Stratified Transfer Learning for
Cross-domain Activity Recognition
Jindong Wang∗† , Yiqiang Chen∗† , Lisha Hu‡ , Xiaohui Peng∗† , Philip S. Yu§∗ Beijing Key Laboratory of Mobile Computing and Pervasive Device

Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China† University of Chinese Academy of Sciences, Beijing, China‡ Institute of Information Technology, Hebei University of Economics and Business, Shijiazhuang, China§ Department of Computer Science, University of Illinois at Chicago, IL, USA
Email:{wangjindong,yqchen,pengxiaohui}@ict.ac.cn, hulisha@heuet.edu.cn, psyu@uic.edu

Abstract— In activity recognition, it is often expensive andtime-consuming to acquire sufficient activity labels. To solve thisproblem, transfer learning leverages the labeled samples fromthe source domain to annotate the target domain which has few
or none labels. Existing approaches typically consider learninga global domain shift while ignoring the intra-affinity between
classes, which will hinder the performance of the algorithms.
In this paper, we propose a novel and general cross-domain
learning framework that can exploit the intra-affinity of classes
to perform intra-class knowledge transfer. The proposed framework, referred to as Stratified Transfer Learning (STL), candramatically improve the classification accuracy for cross-domain
activity recognition. Specifically, STL first obtains pseudo labels
for the target domain via majority voting technique. Then, it
performs intra-class knowledge transfer iteratively to transform
both domains into the same subspaces. Finally, the labels of target
domain are obtained via the second annotation. To evaluate theperformance of STL, we conduct comprehensive experiments on
three large public activity recognition datasets (i.e. OPPORTUNITY, PAMAP2, and UCI DSADS), which demonstrates that STL
significantly outperforms other state-of-the-art methods w.r.t.
classification accuracy (improvement of 7.68%). Furthermore, we
extensively investigate the performance of STL across different
degrees of similarities and activity levels between domains. And
we also discuss the potential of STL in other pervasive computing
applications to provide empirical experience for future research.

I. I NTRODUCTION
Human activity recognition (HAR) is a hot research topic
in pervasive computing. HAR has been widely applied tomany applications such as indoor localization [1], sleep state
detection [2], and smart home sensing [3]. The key to successful HAR is to build accurate and robust models using
sufficient labeled activity data. Unfortunately, it is often expensive and time-consuming to obtain enough labeled data.
In this case, it is necessary to perform cross-domain activity
recognition (CDAR) by exploiting the labeled activity datafrom one auxiliary domain to annotate the unlabeled activities
in another domain.
An intuitive example of CDAR is given in Fig. 1, whichshows two accelerometer readings on the chest (C) and theleg (L) from one person. Such scenarios happen very often: If
we only have the activity data and labels on C but labels on L
are missing or wrongly labeled, we can certainly use the data

Fig. 1. Two accelerometer readings of the same device when a person iswalking. It is obvious that those two readings follow different distributions.

from C to recognize the activity on L. Because the signals of C
and L can be related according to the body structure. Then thechallenge arises: It can be seen that the two sensor readings areunder two totally different distributions from Fig. 1. Therefore,
it is challenging to design algorithms to tackle CDAR problem.
Several dimensionality reduction methods have been proposed to resolve CDAR, such as principal component analysis (PCA), locally linear embedding (LLE), and kernel principal component analysis (KPCA) [4]. Dimensionality reduction does not require domain knowledge, but it ignores thedivergence between domains. To this end, transfer learning [5]has made considerable progress for cross-domain tasks byleveraging the labeled samples from other auxiliary domains.
The key to transfer learning is to utilize the similarity between
those different but related domains. Existing transfer learning
approaches disentangled the cross-domain learning problems
either by exploiting the correlations between features [6], [7],or transforming both the source and target domains into a newshared feature space [8], [9], [10].
Those approaches tend to learn a global domain shift byprojecting all samples in both domains into a single subspace. However, they fail to consider the intra-affinity withinclasses [11]. According to Fig. I, learning the global domain
shift (Fig. 2(b)) can only learn a general hyperplane between
classes, and this hyperplane is loose; while by exploiting intraclass affinity (Fig. 2(c)), classes can further be clustered moreII. R ELATED W ORK
Our work is mainly related to activity recognition andtransfer learning. In this section, we will discuss those twoareas and their intersections.
(a) Original target(b) Learn global shift (c) Exploit intra-affinity
Fig. 2. Illustration of learning global domain shift (existing approaches) and
exploiting intra-affinity (STL) for the same original target domain.

tightly. Therefore, it is necessary to exploit the intra-affinityof classes to overcome the limitation of global domain shift.
According to [12], the data samples from the same classshould lay on the same subspace, even if they belong todifferent domains. By using this assumption, in this paper,
we propose a novel and general Stratified Transfer Learning (STL) framework. STL can simultaneously transformthe same classes of the source and target domains into thesame subspaces. Compared to existing methods, STL exploits
the intra-affinity of classes to perform intra-class knowledgetransfer. Thus, the global domain shift can be alleviated. Concretely speaking, STL first obtains pseudo labels for the target
domain via a majority voting technique. Then, it performs
intra-class knowledge transfer to transform the source andtarget domain into the same subspaces. Finally, the labelsof target domain are obtained through a second annotation
step. Comprehensive experiments on three large public activity
recognition datasets (i.e. OPPORTUNITY, PAMAP2, and UCI
DSADS) demonstrate that STL outperforms other five stateof-the-art methods with a significant improvement of 7.68%
w.r.t. classification accuracy.
Contributions. Our contributions are mainly three-fold:
1) We propose a novel and general cross-domain learning
framework STL. Different from existing methods that only
obtain a global domain shift, STL is capable of exploiting
the intra-affinity of classes to perform intra-class knowledgetransfer. STL is a general framework and can be tailoredaccording to specific applications.
2) We conduct comprehensive experiments for cross-domain
activity recognition on three public datasets (i.e. OPPORTUNITY, PAMAP2, and UCI DSADS) to evaluate STL.
Experiments demonstrate the superiority of STL over otherstate-of-the-art methods w.r.t. classification accuracy.
3) We extensively investigate the performance of STL on
different degrees of task similarity and different levels ofactivities. And we additionally explore the potential of STL inother pervasive computing applications, providing experiencefor future research.
The rest of this paper is organized as follows. In Section II,
we review the related work. Section III introduces the proposed
STL framework. In Section IV we present experimental evaluation and analysis of STL and other comparison methods.
In Section V, we discuss the potential of STL in otherreal applications. Finally, the conclusion and future work arepresented in Section VI.

A. Activity Recognition
Human Activity recognition has been a popular research
topic in pervasive computing [13] for its competence inlearning profound high-level knowledge about human activity
from raw sensor inputs. Several survey articles have elaborated
the recent advance of activity recognition using conventional
machine learning [13], [14] and deep learning [15] approaches.
Conventional machine learning approaches have madetremendous progress on HAR by adopting machine learningalgorithms such as similarity-based approach [16], [17], active
learning [18], crowdsourcing [19], and other semi-supervised
methods [20], [21]. Those methods typically treat HAR as astandard 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 arewith the same distribution. As for CDAR where the training (source) and the test (target) data are from different feature
distributions, those conventional methods are prune to underfitting since their generalization ability will be undermined [5].
Deep learning based HAR [15] achieves the state-of-the-art
performance than conventional machine learning approaches.
The reason is that deep learning is capable of automatically extracting high-level features from the raw sensor readings [22].
Therefore, the features are likely to be more domain-invariant
and tend to perform better for cross-domain tasks. A recent
work evaluated deep models for cross-domain HAR [23],which provides some experience for future research on thisarea. There are stll many open problems for deep learning
based CDAR. In this paper, we mainly focus on the traditional
approaches.
B. Transfer Learning
Transfer learning has been successfully applied in many
applications such as Wi-Fi localization [24], natural language
processing [6], and visual object recognition [25]. According
to the literature survey [5], transfer learning can be categorized
into 3 types: instance-based, parameter-based, and featurebased methods.
Instance-based methods perform knowledge transfer
mainly through instance re-weighting techniques [26], [27].
Parameter-based methods [28], [29] first train a model using
the labeled source domain, then perform clustering on thetarget domain.
Our framework belongs to the feature based category, whichbrings the features of source and target domain into the same
subspace where the data distributions can be the same. A
fruitful line of work has been done in this area [30], [31],[10]. The proposed 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, then trained
a domain-adapted classifier. Instead of modeling the relationship of domain features, STL transforms the domain data
into a new subspace, which does not depend on the domain
knowledge in modeling features.
Transform domains into new feature space. [24] 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), which learns
a kernel in RKHS. [32] adopted a similar idea. [33] learns
target predictive function with a low variance. [34] sampled
the domain features by viewing the data in a Grassmann manifold to obtain subspaces. [9] exploited the low-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 STL focuses on the marginal distribution.
[10] proposed transfer kernel learning (TKL), which learned adomain-invariant kernel in RKHS. [35] studied the conditionaltransfer components between domains. Methods in those literature tend to learn some common representations in the newfeature space, then a global domain shift can be achieved.
However, the difference between individual classes is ignored.
C. Transfer Learning based Activity Recognition
Some existing work also focused on transfer learning based
HAR. A detailed survey is provided in [36]. Among existing
work, Zhao et al. proposed a transfer learning method called
TransEMDT [29] using decision trees, but it ignored the intraclass similarity within classes. [37] proposed the TransActframework, which is a boosting-based method and ignores thefeature transformation procedure. Thus it is not feasible inmost activity cases. Feuz et al. [38] proposed a heterogeneoustransfer learning method for HAR, but it only learns a global
domain shift.
To circumvent the global domain shift, [12] clustered thedata points in a low-dimensional space using sparse subspaceclustering. [11] identified a compact joint subspace for eachclass, then measured the distance between classes using principal angle. The main difference between STL and [11] isthat STL learns pseudo labels using majority voting techniqueon both domains, instead of performing metric clustering on
the target domain alone. Thus, STL can obtain more reliablecandidates by taking advantage of both domains.
III. S TRATIFIED T RANSFER L EARNING
In this section, we introduce the proposed Stratified Transfer
Learning (STL) framework. First, we present the problem
definition of CDAR and the main idea of STL. Then, eachstep of STL is presented in detail.

Source domain

Target domain
Residual

1
Majority
voting2

Candidate

Intra-classtransfer

Trans.

Residual

predict

Trans.
Trans.

3
Secondannotation

CandidateFig. 3. Main idea of stratified transfer learning (STL) framework. There aremainly three steps: (1) Candidates generating through majority voting technique; (2) Perform intra-class transfer between source domain and candidates;(3) Fully label the target domain via second annotation.

A. Problem Definition
CDAR is a typical cross-domain learning problem, whichsoften consists of a labeled source domain Ds = {(xi , yi )}ni=1,nt
and an unlabeled target domain Dt = {xj }j=1 . Ds and Dt
have the same dimensionality and label spaces, i.e. xi , xj ∈Rd where d is the dimensionality, and Ys = Yt . In crossdomain learning, they follow different feature distributions.
Concretely speaking, we use P and Q to denote the marginal
and conditional distributions, respectively. Then, P (xs ) 6=
P (xt ), and Q(ys |xs ) 6= Q(yt |xt ). The goal of cross-domain
learning is to obtain the labels yt for the target domain Dt
using the labeled source domain Ds . Specifically in CDAR, thegoal is to use the labeled activity information in one domain
to learn the labels for another domain.
STL can simultaneously transform the individual classes ofthe source and target domains into the same subspaces by
exploiting the intra-affinity of classes. Compared to existing
approaches which only learn a global domain shift, we adopt
the assumption that data samples from the same class should
lay on an intrinsic subspace [12]. Fig. 3 illustrates the mainidea of STL. There are mainly three steps. Initially, STL
generates pseudo labels for the target domain through majority
voting technique. Then, it performs intra-class knowledgetransfer between domains. Finally, a second annotation stepis performed on the newly transformed subspaces.
Now we elaborate each step in detail.
B. Majority Voting
As a preprocessing step of STL, this step generates pseudolabels for the target domain based on several classifiers trainedon source domain. Those samples with pseudo labels are calledcandidates. To this end, majority voting technique is developed
to exploit the knowledge from the crowd [39]. Specifically,
STL makes use of some base classifiers learned on Ds tocollaboratively learn the labels for Dt .
Let Aj (j = 1, 2, · · · , n2 ) denote the final result of majority
voting on xtj , and ft (j) denotes the prediction of the j-thsample by the t-th classifier ft (·), we have(
majority({ft (j), t) if majority holds
Aj =−1otherwise,

majority voting. For the candidates and the source domain, we
present their intra-class MMD distance as(1)2

where t ∈ {1, 2, · · · } denotes the index of classifier.
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, Ai could be defined as a) if most classifiers havesame 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 (similar to the deep forest
proposed by Zhou and Feng [40]). In theory, the classifiers
can be of any type in our framework.
Using majority voting, STL can generate pseudo labels forthe target domain. Label ‘-1’ means that there is no majority
consensus for that sample. The samples with this label arecalled residuals, and they will be annotated later. In the sequel,
we will use Xcan and Xres to denote the candidates andecan denotes the pseudo labels
residuals, respectively. And yfor the candidates.
C. Intra-class Transfer
In this step, STL exploits the intra-affinity of classes tofurther transform each class the candidates and source domain
into the same subspace. Initially, Ds and Xcan are divided
to 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, theresults of distinct subspaces are merged.
The key to successful knowledge transfer is to utilize thesimilarity between the source and the target domain. Hence,
how to measure the similarity (or divergence) is critical.
We adopt maximum mean discrepancy (MMD) [41] as themeasurement. MMD is a nonparametric method to measure thedivergence 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 formallycomputed as
D(Ds , Dt ) =1
nsP
xi ∈Dsφ(xi ) − n1tP
xj ∈Dt2

φ(xj )

D(Ds , Xcan )(2)Hwhere H denotes reproducing kernel Hilbert space (RKHS).
Here φ(·) denotes some feature map to map the original
samples to RKHS. The reason we do not use the original datais that the features are often distorted in the original feature
space, and it can be more efficient to perform knowledgetransfer in RKHS [8].
The above Eq. 2 derives a global domain shift for the source
and target domain just similar to many existing methods [8],[10]. In order to achieve intra-class transfer, we need to
calculate the MMD distance between each class. Since thetarget domain has no labels, we use the pseudo labels from

=

C
X

1

c=1

(c)
ns

X
(c)

xi ∈Dsφ(xi ) −

1

X

(c)
nt
(c)
x ∈X
j

φ(xj )

(3)

can

H
(c)
(c)
where c ∈ {1, 2, · · · , C} denote the class label. Ds and Xcan

denote the samples belonging to class c in the source and
(c)
(c)
(c)
(c)
candidates, respectively. ns = |Ds |, and nt = |Xcan |.
Unfortunately, it is non-trivial to solve Eq. (3) directly
since the mapping function φ(·) is to be determined. Thus,
we turn to some kernel methods. We define a kernel matrix
K ∈ R(n1 +n2 )×(n1 +n2 ) , which can be constructed by the innerproduct of the mapping
Kij = hφ(xi ), φ(xj )i = φ(xi )> φ(xj )(4)where xi and xj are samples from either Ds or Xcan .
We further introduce a feature transformation matrix W ∈R(n1 +n2 )×m to transform the samples of both domains fromthe original space to the RKHS. Here m  d denotes thedimension after feature transformation. Then, by applying
kernel tricks, Eq. 3 can be eventually formulated as thefollowing trace optimization problem:
min
W

C
X

tr(W> KLc KW) + λtr(W> W)

c=1
>

(5)

s.t. W KHKW = I
There are twoPterms in the objective function of Eq. (5).
C
The first term ( c=1 tr(W> KLc KW)) denotes the MMD
distance of each class between source and target domain, andthe second one (λtr(W> W)) denotes the regularization term
to ensure the problem is well-defined with λ the trade-off
parameter. The constraint in Eq. 5 is used to guarantee thatthe transformed data (W> K) will still preserve some structure
property of the original data. In1 +n2 is the identical matrix,and H = In1 +n2 − 1/(n1 + n2 )11> is the centering matrix.
For notational brevity, we will drop the subscript for In1 +n2
in the sequel. Lc is the intra-class MMD matrix, which canbe constructed as: 1(c)xi , xj ∈ Ds2
 (n(c)
)

1


(c)
 1 2

xi , xj ∈ Xcan (n(c) )
2
(
(c)
(c)
(6)
(Lc )ij =xi ∈ Ds , xj ∈ Xcan

1

−

(c)
(c)
(c)
(c)

n1 n2

xi ∈ Xcan , xj ∈ Ds0otherwise
Learning algorithm: Acquiring the solution of Eq. 5 is nontrivial. To this end, we adopt Lagrange method. We denote Φ
the Lagrange multiplier, then the Lagrange function can bederived as
!
C
X
>
>
L = tr W K
Lc K W + λtr(W> W)
(7)
c=1

>
>
+ tr (I − W KHK W)Φ

Setting the derivative ∂L/∂W = 0, Eq. 7 can be finallyformalized as an generalized eigen-decomposition problem!
CXK
Lc K> + λI W = KHK> WΦ(8)
c=1

Solving Eq. 8 refers to solve this generalized eigendecomposition problem and take the m smallest eigenvectors
to construct W. W can transform both domains into the same
subspace with minimum domain distance while preserving
their properties. Since the knowledge transfer pertains toeach class, we call this step intra-class transfer, and that iswhere the name stratified originates from. After this step, thesource and target domains belonging to the same class are
simultaneously transformed into the same subspaces.
D. Second annotation
The objective of this step is to annotate the residual partusing the transformed source domain and candidates. The majority voting provides pseudo labels (eycan ) for the candidates,
which can be transformed into the same subspaces with thetarget domain after intra-class transfer. Under this circumstance, it is easy to get more reliable predictions (ŷcan ) of thecandidates. Specifically, we train a standard classifier using{[W> K]1:n1 ,: , ys } and apply prediction on [W> K]n1 +1:n2 ,: .
Finally, the labels of residuals can be obtained by trainingclassifier on instances {Xcan , ŷcan }.
Since this step requires annotating the candidates again withmore concrete labels, we call it second annotation. The labelsof 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.
E. Iterative refinement
It should be noted that STL could achieve a better prediction
if we use the result of second annotation as the initial state andrun intra-class transfer iteratively. This EM-like algorithm is
empirically effective and will be validated in the following
experiments. Additionally, we only use majority voting in
the first round of the iteration, then the proposed STL could
iteratively refine the labels for the target domain by only using
its previous results.
The overall process of STL is described in Algorithm 1.
Remark: STL is a general framework for transfer learningand it can be implemented in different ways according to
the specific applications. We only provide one feasible implementation of STL in this section. Meanwhile, each stepof STL can be tailored according to certain applications:
1) majority voting could have different classifiers and voting
techniques; 2) intra-class transfer could use existing transfer
learning approaches such as GFK [9] and TransACT [37];3) second annotation could use different classifiers. Therefore,by considering the characteristics of certain applications, STL
can be more effective and efficient in solving these problems.
IV. E XPERIMENTAL E VALUATIONIn this section, we evaluate the performance of STL via
extensive experiments on cross-domain activity recognition.

Algorithm 1 STL: Stratified Transfer Learning
Input: Source domain Ds = {Xs , ys }, target domain Dt ={Xt }, #dimension m.
Output:
The labels for the target domain: {yt }.
1: Perform majority voting on Dt using Eq. 1 to getecan } and Xres ;{Xcan , y2: Construct kernel matrix K according to Eq. (4) using Xsrc
and Xcan , and compute the intra-class MMD matrix Lc
using Eq. 6;
3: repeat4:
Solve the eigen-decomposition problem in Eq. 8 andtake the m smallest eigen-vectors to obtain the transformation matrix W;
5:Transform the same classes of Xs and Xcan into thesame subspaces using W, and then merge them;
6:
Perform second annotation to get {ŷcan } and {ŷres };7:Construct kernel matrix K and compute the intra-class
MMD matrix Lc using Eq. 6;
8: until Convergence
9: return {yt }.

A. Cross-domain activity recognition
Cross-domain activity recognition (CDAR) aims at labelingthe activity of one domain using the labeled data from anotherrelated domain. There are several types of CDAR: crossperson, cross-device, cross-environment activity recognition,and so on. In our experiments, we choose cross-position
activity recognition. Specifically, it refers to the situation
where the activity labels of some body parts are missing, so
it is necessary and feasible to leverage the labeled data fromother similar body parts to get the labels of those body parts.
Why cross-position activity recognition: We need to extensively investigate the performance of transfer learning atdifferent degrees of similarities between the source and target
domain. In cross-position tasks, there are different degrees ofsimilarities, since body parts are different at certain degrees.
For instance, there is more similarity between both arms thanbetween arm and torso. Compared to other types of CDAR
such as cross-person or cross-device, cross-position tasks canprovide more detailed information about domain similarities,
thus more experience about activity transfer can be revealed.
Why knowledge can be transferred between body parts: Firstof all, different body parts tend to share similar structure andfunctions. Then, the activity patterns of different body parts
are often related. Thus, annotating the activity becomes across-domain learning problem because the data distribution
is different on body parts.
B. Datasets and Preprocessing
Three large public datasets are adopted in our experiments.
TABLE I provides a brief introduction to those three datasets.
In the following, we briefly introduce those datasets, and more
information can be found in their original papers. OPPORTUNITY dataset (OPP) [42] is composed of 4 subjects executing
different levels of activities with sensors tied to more than 5

TABLE I
B RIEF INTRODUCTION OF THREE PUBLIC DATASETS FOR ACTIVITY RECOGNITION
DatasetOPPORTUNITYPAMAP2DSADS#Subject498#Activity
4
18
19

OPPORTUNITY
Right Upper
Arm

Right Lower
Arm#Sample701,366
2,844,868
1,140,000#Feature
459
243
405

DSADS

PAMAP2
Chest

Back
Left Upper
Arm
Left Lower
Arm

Body parts
Back (B), Right Upper Arm (RUA), Right Left Arm (RLA), Left Upper Arm (LLA), Left Lower Arm (LLA)
Hand (H), Chest(C), Ankle (A)Torso (T), Right Arm (RA), Left Arm (LA), Right Leg (RL), Left Leg (LL)

Torso

Right Arm
Hand

TABLE IIF EATURES EXTRACTED PER SENSOR ON EACH BODY PARTRight Leg

Left Arm

Left Leg

Ankle

Fig. 4. Different positions on OPPOPTUNITY, PAMAP2 and DSADS.

body parts. PAMAP2 dataset (PAMAP2) [43] is collected by 9
subjects performing 18 activities with sensors on 3 body parts.
UCI daily and sports dataset (DSADS) [44] consists of 19
activities collected from 8 subjects wearing body-worn sensors
on 5 body parts. Accelerometer, gyroscope, and magnetometerare all used in three datasets.
Fig. 4 illustrates the positions we investigated in threedatasets. In our experiments, we use the data from all three
sensors in each body part since most information can beretained in this way. For onep
sensor, we combine the data from
3 axes together using a = x2 + y 2 + z 2 . Then, we exploit
the sliding window technique to extract features (window
length is 5s). The feature extraction procedure is mainly
executed according to existing work [45]. In total, 27 featuresfrom both time and frequency domains are extracted for asingle sensor (see TABLE II). Since there are three sensors (i.e.
accelerometer, gyroscope, and magnetometer) on one bodypart, we extracted 81 features from one position.
In order to investigate more detailed information during activity knowledge transfer, we perform CDAR in the following
three scenarios according to the different similarities between
body parts. Those three scenarios represent three different
degrees of similarities between domains. In the sequel, we
use the notation A → B to denote labeling the activity of
domain B using the labeled domain A.
• a) similar body parts of the same person, which refers tohighly similar body parts such as left and right arms on
the same person. Specifically, we extracted the data from
OPP and DSADS (PAMAP2 is not included since there
are no similar parts), and constructed 8 tasks: RA → LA,
RL → LL, RUA → LUA, RLA → LLA, and vice versa.
• b) different body parts of the same person, which refers
to different body parts like torso and arm of the same
person. Specifically, we constructed 8 tasks from threedatasets: RA → T, H → C, RLA → T, RUA → T, andvice versa.
• c) similar body parts of different person, which refers toactivity recognition on same body parts across different
datasets. Specifically, we constructed 6 tasks for T → T

IDFeatureDescription

1
2
3
4
5
6
7
8
9-13
14-18
19
20-23
24-27

Mean
STD
Minimum
Maximum
Mode
Range
Mean crossing rate
DC
Spectrum peak position
Frequency
EnergyFour shape features
Four amplitude features

Average value of samples in window
Standard deviation
Minimum
Maximum
The value with the largest frequency
Maximum minus minimum
Rate of times signal crossing mean value
Direct component
First 5 peaks after FFT
Frequencies corresponding to 5 peaks
Square of norm
Mean, STD, skewness, kurtosis
Mean, STD, skewness, kurtosis

across three datasets 1 .
In total, we constructed 22 tasks. Note that there aredifferent activities in three datasets. For scenario a) and b),
we simply use all the classes in each dataset; for scenarioc) which is cross-dataset, we extract 4 common classes foreach dataset (i.e. Walking, Sitting, Lying, and Standing). In
addition, we did not include the scenario ‘different body partsof different person’ since 1) all the methods perform poorly
in that scenario, and 2) that scenario does not have reasonablefeasibility in real applications.
C. Comparison Methods and Implementation Details
We adopt five state-of-the-art comparison methods:
PCA: Principal component analysis [4].
KPCA: Kernel principal component analysis [4].
• TCA: Transfer component analysis [8].
• GFK: Geodesic flow kernel [9].
• TKL: Transfer kernel learning [10].
••PCA and KPCA are classic dimensionality reduction methods, while TCA, GFK, and TKL are representative transfer
learning approaches. The codes of PCA and KPCA are provided in Matlab. The codes of TCA, GFK, and TKL can beobtained online 2 . The constructed datasets and STL code arereleased online 3 .
We construct the tasks according to each scenario anduse the labels for target domain only for testing. Then we
perform CDAR using STL and all comparison methods. 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 is learned
using the source domain and then the target domain can be
1 In this paper, for brevity, we use “T” to denote the Torso / Back / Chest
in three datasets, respectively.
2 https://tinyurl.com/y79j6twy
3 https://tinyurl.com/y7en6owt

TABLE III
C LASSIFICATION ACCURACY (%) OF STL AND OTHER COMPARISON METHODS ON DIFFERENT CDAR TASKS .

Scenario

DatasetDSADS

Similar body parts on same person
OPP

Different body parts on same person

DSADS
PAMAP2OPP

PAMAP2 → OPP
DSADS → PAMAP
OPP → DSADS
Average

Similar body parts on different person

Task
RA → LARL → LL
RUA → LUA
RLA → LLA
RA → T
H→C
RLA → T
RUA → T
T→T
T→T
T→T

labeled. To be more specific, we use the random forest classifier (#T ree = 30) as the final classifier for all the 6 methods.
For majority voting in STL, we simply use SVM (C = 100),kNN (k = 3), and random forest (#T ree = 30) as thebase classifiers. Other parameters are searched to achieve theiroptimal performance. The #iteration is set to be T = 10 for
STL. It is noticeable that we randomly shuffle the experimental
data for 5 times in order to gain robust results.
Classification accuracy on the target domain is adopted as
the evaluation metric, which is widely used in existing transfer
learning methods [10], [8]Accuracy =|x : x ∈ Dt ∧ ŷ(x) = y(x)|x : x ∈ Dt

(9)where y(x) and ŷ(x) are the truth and predicted labels,
respectively.
D. Classification Accuracy of STL
We run STL and other methods on all CDAR tasks andreport the classification accuracy in TABLE III. For brevity,
we only report the results of A → B since its result is close to
B → A. It is obvious that STL significantly outperforms othermethods in most cases (with a remarkable improvement of
7.68% over the best baseline GFK). Compared to traditional
dimensionality reduction methods (PCA and KPCA), STL
improves the accuracy by 10% ∼ 20%, which implies that
STL is better than typical dimensionality reduction methods.
Compared to transfer learning methods (TCA, GFK, andTKL), STL still shows an improvement of 5% ∼ 15%.
Therefore, STL is more effective than all the comparison
methods in most cases.
The performance of TKL is the worst, because of theinstability 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 STL, 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 and GFK are: 1) STL outperforms GFK in most cases with significant improvement;2) STL strongly outperforms GFK in less similar scenarios (scenarios a) and b)), indicating that STL is more robust in

PCA
59.91
69.46
76.12
62.17
38.89
34.97
59.10
67.95
32.80
23.19
44.30
51.71

KPCA
62.17
70.92
65.64
66.48
30.20
24.44
46.99
54.52
43.78
17.95
49.35
48.40

TCA
66.15
75.06
76.88
60.60
39.41
34.86
55.43
67.50
39.02
23.66
46.91
53.23

GFK
71.07
79.71
74.62
74.62
44.19
36.24
48.89
66.14
27.64
19.39
48.07
53.69

TKL
54.10
61.63
66.81
66.82
32.72
35.67
47.66
60.49
35.64
21.65
52.79
48.73

STL
71.04
81.60
83.96
83.93
45.61
43.47
56.88
75.15
40.10
37.83
55.45
61.37

recognizing different levels of activities. For STL, it performs
intra-class knowledge transfer after generating pseudo labels
for candidates. Thus, better performance can be achieved by
exploiting the intra-affinity of classes.
E. Performance on Different Degrees of Similarities
We explore the performance of the transfer learning methods
under different degrees of similarities between the source andtarget domain. The average classification accuracy of eachmethod is shown in Fig. 5(a). For all the methods, the accuracy
drops as the domain similarity becomes less. Additionally, theperformance of STL is the best in all scenarios.
More elaborate observations can be given combining TABLE III and Fig. 5(a). In different scenarios, the changeof classification accuracy of each method follows the sametendency. Specifically, the performance of all the methods isthe best between similar body parts for the same person (e.g.
RA → LA). The performance becomes worse for different
body parts (e.g. RA → T). This is because Right Arm (RA)is more similar to Left Arm (LA) than to Torso (T). For adifferent person, all methods produce the worst results because
different people have exactly different body structure andmoving 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 moresimilarity between Right Upper Arm (RUA) and Torso (T)than between Right Lower Arm (RLA) and Torso (T). Other
positions also share the similar discovery.
All the experimental results indicate that the similarity
between the source and target domain is important for crossdomain learning. It is critical to find the right auxiliary
domain to perform successful knowledge transfer. In our
CDAR experiments, the body structure and moving patterns
contribute to the similarity. In real life, other factors such as
age and hobby also help define the similarity of activities. For
other cross-domain tasks (image classification etc.), finding
the relevant domain is also important. For example, the mostsimilar image set for a dog is probably a cat, since those twokinds of animals have similar body structures, moving patterns,
and living environments.

90

90

Accuracy (%)

80
70
60
50
40

P1
P2
P3

80

Accuracy (%)

PCA
KPCA
TCA
GFK
TKL
STL

70
60
50
40

30

30
Highly likely

LikelyLess likely

Levels of similarity

OPP-LLOPP-MLOPP-HL

Levels of activitiy(a) Different degrees of similarities(b) Different levels of activities of 3 persons
Fig. 5. Classification accuracy of (a) different degrees of similarities and (b) different levels of activities in transfer learning.

F. Performance on Different Levels of Activities
Different levels of activities imply the different depths ofactivity granularities. In this section, we extensively investigate
the performance of our proposed STL on CDAR tasks at different activity levels. By taking advantage of the diverse activity
classes in OPP dataset [42], we analyze the transfer learning
performance on low-level (OPP-LL), middle-level (OPPML), and high-level (OPP-HL) activities. The results arepresented in Fig. 5(b). It indicates the best performance isachieved at middle-level activities, while it suffers from lowlevel and even worse at high-level activities.
Low-level activities such as Walking and middle-level activities such as Closing are mostly contributed by the atomic
movements of body parts and they are likely to achieve bettertransfer results than the high-levels. On the other hand, highlevel activities such as Coffee Time not only involve basic
body movements, but also contain contextual information likeambient or objects, which is difficult to capture only by
the body parts. Since the bridge of successful cross-positiontransfer learning is the similarity of body parts, it is not ideal toachieve good transfer performance by only using body parts.
The reason why results on OPP-ML are better than OPP-LL isthat activities of OPP-ML are more fine-grained than OPP-LL,
making it more capable of capturing the similarities between
the body parts.
G. Effectiveness verification of STL
In this section, we verify the effectiveness of STL in several
aspects. The core idea of STL is intra-class transfer, where
the pseudo labels of the candidates are acting as the evidenceof transfer learning. It is intuitive to ask the following threequestions. Firstly, Can the confidence of the pseudo labels
have an influence on the algorithm? It seems that STL will
not achieve good performance if there is not enough reliablecandidates available. Secondly, Can the choice of majority
voting classifiers affect the framework? If we use different
classifiers, the performance is likely to vary. Thirdly, Can
intra-class transfer be implemented in parallel? Since in realapplications, there are often several classes, which would
require a large amount of training time if not in parallel. In

this part, we answer those questions through the following
experiments.
1) The confidence of the candidates: We control thepercentage of the candidates from 10% to 100% in every
trial and make the rest belong to the residual part. Then wetest the performance of STL. We test on the task LA → RA
on DSADS and compare with other 2 methods (PCA and
TCA). The result is shown in Fig. 6(a). For simplicity, weonly compare STL with PCA and TCA, since they are bothclassic dimensionality reduction methods. From the results,
we can observe that the performance of STL is increasingalong with the increment of candidates percentage. More
importantly, STL outperforms the other two methods with lessthan 40% of candidates. It reveals that STL does not largely
rely on the confidence of the candidates and can achieve good
performance even with fewer candidates.
2) Majority voting classifiers and iteration: To test
the effectiveness of majority voting classifiers, we choose
1 nearest neighbor (1NN) as the base classifier of majority
voting. Then we run STL iteratively. The results are shown in
Fig. 6(b), where ‘1NN-STL’ and ‘STL’ denotes the result of
STL using 1NN and random forest as the base majority votingclassifier, respectively. From those results, we can observe: 1)
STL can iteratively improve the classification accuracy evenwith some weak majority voting classifier. 1NN-STL achieves
slightly worse than STL, indicating that STL is rather robust
to the base classifiers. Since more powerful classifiers would
lead to better performance, we strongly suggest using morereliable classifiers for majority voting in real problems. 2) STL
can reach a quick convergence within fewer than 10 iterations.
This indicates that STL can be efficiently trained.
3) Potential of parallel deployment: STL has anothersignificant advantage: it can easily be implemented in parallel,
which is rather important in real applications. Two stepsof STL intuitively have that excellence: 1) majority voting
involves more than one classifier, where each classifier can betrained and used individually; 2) the intra-class transfer can be
performed within each class separately. Those two properties
demonstrate that STL could be more powerful and efficient if
deployed in parallel in real applications. We will continue toexplore that advantage in the future.

70

70

65

60
PCA
TCA
STL

55

50
10

72
70

Accuracy (%)

75

Accuracy (%)

Accuracy (%)

75

65
PCA
KPCA
TCA
GFK
TKL
1NN-STL
STL

60

55

30

40

50

60

70

80

90

100

Candidate usage (%)

0

66
PCA
KPCA
TCA
GFK
STL

64
62

50
20

68

5

10

15

# Iteration

20

60
10

20

30

40

# Dimension(a) Candidate usage(b) Iteration(c) Parameter sensitivity
Fig. 6. Detailed results of a) STL with increasing usage of candidates for RA → LA on DSADS dataset; b) 1NN-STL and STL with other methods; c)parameter sensitivity of STL in comparison with other methods

H. Parameter Sensitivity
STL involves two parameters: the dimension m, and tradeoff parameter λ. In this experiment, we empirically evaluate
the sensitivity of m. The evaluation of λ is omitted due topage limit and our experiments have verified its robustness.
We set m ∈ {10, 20, 30, 40} and test the performance of
STL and other dimensionality reduction methods. As shownin Fig. 6(c), STL achieves the best accuracy under different
dimensions. Meanwhile, the accuracy of STL almost does notchange with the decrement of m. The results reveal that STL
is much more effective and robust than other methods under
different dimensions. Therefore, STL can be easily applied tomany cross-domain tasks which require robust performance
w.r.t. different dimensions.
V. D ISCUSSION
We studied cross-domain activity recognition via the STL
framework and evaluated its performance on cross-position
HAR tasks. There are more applications in pervasive computing that STL could be applied to. In this section, we discuss thepotential of STL in other applications and give some empiricalsuggestions.
1) Activity recognition. The results of activity recognition
can be different according to different devices, users, andwearing positions. STL makes it possible to perform crossdevice/user/position activity recognition with high accuracy. In
case cross-domain learning is needed, finding and measuring
the similarity between the device/user/position is critical.
2) Localization. In WiFi localization, the WiFi signal
changes with the time, sensor, and environment, causing the
distributions different. So it is necessary to perform crossdomain localization. When applying STL to this situation, it
is also important to capture the similarity of signals according
to time/sensor/environment.
3) Gesture recognition. For gesture recognition, due todifferences in hand structure and moving patterns, the modelcannot generalize well. In this case, STL can also be a good
option. Meanwhile, special attention needs to be paid to thedivergence between the different characteristic of the subjects.
4) Other context-related applications. Other applications include smart home sensing, intelligent city planning, healthcare,and human-computer interaction. They are also context-related
applications. Most of the models built for pervasive computing
are only specific to certain contexts. Transfer learning makes
it possible to transfer the knowledge between related contexts,of which STL can achieve the best performance. But whenrecognizing high-level contexts such as Coffee Time, it israther important to consider the relationship between different
contexts in order to utilize their similarities. The research on
this area is still on the go.
5) Suggestions for using STL. Firstly, before using STL andother transfer learning approaches, it is critical to investigate
the similarity between the source and target domain in advance. Secondly, it is better to use rather strong classifiers
for majority voting since it makes the convergence quick.
Thirdly, STL can be more efficient if deployed in parallel.
Additionally, each step of STL can be tailored according to
specific applications.
VI. C ONCLUSION AND F UTURE W ORK
The label scarcity problem is very common in pervasive
computing. Transfer learning addresses this issue by leveraging labeled data from auxiliary domains to annotate thetarget domain. In this paper, we propose a novel and general Stratified Transfer Learning (STL) framework for crossdomain learning in pervasive computing. Compared to existing
approaches which only obtain a global domain shift, STL
can exploit the intra-affinity of each class between different
domains. We also provide a solution to implement STL.
Experiments on three large public datasets demonstrate thesignificant superiority of STL over existing five state-of-the-art
methods. In addition, we extensively analyze the performanceof transfer learning under different degrees of similarities anddifferent levels of activities. We also extensively discuss thepotential of STL in other pervasive computing applications. In
addition, STL is a general framework where each step can be
tailored according to specific applications, making STL more
effective and efficient in solving other problems.
In the future, we plan to extend STL using deep learning, as
well as evaluating STL through more cross-domain learning
problems in pervasive computing.

ACKNOWLEDGMENTS
J. Wang would like to thank Dr. Shuji Hao from A*star,
Singapore, and Dr. Mingsheng Long from THU, China, fortheir valuable comments. This work is supported in part by
National Key R & D Plan of China (No.2016YFB1001200),
NSFC (No.61572471), and Science and Technology Planning
Project of Guangdong Province (No.2015B010105001).
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