore, for the even challenging Cross Dataset distance
where the similarity between the source and the target domains are little, SD could significantly outperform the traditional
GD distance. This indicates the effectiveness of our proposed STL-SDS algorithm.
Now we dig deeper into the results. Table 2 shows the selected source domains of GD and SD, and their accuracies are
in Table 3. We also report the accuracy when target itself is as the source domain for comparison (which is the ideal statethat can never be satisfied). From these tables, we observe: (1) The proposed Stratified distance can select better source
domain than the traditional global distance with close performance with the ground truth. (2) The situation when thetarget domain as the source domain can achieve the best performance. However, it is only the ideal state since there arealways the label scarcity problems. It indicates that CPAR is a challenging task since both of the Within Dataset and Cross
Dataset aspects only achieve worse performance, which ensures the necessity of transfer learning algorithm. (2) Generally
speaking, the most similar body parts to a side Arm or Leg is its other side. This observation is much easier to understandas common sense. (3) Torso (or Back/Chest) is the most similar body part to other body parts such as Arms and Legs. Thisis probably because the Torso is physically connected to Arms and Legs, leading to similar moving patterns. Therefore,

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Table 4
Classification accuracy (%) and F1 score of STL-SAT and comparison methods.
Dataset

Task

PCA

KPCA

TCA

GFK

TKL

STL-SATDSADSRA → LARL → LL
RA → T

59.9 (0.72)
69.5 (0.72)
38.9 (0.62)

62.2 (0.72)
70.9 (0.73)
30.2 (0.62)

66.2 (0.76)
75.1 (0.77)
39.4 (0.56)

71.0 (0.73)
79.7 (0.73)
44.2 (0.62)

54.1 (0.56)
61.6 (0.67)
32.7 (0.58)

71.1 (0.81)
81.6 (0.69)
45.6 (0.77)

OPP

RUA → LUA
RLA → LLARLA → T
RUA → T

76.1 (0.72)
62.2 (0.60)
59.1 (0.47)
68.0 (0.64)

65.6 (0.73)
66.5 (0.61)
47.0 (0.47)
54.5 (0.67)

76.9 (0.79)
60.6 (0.68)
55.4 (0.56)
67.5 (0.70)

74.6 (0.73)
74.6 (0.62)
48.9 (0.48)
66.1 (0.66)

66.8 (0.68)
66.8 (0.55)
47.7 (0.49)
60.5 (0.58)

84.0 (0.80)
83.9 (0.70)
56.9 (0.59)
75.2 (0.75)

PAMAP
MHEALTH

H → C
C → RW

35.0 (0.24)
40.5 (0.41)

24.4 (0.25)
41.2 (0.43)

34.9 (0.27)
43.2 (0.46)

36.2 (0.25)
45.6 (0.52)

35.7 (0.26)
44.2 (0.47)

43.5 (0.33)
48.7 (0.54)

PAMAP → OPP
DSADS → P
OPP → DMHEALTH → PAMAPMHEALTH → OPP
MHEALTH → DSADS

C → B
T → C
B → T
C → C
B → C
C → T

32.8 (0.32)
23.2 (0.22)
44.3 (0.46)
45.2 (0.46)
39.8 (0.39)
42.3 (0.44)

43.8 (0.42)
18.0 (0.20)
49.4 (0.50)
46.1 (0.48)
42.1 (0.41)
42.8 (0.43)

39.0 (0.37)
23.7 (0.25)
46.9 (0.48)
44.9 (0.49)
43.2 (0.42)
44.5 (0.45)

27.6 (0.27)
19.4 (0.24)
48.1 (0.50)
46.7 (0.52)
44.5 (0.46)
44.9 (0.48)

35.6 (0.27)
21.7 (0.23)
52.8 (0.54)
46.2 (0.49)
44.4 (0.42)
43.1 (0.46)

40.1 (0.44)
37.8 (0.39)
55.5 (0.59)
49.3 (0.55)
46.8 (0.49)
46.2 (0.51)

49.1

47.0

50.7

51.5

47.6

57.8

Within dataset

Cross dataset

Averagemost of the target domains can leverage the labeled information from Torso to build models. (4) It is important to noticethat although SD achieves good results, its performance is not 100% right. This indicates that it is extremely difficult toperform source selection. We expect to increase the performance of SD in future research.
4.3. Evaluation of stratified activity transfer
We evaluate the performance of STL-SAT in both Within Dataset and Cross Dataset aspects. The state-of-the-art comparison methods include: (1) PCA: Principal component analysis [40], (2) KPCA: Kernel principal component analysis [40],(3) TCA: Transfer component analysis [8], (4) GFK: Geodesic flow kernel [9], and (5) TKL: Transfer kernel learning [10].
PCA and KPCA are classic dimensionality reduction methods, while TCA, GFK, and TKL are representative transfer learning
approaches.
We construct several CPAR tasks according to each scenario and use the labels for the target domain only for testingby following the common setting in existing work [5,26]. Other than TKL, all other methods require dimensionality
reduction. Therefore, they were tested using the same dimension. After that, a classifier with the same parameter islearned using the source domain and then the target domain can be labeled. To be more specific, we use the random
forest classifier (#Tree = 30) as the final classifier for all the 6 methods. For majority voting in STL-SAT, we simply use
SVM (C = 100), kNN (k = 3), and random forest (#Tree = 30) as the base classifiers. Other parameters are searched toachieve their optimal performance. The iteration number is set to be T = 10 for SAT. Other parameters of STL-SAT are set
λ = 1.0, d = 30, kernel = linear. It is noticeable that we randomly shuffle the experimental data 5 times in order to gain
robust results. Classification accuracy on the target domain is adopted as the evaluation metric, which is widely used inexisting transfer learning methods [8,10]
Accuracy =|x : x ∈ Dt ∧ ŷ(x) = y(x)||x : x ∈ Dt |(12)

where y(x) and ŷ(x) are the truth and predicted labels, respectively. Additionally, we also use the F1 score as anothermeasurement of the results. F1 score can be calculated as
F1 =

2PR
P +R

(13)

where P , R are the precision and recall, respectively.
We run STL-SAT and other methods on all tasks and report the classification accuracy and F1 score in Table 4. For
brevity, we only report the results of A → B since its result is close to B → A. It is obvious that SAT significantly
outperforms other methods in most cases (with a remarkable improvement of 6.3% over the best baseline GFK). Compared
to traditional dimensionality reduction methods (PCA and KPCA), STL-SAT improves the accuracy by 10%∼20%, which
implies that SAT is better than typical dimensionality reduction methods. Compared to transfer learning methods (TCA,
GFK, and TKL), STL-SAT still shows an improvement of 5%∼15%. Therefore, STL-SAT is more effective than all thecomparison methods in most cases.
The performance of TKL is the worst, because of the instability of the transfer kernel. TCA only learns a global domain
shift, thus the similarity within classes is not fully exploited. The performance of GFK is second to SAT, even if GFK also
learns a global domain shift. Because the geodesic distance in high-dimensional space is capable of preserving the intra
properties of domains. The differences between STL-SAT and GFK are: (1) STL-SAT outperforms GFK in most cases with

Y. Chen, J. Wang, M. Huang et al. / Pervasive and Mobile Computing 57 (2019) 1–13

11

Table 5
Confusion matrix on RUA → LUA of OPP dataset.
PCA

Acc = 72.5

KPCA

Walking

Sitting

LyingStanding

Walking
Sitting
LyingStanding

1426
57
278
38

144
492
10
1

445
6
1013
54

18
0
34
121

GFK

Acc = 74.3

Walking
Sitting
LyingStanding

Walking

Sitting

LyingStanding

1449
57
272
37

141
492
12
1

435
6
1015
57

8
0
36
119

Acc = 74.5
Walking

Sitting

LyingStanding

Walking
Sitting
LyingStanding

1456
57
278
38

134
492
10
1

435
6
1013
54

8
0
34
121

TKL

Acc = 67.8

Walking
Sitting
LyingStanding

Walking

Sitting

LyingStanding

1423
114
397
50

157
430
26
1

443
11
830
40

10
0
82
123

TCA

Acc = 76.2
Walking

Sitting

LyingStanding

Walking
Sitting
LyingStanding

1423
152
369
65

155
403
4
0

445
0
936
30

10
0
26
119

STL

Acc = 78.6
Walking

Sitting

LyingStanding

Walking
Sitting
LyingStanding

1658
53
357
33

67
496
6
0

303
6
912
58

5
0
60
123

Fig. 6. Classification accuracy of (a) different degrees of similarities and (b) different levels of activities in transfer learning.

significant improvement; (2) STL-SAT strongly outperforms GFK in Within Dataset category, indicating that SAT is morerobust in recognizing different levels of activities. For SAT, it performs intra-class knowledge transfer after generating
pseudo labels for candidates. Thus, better performance can be achieved by exploiting the local property of classes.
We further did a case study by showing the confusion matrices of all methods for task RUA → LUA on OPP dataset
in Table 5 and the performance of each person in Fig. 5(b). The confusion matrix helps to analyze which class is easier
to classify. From the results, we can observe that in CPAR, all the classes are easy to be wrongly classified since there is
distribution divergence between domains. Of all the classes, Walking and Standing are two classes that are more easily
to be misclassified. In this situation, our proposed STL-SAT could significantly outperform other comparison methods.
In other situations, STL-SAT can still obtain comparable performance. Overall, STL-SAT achieves the best classification
accuracy. On other tasks, the results are almost the same. It indicates the superiority of STL-SAT. We also noticed that onsome persons (P6, P7, and P8), the performance of STL-SAT is worse. This may be because the sensor data of these three
persons are a little mixed during the activity transition. We will explore more fine-grained classes for future research.
4.4. Performance on similarity and activity level
We explore the performance on different similarity and activity levels in Fig. 6. For similarity level, we use Highly
Likely to denote the similar body parts such as RA → LA, Likely to denote the dissimilar body parts such as RA → T,
and Less Likely to denote the Within Dataset for notational consistency. For activity level, we analyze low-level (OPP-LL),
middle-level (OPP-ML), and high-level (OPP-HL) activities.
Firstly, the accuracies of all methods drop as the domain similarity becomes less and activity level becomes high.
Additionally, the performance of STL-SAT is the best in all scenarios. For a different person, all methods produce the worst
results because different people have exactly different body structure and moving patterns (e.g. T → T across datasets). At
the same degree of similarity, the results are also different. For example, the performance of RUA → T is better than RLA→ T in the same dataset. Because there is more similarity between Right Upper Arm (RUA) and Torso (T) than between
Right Lower Arm (RLA) and Torso (T). Other positions also share a similar discovery.

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Fig. 7. (a) Candidates usage of STL-SAT for RA → LA on DSADS dataset; (b) Convergence of 1NN-SAT and STL-SAT; (c) Parameter sensitivity.

Secondly, it indicates the best performance is achieved at middle-level activities, while it suffers from low-level andeven worse at high-level activities. Low-level activities such as Walking and middle-level activities such as Closing aremostly contributed by the atomic movements of body parts and they are likely to achieve better transfer results than thehigh-levels. High-level activities such as Coffee Time not only involve basic body movements but also contain contextual
information like ambient or objects, which is difficult to capture only by the body parts. Since the bridge of successful
cross-position transfer learning is the similarity of body parts, it is not ideal to achieve good transfer performance by
only using body parts. The reason why results on OPP-ML are better than OPP-LL is that activities of OPP-ML are morefine-grained than OPP-LL, making it more capable of capturing the similarities between the body parts.
4.5. Effectiveness analysis
In this section, we verify the effectiveness of STL-SAT in several aspects.
(1) The confidence of the candidates: We control the percentage of the candidates from 10% to 100% in every trial
and make the rest belong to the residual part. Then we test the performance of STL-SAT on the task LA → RA on DSADS
and compare with other 2 methods (PCA and TCA). The result is shown in Fig. 7(a). From the results, we can observe thatthe performance of STL-SAT is increasing along with the increment of candidates percentage. More importantly, STL-SAT
outperforms the other two methods with less than 40% of candidates. It reveals that SAT does not largely rely on theconfidence of the candidates and can achieve good performance even with fewer candidates.
(2) Majority voting classifiers and iteration: We choose 1 nearest neighbor (1NN) instead of three classifiers as thebase classifier. The results are in Fig. 7(b), where ‘1NN-SAT’ and ‘SAT’ denotes the result of STL-SAT using 1NN and random
forest as the base majority voting classifier, respectively. From those results, we can observe: (1) STL-SAT can iteratively
improve the classification accuracy even with some weak majority voting classifier. 1NN-SAT achieves slightly worse than
STL-SAT, indicating that STL-SAT is rather robust to the base classifiers. Since more powerful classifiers would lead to better
performance, we strongly suggest using more reliable classifiers. (2) STL-SAT can reach a quick convergence within fewer
than 10 iterations. This indicates that STL-SAT can be efficiently trained.
(3) Parameter sensitivity. STL-SAT involves two parameters: the dimension m, and trade-off parameter λ. In thisexperiment, we evaluate the sensitivity of m. We set m ∈ {10, 20, 30, 40} and test the performance of SAT and otherdimensionality reduction methods. As shown in Fig. 7(c), STL-SAT achieves the best accuracy under different dimensions.
Meanwhile, the accuracy of STL-SAT almost does not change with the decrement of m. The results reveal that STL-SAT ismuch more effective and robust than other methods under different dimensions.
5. Conclusions and future work
In this paper, we propose a novel Stratified Transfer Learning (STL) framework for cross-domain HAR. STL can address
both the source domain selection (by STL-SDS) and knowledge transfer (by STL-SAT) problems in CPAR by exploiting
the local property of each class between different domains. Experiments on three large public datasets demonstrate
the significant superiority of STL over five state-of-the-art methods. We extensively analyze the performance of transfer
learning under different degrees of similarities and different levels of activities.
In the future, we plan to extend STL in the following research directions:
Deep STL. The biggest difference between this paper and the deep version is we can exploit deep networks toautomatically extract features and then perform domain selection and activity transfer. All these steps can be operated
in one neural network.
Heterogeneous STL. In heterogeneous HAR, the features for different domains may be different. For instance, if thesource domain contains activity information of the accelerometer and the target domain has information of the gyroscope,
we need to develop heterogeneous algorithms accordingly.

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13

Acknowledgments
This work is supported in part by National Key R & D Plan of China (No. 2017YFB1002802), NSFC (No. 61572471,
61472399, 61702520), and Beijing Municipal Science & Technology Commission (No. Z171100000117017).
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