SSLLE: SEMI-SUPERVISED LOCALLY LINEAR EMBEDDING

BASED LOCALIZATION METHOD FOR INDOOR

WIRELESS NETWORKS

Vinod Kumar Jain, Shashikala Tapaswi and Anupam Shukla

Atal Bihari Vajpayee, Indian Institute of Information Technology & Management, Gwalior, (M.P.), India

Keywords:

Location aware services, User location and tracking, Wireless LANs, Dimensional reduction techniques,

Locally Linear Embedding(LLE), Semi-supervised learning.

Abstract:

Due to vast applications of mobile devices and local area wireless networks, location based services are pop-

ularized and location information use has become important . The paper proposes a method based on Semi-

supervised Locally Linear Embedding for localization in indoor wireless networks. Previous methods for

location estimation in indoor wireless networks require a large amount of labeled data for learning the radio

map. However labeled instances are often difﬁcult, expensive, or time consuming to obtain, as they require

great efforts, meanwhile unlabeled data may be relatively easy to collect. So the use of semi-supervised learn-

ing is more feasible. In the experiment 101 access points (APs) have been deployed so the Received Signal

Strength (RSS) vector received by the mobile station has large dimensions (i.e.101). First we have used Lo-

cally Linear Embedding, a dimensional reduction technique to reduce the dimensions of data, and then we have

used semi-supervised learning algorithm to learn the radio map. The algorithm performs nonlinear mapping

between the received signal strengths from nearby access points and the user’s location. It is shown that the

proposed scheme is easy in training and implementation. Experimental results are presented to demonstrate

the feasibility of the proposed SSLLE algorithm.

1 INTRODUCTION

For mobile devices in Wireless Networks, Location

Estimation Systems have become very popular in re-

cent years. These systems provide a new layer of au-

tomation called automatic object location detection.

Real world applications depending on such automa-

tion are many. A variety of applications and services

such as enhanced-911, improved fraud detection, lo-

cation sensitive billing, intelligent transport systems

and improvedtrafﬁcmanagement can be examplesfor

cellular networks (Gezici, 2008). On the other hand,

applications such as inventory tracking, location de-

tection of products stored in a warehouse, location de-

tection of medical personnel or equipment in a hospi-

tal, intruder detection, and patient monitoring etc. are

the example of short range networks (Liu et al., 2007).

These applications depend heavily on the underlying

location estimation techniques.

In order to estimate the user location, a system

needs to measure a quantity that is a function of dis-

tance. Moreover, the system needs one or more refer-

ence points to measure the distance. In case of the

Global Positioning System (GPS)(Burrell and Kao,

2011; Enge and Misra, 1999) the reference points are

the satellites and the measured quantity is the time

of arrival of the satellite signal to the GPS receiver,

which is directly proportional to the distance between

the satellite and the GPS receiver. In case of Wireless

Local Area Network (WLAN) location determination

systems, the reference points are the access points and

the measured quantity is the signal strength, which

decays logarithmically with distance in free space.

Unfortunately, in indoor environments, the wireless

channel is very noisy and the radio frequency (RF)

signal can suffer from reﬂection, diffraction, and mul-

tipath effect, which makes the signal strength a com-

plicated function of distance. To overcome this prob-

lem, WLAN location determination systems tabulate

this function by sampling it at selected locations in

the area of interest. This tabulation has been known

in literature as the radio map (Bahl and Padmanab-

han, 2000; Bahl et al., 2000; Battiti et al., 2002; Ding

et al., 2008; Youssef and Agrawala, 2004; Youssef

and Agrawala, 2008) which captures the signature of

each access point at certain points in the area of in-

138

Jain V., Tapaswi S. and Shukla A..

SSLLE: SEMI-SUPERVISED LOCALLY LINEAR EMBEDDING BASED LOCALIZATION METHOD FOR INDOOR WIRELESS NETWORKS.

DOI: 10.5220/0003676801380146

In Proceedings of the International Conference on Neural Computation Theory and Applications (NCTA-2011), pages 138-146

ISBN: 978-989-8425-84-3

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

terest. Different WLAN location determination tech-

niques differs in the way, that how they construct the

radio map and what algorithm is used to compare a

received signal strength vector with the stored radio

map in the location determination phase.

Although the RSS data sets collected for location

estimation has high dimensionality and contains sev-

eral features, but it may be described as a function

of only a few underlying parameters. That is, the

data points actually belong to a low-dimensionalman-

ifold that is embedded in a high-dimensional space.

Our method uses the Locally Linear Embedding Al-

gorithm (Roweis and Saul, 2000) to get the low di-

mension manifold from high dimensional data.

The collection of training data with labels is an ar-

duous work. Traditional classiﬁers use only labeled

data (feature / label pairs) to train. Labeled instances

however are often difﬁcult, expensive, or time con-

suming to obtain, as they require the efforts of ex-

perienced human annotators. Meanwhile unlabeled

data may be relatively easy to collect, but there has

been few ways to use them. Semi-supervised learning

addresses this problem by using large amount of un-

labeled data, together with the labeled data, to build

better classiﬁers. Because semi-supervised learning

requires less human effort and gives higher accuracy,

it is of great interest both in theory and in practice.

In order to meet the requirement of higher ac-

curacy and lower calibration effort, we have pro-

posed a semi-supervised locally linear embedding

method for location estimation in indoor wireless net-

works. The key feature of the proposed method is

that advantages of locally linear embedding and semi-

supervised learning are integrated to improve the lo-

calization efﬁciency.

Experimental results are presented to demonstrate

the feasibility of the proposed scheme. The rest of the

paper is organized as following. In section 2 we re-

view some existing work for indoor location estima-

tion in wireless networks. In section 3, we describe

the Semi-Supervised Locally Linear Embedding Al-

gorithm for location estimation. Section 4 describes

the detailed method of localization. Experimental re-

sults are presented in section 5 and ﬁnally the paper is

concluded in section 6.

2 RELATED WORK

All previous techniques have been proposed for loca-

tion estimation in wireless networks can be divided

into three categories:

2.1 Triangulation

Triangulation is a geometric method based on the ge-

ometric properties of triangles to estimate the target

location. It is very sensitive to wireless signal propa-

gation. It has two derivations: lateration and angula-

tion.

Lateration determine the location of mobile de-

vice by measuring its distances from multiple refer-

ence points. Received Signal Strengths (RSS), time

of arrival (TOA) or time difference of arrival (TDOA)

are usually measured; to derive the distance by com-

puting the attenuation of the emitted signal strength or

by multiplying the radio signal velocity and the travel

time (Liu et al., 2007).

Angulation estimates the location of mobile de-

vice by computing angles relative to multiple refer-

ence points. In Angle of Arrival (AOA), the location

of the desired mobile device can be determined by the

intersection of several pairs of angle direction lines,

each formed by the circular radius from a base sta-

tion or a beacon station to the mobile target(Liu et al.,

2007).

2.2 Vicinity

It measures closeness to a known set of locations.

Vicinity algorithms providesymbolic relative location

information. It depends upon a dense grid of anten-

nas, each having a well-known position. When a mo-

bile device is in the range of a single antenna, it is

considered to be co-located with it. When mobile de-

vice is in the range of more than one antenna, it is

considered to be co-located with the one that receives

the strongest signal. This method is relatively simple

to implement. It can be implemented over different

types of physical media(Liu et al., 2007).

2.3 Radio Finger-printing

It examines a view from a particular vantage point.

RF-based ﬁnger-printing refers to the type of algo-

rithms that ﬁrst collect features (ﬁngerprints) of a

scene and then estimate the location of an object by

matching online measurements with the closest a pri-

ori location ﬁngerprints. RSS-based location ﬁnger-

printing is commonly used in Radio Finger-Printing

methods. (Chen, 2005; Krishnan et al., 2004; Youssef

and Agrawala, 2004; Youssef and Agrawala, 2008).

There are two stages for location ﬁngerprinting: of-

ﬂine stage and online stage (or run-time stage). Dur-

ing the ofﬂine stage, a site survey is performed in

an environment. The location coordinates/labels and

SSLLE: SEMI-SUPERVISED LOCALLY LINEAR EMBEDDING BASED LOCALIZATION METHOD FOR INDOOR

WIRELESS NETWORKS

139

Figure 1: Radio Fingerprinting based methods for Location

Estimation.

respective signal strengths from nearby Base Sta-

tions/Access Points are collected. During the online

stage, a location positioning technique uses the cur-

rently observed signal strengths and previously col-

lected information to ﬁgure out an estimated location.

The main challenge to the techniques based on loca-

tion ﬁngerprinting is that the received signal strength

could be affected by diffraction, reﬂection, and scat-

tering in the propagation indoor environments(Bahl

and Padmanabhan, 2000; Bahl et al., 2000; Battiti

et al., 2002).

Radio Finger Printing techniques, which are also

known as location ﬁngerprinting, can be categorized

into three broad categories: deterministic techniques,

probabilistic techniques, and machine learning based

techniques as shown in Figure 1. Deterministic tech-

niques, represent the signal strength of an access point

at a location by a scalar value, for example, the mean

value, and use non-probabilistic approaches to esti-

mate the user location. For example, in the Radar

(Bahl et al., 2000) system the authors use nearest

neighborhood techniques to infer the user location.

The accuracy of RADAR is about three meters with

ﬁfty percent probability. K. Pehlavan et al. also used

kNN (k-nearest neighbour) technique and achieved

2.8 meter distance error (Pahlavan et al., 2002). On

the other hand, probabilistic techniques, store infor-

mation about the signal strength distributions from the

access points in the radio map and use probabilistic

techniques to estimate the user location. For example,

the Horus (Youssef and Agrawala, 2004; Youssef and

Agrawala, 2008) system from the Universityof Mary-

land uses the stored radio map to ﬁnd the location

that has the maximum probability given the received

signal strength vector. Probabilistic approaches like

Bayesian networks based solutions achieve better per-

formance but they are computationally exhaustive and

difﬁcult to scale.

In a heterogeneous environment, e.g. inside a

building or in a variegated urban geometry, the re-

ceived signal strength is a very complex function of

the distance, the geometry, and the materials. The

complexity of the inverse problem (to derive the po-

sition from the signals) and the lack of complete in-

formation, motivate to consider ﬂexible models based

on machine learning approaches (i.e. artiﬁcial neural

networks, genetic algorithms, fuzzy systems) (Ahmad

et al., 2008; Battiti et al., 2002; Chen, 2005; Ding

et al., 2008; Gupta et al., 2009; Yang et al., 2010;

Youssef and Agrawala, 2008). Battiti et al. (Battiti

et al., 2002) have employed neural networks for this

problem. Battiti et al. used feed forward back prop-

agation network that takes RSS of 3 Wireless Access

Points (AP) to cover 624 square meter area, and re-

ported median estimation distance error of 1.75 me-

ter. This model assumes that the signals of all the ac-

cess points are available at every location all the time.

Practically, this approach has limited applicability be-

cause in real life scenario some AP may not be visi-

ble (not in range) at all the locations for all the time

(Ahmad et al., 2008). The beneﬁt of machine learn-

ing based methods are that they do not need ad-hoc

infrastructure in addition to the wireless LAN, while

the ﬂexible modeling and learning capabilities of ma-

chine learning approaches achieve lower errors in de-

termining the position, and are scalable to incremen-

tal improvements. A user needs only a map of the

working space and some identiﬁed locations to train a

system.

3 SSLLE: SEMI-SUPERVISED

LOCALLY LINEAR

EMBEDDING

The RSS dataset collected for location estimation has

high dimensionality and contains several features but

it may be described as a function of only a few under-

lying parameters. Therefore for computing efﬁciency,

dimensional reduction technique is used to ﬁnd out

the low dimensional manifold that is embedded in

a high dimensional space. We use Locally Linear

Embedding (LLE) (Roweis and Saul, 2000; Saul and

Roweis, 2003) algorithm which computes low dimen-

sional embedding of high dimensional data so that

neighborhoodinformation is preserved. LLE does not

estimate the pair-wise distances between widely sepa-

rated data points. Unlike Principle Component Anal-

ysis (PCA), Multi Dimensional Scaling (MDS), LLE

recovers nonlinear structure from locally linear ﬁts.

LLE attempts to discover nonlinear structure in high

dimensional data by exploiting the local symmetries

of linear reconstructions. Notably, LLE maps its in-

puts into a single global coordinate system of lower

dimensionality, and its optimizations, though capable

of generating highly nonlinear embeddings, do not in-

NCTA 2011 - International Conference on Neural Computation Theory and Applications

140

volve local minima. LLE maps high-dimensional in-

puts into a low dimensional ”description” space with

as many coordinates as observed modes of variability.

Suppose the data consist of N real-valued vectors

−→

each of dimensionality D, sampled from some un-

derlying manifold. LLE expects each data point and

its neighbors to lie on or close to a locally linear patch

of the manifold. Characterize the local geometry of

these patches by linear coefﬁcients that reconstruct

each data point from its neighbors. Reconstruction

errors are measured by the cost function

ε(W) =

∑

−→

−

∑

−→

(1)

which adds up the squared distances between all the

data points and their reconstructions. Minimize the

cost function subject to two constraints:

First, each data point

−→

is reconstructed only

from its neighbors, enforcing W

= 0 if

−→

does not

belong to the set of neighbors of

−→

, second that the

rows of the weight matrix sum to one:

∑

= 1.

Consider a particular data point

−→

x with k nearest

neighbors

−→

and reconstruction weights w

that sum

to one. The reconstruction |

−→

X −

∑

j=1

−→

is min-

imized:

−→

X −

∑

j=1

−→

= |

∑

j=1

(

−→

X −

−→

∑

we have introduced the ”local” Gram matrix G

(

−→

X −

−→

)(

−→

X −

−→

) .

By construction, this Gram matrix is symmetric

and semipositive deﬁnite. The reconstruction error

can be minimized analytically using a Lagrange mul-

tiplier to enforce the constraint that

∑

= 1. Then,

compute the reconstruction weights:

∑

−1

∑

−1

If the correlation matrix G is nearly singular, it

can be conditioned (before inversion) by adding a

small multiple of the identity matrix. This amounts

to penalizing large weights that exploit correlations

beyond some level of precision in the data sampling

process. The constrained weights that minimize these

reconstruction errors obey an important symmetry:

for any particular data point, they are invariant to ro-

tations, rescaling, and translations of that data point

and its neighbors. Suppose the data lie on or near a

smooth nonlinear manifold of lower dimensionality

d ≪ D . By design, the reconstruction weights W

re-

ﬂect intrinsic geometric properties of the data that are

invariant to exactly such transformations.

Each high-dimensional observation

−→

is mapped

to a low-dimensional vector

−→

representing global

internal coordinates on the manifold. This is done

by choosing d-dimensional coordinate

−→

to minimize

the embedding cost function

Φ(Y) =

∑

−→

−

∑

−→

(2)

This cost function, like the previous one, is based

on locally linear reconstruction errors, but here the

weights W

are ﬁxed, while optimizing the coordi-

nates

−→

. Subject to constraints that make the problem

well-posed, it can be minimized by solving a sparse

N × N eigen value problem, whose bottom d nonzero

eigenvectors provide an ordered set of orthogonal co-

ordinates centered on the origin.

The embedding vectors

−→

are found by mini-

mizing the cost function Φ(Y) =

∑

−→

−

∑

−→

over

−→

with ﬁxed weights W

. To avoid degener-

ate solutions, we constrain the embedding vectors to

have unit covariance, with outer products that satisfy

∑

−→

= I where I = d × d. Now the cost

deﬁnes a quadratic form Φ(Y) =

∑

(

−→

) in-

volving inner products of the embedding vectors and

the symmetric N × N matrix M

= δ

−W

∑

where δ is 1 if i = j and 0 otherwise.

The optimal embedding, up to a global rotation of

the embedding space, is found by computing the bot-

tom d+1 eigenvectors of this matrix. For such imple-

mentations of LLE, the algorithm has only one free

parameter: the number of neighbors, K.

The output received after performing the LLE is

low dimensional data set. Let the dataset consists

of N instances, where the ﬁrst l instances are the la-

beled data, and the rest of them are the unlabeled data.

The i-th data is given as (X

(i)

, L

(i)

) where X

(i)

∈ R

the vector of the Received Signal Strength (RSS) val-

ues from the WiFi Access Points (APs), and L

(i)

∈

{1, 2, 3, ......c} is the location label assigned to the

RSS vector. As for the unobserved RSS values, we

ﬁlled them by -100, since all RSS values are in the

range of [−100, 0] and unobserved RSS value implies

that it was too weak to detect. The objective of this

task is to predict the location labels of the unlabeled

data, L

(l+1)

...........L

since they are not given.

Let f

(i)

which the location label of the i-th instance is c. For

the labeled data i ≤ l, the following holds

(i)



1 if c = L

(i)

0 (otherwise)

(3)

The task is to predict f(i)(L

(i)

) for i > l and ∀c, with

which we obtain the prediction ˆc(i) for i > l by

ˆc(i) = argmax

(i)

SSLLE: SEMI-SUPERVISED LOCALLY LINEAR EMBEDDING BASED LOCALIZATION METHOD FOR INDOOR

WIRELESS NETWORKS

141

In the label propagation framework, we try to

minimize the discrepancies of the label distributions

among neighbourhood instances, which is deﬁned as,

∑

(i, j)

∑

( f

(c)

− f

(c)

)

here w

is a constant called the afﬁnity indicating the

similarity between the i

instance and j

instance,

which we will deﬁne later. It is easy to see that the

solution of the above optimization problem satisﬁes

(c)

∑

(ij)

(c)

∑

(ij)

(5)

for ∀i > l and ∀c. Therefore, instead of solving the

large optimization problem directly, we can iteratively

apply Eq. 5 to make local updates of predictions until

convergence.

Our deﬁnition of the afﬁnity tries to imply that

two instances are similar if their RSS vectors are simi-

lar. For the afﬁnity between two RSS vectors X

(i)

and

( j)

, we used a heat-kernel like function

(i, j)

= exp







−



(i)

− X

( j)









, (6)

where σ is a scale parameter. Also, k.k

is the

q-norm which is deﬁned as

kXk

∑

and we set q = 0.5 based on the observation that this

choice performed well in our preliminary analysis us-

ing the nearest neighbor classiﬁer for the labeled data

(Kashima et al., 2007; Yang et al., 2008).

4 THE DETAILED LOCATION

ESTIMATION METHOD

4.1 Signal Characteristics

In the experimental testbed, there are a total of 101

APs deployed. Some APs are deployed within the

same ﬂoor of testbed, others are deployed on other

ﬂoors or in neighboring buildings. Since, many

APs are detected occasionally therefore mobile device

didn’t receive RSS from all the APs on every location

at a particular moment. Figure 2 shows the proba-

bility distribution of signal strength received from an

AP at a particular ﬁxed location. It illustrates that the

signal strength of AP’s varies with time and the prob-

ability distribution of RSS from AP is Gaussian. Fig-

ure 3 shows the number of locations covered by each

AP and Figure 4 shows the number of AP’s detected

at each location space.

4.2 The Detailed Location Estimation

Algorithm

The proposed location algorithm which is based on

semi-supervised locally linear embedding learning al-

gorithm has two phases: an ofﬂine radio map training

phase , and an online location estimation phase.

Figure 2: Probability distribution of RSS from a AP at ﬁxed

location with time.

Figure 3: Number of Locations covered by each AP.

Figure 4: Number of AP’s detected at each location.

(1) Ofﬂine Radio Map Training Phase. At ﬁrst in

the ofﬂine radio map training phase the labeled (rss

signal and location id pair) and unlabeled rss sig-

nal data by mobile device at various locations is col-

lected. Since all the access points are not visible

at every location, so for unobserved rss values we

ﬁlled them with -100. Let the whole dataset con-

sists of N instances, where the ﬁrst l instances are

NCTA 2011 - International Conference on Neural Computation Theory and Applications

142

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

Real X Coordinates

of Test Data

Real Y Coordinates

of Test Data

(a) Real Locations of Test Data

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

SSLLE Estimated X Coordinates

of Test Data

SSLLE Estimated Y Coordinates

of Test Data

(b) SSLLE Estimated Locations of Test Data

Figure 5: Comparison of Real and SSLLE Estimated Locations.

the labeled data, and the rest of them are the unla-

beled data. The i

data is given as (X

(i)

, L

(i)

) where

(i)

∈ R

is the vector of the received signal strength

(RSS) values from the WiFi Access Points (APs), and

(i)

∈ {1, 2, 3, .....c} is the location label assigned to

the RSS vector. As there are 101 access points de-

ployed in the testbed , the data set has very high di-

mension, so then we use locally linear embedding al-

gorithm to reduce the dimensionality of data, and ﬁ-

nally semi-supervised multiclass label propagation al-

gorithm is applied for training the radio map.

The detailed steps for ofﬂine radio map training

phase are as follows:

Step 1: Compute the K nearest neighbors of each

high dimensional data point,

−→

Step 2: Compute the weightsW

that best reconstruct

each data point

−→

from its neighbors, mini-

mizing the cost in Eq. 1 by constrained linear

ﬁts.

Step 3: Compute the low dimensional embedding

vectors

−→

best reconstructed by the weights

, minimizing the quadratic form in Eq. 2

by its bottom nonzero eigenvectors.

Step 4: Initialize f

(i)

by using Eq. 3 for the labeled

instances i ≤ l .

Step 5: Compute the afﬁnities w

(i, j)

between all pairs

of instances by using Eq. 6.

Step 6: Continue the following steps, 6(a) and 6(b),

until convergence.

(a) Select i > l uniformly at random.

(b) Update f

(i)

Step 7: Location label prediction for i > l (i.e. unla-

beled data) by using Eq. 4.

(2) Online Location Estimation Phase. In the sec-

ond phase the captured signal vector by the target mo-

bile device from various access points is used to esti-

mate the location of target mobile device. For this

purpose the mapping function which is estimated in

ofﬂine training phase is used.

The detailed steps are as follows:

Step 1: The mobile device captured the signal

strength from various detected access points

at its location, and then form the rss vector

−→

by ﬁlling -100 for unobserved AP

Step 2: Use the semi-supervised locally linear em-

bedding algorithm to estimate the location as

described in the ofﬂine radio map training

phase.

5 EXPERIMENTAL RESULTS

We have used the ICDM DMC’07 dataset for the

experiment and to evaluate our proposed algorithm

(Qiang Yang, 2007). IEEE ICDM Data Mining Con-

test (IEEE ICDM DMC’07) published the realistic

public benchmark data for indoor location estimation

from radio signal strength received by a client de-

vice from various WiFi AP

. They collected the data

sets in an academic building in the Hongkong Uni-

versity of Science and Technology, consisting of an

area of 145.5m 37.5m. Locations were divided into

247 grids, each of which has a size of about 1.5m

1.5m. There were 101 wireless access points (AP

)

deployed in the building. A person holding a wire-

less client device walks around a building ﬂoor. The

client device (which can be a Personal Digital As-

sistant (PDA) or Laptop) is equipped with a wire-

less card that can receive signals from wireless ac-

cess points (AP

) which are visible out of 101 sur-

rounding wireless access points (AP

). Each of these

is identiﬁable with a unique ID. Since, collect-

ing the (RSS values, Location Label) pairs as training

data in a large building are very costly, because hu-

mans need to take a mobile device and walk through

the building to collect the RSS values and mark down

the ground locations. Therefore some data are given

without labels; that is for those data only the RSS val-

ues are given. In addition, a collection of partially

labeled user traces are given, which corresponds to a

sequence of RSS values collected as a user continu-

ously walks around a building. In the experiment we

SSLLE: SEMI-SUPERVISED LOCALLY LINEAR EMBEDDING BASED LOCALIZATION METHOD FOR INDOOR

WIRELESS NETWORKS

143

Table 1: Performance of Different Methods.

Methods Min Error Max Error Mean Error Standard Deviation

Distance Distance Distance Error Distance

(in meters) (in meters) (in meters) (in meters)

SSLLE 0 21.6 3.7033 3.4567

RADAR 0 36.837 6.1374 6.442

Semi-supervised 0 138.2 19.348 27.859

Method used in

(Kashima et al., 2007)

use total 5333 samples (labeled and unlabeled both)

for training the mapping function, and use 2137 sam-

ples of test data to test the performance of method.

Based on the collection of signal strength values (RSS

values), a semi-supervised locally linear embedding

algorithm running on the client device tries to ﬁgure

out the current location of the user. The compari-

son between SSLLE estimated locations and real lo-

cations are shown in Figure 5, and some of the results

obtained from SSLLE out of 2137 test results are re-

ported in Table 2.

As shown in the Table 1. the proposed algorithm

performs well. The mean error is 3.7033m, and the

standard deviation of error is 3.4567m. We also per-

formed experiment to compare the results with the

method used in (Kashima et al., 2007) and with the

RADAR (Ahmad et al., 2008). The detailed exper-

imental results are summarized in Table 1. As can

be seen, the proposed algorithm has a better perfor-

mance than the others. The proposed algorithm has

the smallest mean, standard deviation, minimum and

maximum error distances.

6 CONCLUSIONS

In this paper, we describe a semi-supervised locally

linear embedding algorithm to estimate the location

of mobile device in indoor wireless networks. In this

method locally linear embedding is used to reduce the

dimensionality of data. In ofﬂine radiomap training

phase a mapping function is learned between the sig-

nal space and physical space using labeled and unla-

beled data. And then in location determination phase,

we use this function to estimate the location of mo-

bile device. SSLLE uses only a small amount of la-

beled data and a large amount of unlabeled data. So

it greatly reduce the calibration effort since, collect-

ing the (RSS values, Location Label) pairs as training

data in a large building are very costly and difﬁcult.

The experimental results shows that SSLLE outper-

forms in terms of mean, standard deviation , mini-

mum, and maximum of error distances in comparison

to benchmark methods RADAR (Ahmad et al., 2008),

and semi-supervised method used in (Kashima et al.,

2007).

ACKNOWLEDGEMENTS

This work was supported by Atal Bihari Vajpayee In-

dian Institute of Information Technology & Manage-

ment , Gwalior (M.P.)- India.

REFERENCES

Ahmad, U., Gavrilov, A., Lee, Y., and Lee, S. (2008).

Context-aware, self-scaling Fuzzy ArtMap for re-

ceived signal strength based location systems. Soft

Computing-A Fusion of Foundations, Methodologies

and Applications, 12(7):699–713.

Bahl, P. and Padmanabhan, V. (2000). RADAR: An in-

building RF-based user location and tracking system.

In Proceedings of 19th IEEE Annual Joint Conference

of Computer and Communications Societies, INFO-

COM 2000., volume 2, pages 775–784.

Bahl, P., Padmanabhan, V., and Balachandran, A. (2000).

Enhancements to the RADAR user location and track-

ing system. Microsoft Research, (MSR-TR-2000-

12):13.

Battiti, R., Nhat, T., and Villani, A. (2002). Location-aware

computing: a neural network model for determining

location in wireless LANs. Technical Report DIT-02-

083, Ingegneria e Scienza dell’Informazione, Univer-

sity of Trento.

Burrell, G. and Kao, D. M. (2011). About GPS.

Retrieved from: http://www.garmin.com/aboutGPS/,

Access date: 20.04.2011.

Chen, C. (2005). Hybrid location estimation and tracking

system for mobile devices. In Proceedings of 61st

IEEE Vehicular Technology Conference, VTC 2005.,

volume 4, pages 2648–2652.

Ding, X., Li, H., Li, F., and Wu, J. (2008). A novel in-

frastructure WLAN locating method based on neural

network. In Proceedings of 4th Asian Conference on

Internet Engineering, pages 47–55.

Enge, P. and Misra, P. (1999). Scanning the Special Is-

sue/Technology on the Global Positioning System.

In Proceedings of IEEE, Special Issue on GPS, vol-

ume 87, pages 3–15.

NCTA 2011 - International Conference on Neural Computation Theory and Applications

144

Table 2: Comparison of Real and SSLLE estimated coordinates, and the error distances for some of the data instances used

for testing the SSLLE Method.

Data Real Real SSLLE SSLLE Error

Instance X Coordinates Y Coordiantes Estimated Estimated Distance

No. X Coordinates Y Coordiantes (in Meters)

1 139.5 31.5 138.3 31.5 1.2

2 139.5 31.5 138.3 31.5 1.2

3 139.5 31.5 138.3 31.5 1.2

4 88.5 36 86.1 36 2.4

5 88.5 36 88.2 36 0.3

6 88.5 36 88.2 36 0.3

7 88.5 36 88.2 36 0.3

8 91.5 36 92.1 36 0.6

9 91.5 36 90 36 1.5

10 91.5 36 90 36 1.5

11 94.5 36 92.4 36 2.1

12 96 36 93.6 36 2.4

13 36 36 34.8 36 1.2

14 36 36 34.8 36 1.2

15 36 36 34.8 36 1.2

16 37.5 36 35.1 36 2.4

17 37.5 36 35.1 36 2.4

18 37.5 36 35.1 36 2.4

19 37.5 36 37.2 36 0.3

20 37.5 36 37.2 36 0.3

21 37.5 36 37.2 36 0.3

22 37.5 36 37.2 36 0.3

23 37.5 36 38.1 36 0.6

24 37.5 36 38.1 36 0.6

25 37.5 36 38.1 36 0.6

26 39 36 38.7 36 0.3

27 39 36 38.7 36 0.3

28 39 36 38.7 36 0.3

29 39 36 38.7 36 0.3

30 39 36 39.6 36 0.6

31 40.5 36 39.6 36 0.9

32 40.5 36 39 36 1.5

33 40.5 36 39 36 1.5

34 40.5 36 39.3 36 1.2

35 40.5 36 39.3 36 1.2

36 40.5 36 39.3 36 1.2

37 42 36 39.6 36 2.4

38 42 36 39.6 36 2.4

39 42 36 39.6 36 2.4

40 42 36 40.8 36 1.2

41 42 36 40.8 36 1.2

42 42 36 40.8 36 1.2

43 42 36 42 36 0

44 42 36 42 36 0

45 42 36 42 36 0

46 43.5 36 42 36 1.5

47 43.5 36 42 36 1.5

48 43.5 36 42 36 1.5

49 43.5 36 42.9 36 0.6

50 43.5 36 42.9 36 0.6

SSLLE: SEMI-SUPERVISED LOCALLY LINEAR EMBEDDING BASED LOCALIZATION METHOD FOR INDOOR

WIRELESS NETWORKS

145

Gezici, S. (2008). A survey on wireless position estimation.

Wireless Personal Communications, 44(3):263–282.

Gupta, A., Tapaswi, S., and Jain, V. (2009). Recurrent

Grid Based Voting Approach for Location Estimation

in Wireless Sensor Networks. In Proceedings of Sym-

posia and Workshops on Ubiquitous, Autonomic and

Trusted Computing, UIC-ATC’09., pages 263–267.

Kashima, H., Suzuki, S., Hido, S., Tsuboi, Y., Takahashi,

T., Ide, T., Takahashi, R., and Tajima, A. (2007).

A Semi-supervised Approach to Indoor Location

Estimation. Retrieved from: www.geocities.co.jp/

Technopolis/5893/publication/ICDMDMC2007-1.pdf,

Access Date: 20.04.2011.

Krishnan, P., Krishnakumar, A., Ju, W.-H., Mallows, C.,

and Gamt, S. (2004). A system for lease: location

estimation assisted by stationary emitters for indoor

rf wireless networks. In Proceedings of 23rd IEEE

Annual Joint Conference of Computer and Communi-

cations Societies, INFOCOM 2004., volume 2, pages

1001 – 1011.

Liu, H., Darabi, H., Banerjee, P., and Liu, J. (2007). Sur-

vey of wireless indoor positioning techniques and

systems. IEEE Transactions on Systems, Man,

and Cybernetics, Part C: Applications and Reviews.,

37(6):1067–1080.

Pahlavan, K., Li, X., and Makela, J. (2002). Indoor geolo-

cation science and technology. IEEE Communications

Magazine, 40(2):112 –118.

Qiang Yang, Sinno Jialin Pan, V. W. Z. (2007). IEEE ICDM

Data Mining Contest 2007. Retrieved from: http://

www.cse.ust.hk/ qyang/ICDMDMC07/, Access date:

20.04.2011.

Roweis, S. T. and Saul, L. K. (2000). Nonlinear dimension-

ality reduction by locally linear embedding. Science,

290(5500):2323–2326.

Saul, L. and Roweis, S. (2003). Think globally, ﬁt locally:

unsupervised learning of low dimensional manifolds.

The Journal of Machine Learning Research, 4:119–

155.

Yang, B., Xu, J., Yang, J., and Li, M. (2010). Localiza-

tion algorithm in wireless sensor networks based on

semi-supervised manifold learning and its application.

Cluster Computing, 13(4):435–446.

Yang, Q., Pan, S., and Zheng, V. (2008). Estimatinglocation

using wi-ﬁ. IEEE Intelligent Systems, 23(1):8–13.

Youssef, M. and Agrawala, A. (2004). Handling samples

correlation in the horus system. In Proceedings of

23rd IEEE Annual Joint Conference of Computer and

Communications Societies, INFOCOM 2004., pages

1023–1031.

Youssef, M. and Agrawala, A. (2008). The Horus location

determination system. Wireless Networks, 14(3):357–

374.

NCTA 2011 - International Conference on Neural Computation Theory and Applications

146