Cell Classification in Mobile Networks with Reservoir Computing

Peng Yu, Guo Jia, Peng Xi-yuan Automatic Test and Control Institute

Harbin Institute of Technology Harbin, China

guojia.gm@gmail.com

Abstract—Cell classification in traffic analysis and modeling is an important task which is required by planning and optimization of mobile networks. Because traffic is always nonlinear, nonstatio-nary and influenced by immeasureable factors, accurate analyti-cal traffic model can be hardly obtained. Therefore a new classi-fication method using reservoir computing to cell types is pro-posed. Analysis of field traffic data collected by China Mobile Communications Corporation (CMCC) Heilongjiang Co.Ltd is achieved. Experiments results show that new method adopting reservoir computing is feasible and effective for cell classification by traffic for mobile networks.

Keywords- mobile network management; cell classification; reservoir computing

I. INTRODUCTION Traffic analysis and modeling play increasingly important

roles for network planning and optimization of mobile net-works [1]. As a support for traffic analysis and modeling, cell classification divides cells in mobile networks into several cat-egories. For instance, cell classification contributes to the im-provement of traffic forecasting performance [2].

Researches on traffic modeling for mobile networks have been proposed recently [1][3][4][5]. Authors analyze traffic characterization which can be used to model the traffic in cellu-lar networks in [1]. In [3], a traffic modeling method by means of ring and toroidal cell layouts is proposed and applied to traf-fic analysis of cells operated in rural, suburban and urban envi-ronments. An analytical model for channelized cellular mobile circuit-switched systems that support general arbitrary distri-buted handoff traffic is proposed in [4]. Based on mobility pre-diction, authors in [5] propose a traffic forecasting method by estimating the number of users that have active sessions at each location.

However, traffic is always nonlinear, nonstationary and in-fluenced by immeasureable factors. Accurate analytical traffic model can be hardly obtained as a complex temporal task. Therefore this paper presents a cell classification method by traffic data using reservoir computing as a support for traffic analysis and modeling. Reservoir computing which provides an architecture and learning principle for Recurrent neural net-works (RNNs) has been shown to be powerful to solve com-plex temporal machine learning tasks [6]. RNNs have been used in applications such as system identification or control.

However, due to the high computational training costs and slow convergence, training RNNs is hard in practice. Reservoir computing offers a framework for using temporal processing ability of RNNs without the hassle of training them [6]. By mapping the input to a higher dimension by the dynamics of a random, fixed dynamical system called reservoir and only training a simple output mechanism, reservoir computing has achieved state-of-the-art performance in practical temporal problems, such as time series prediction [7] and classification [8]. Echo State Networks (ESNs) [9] and Liquid State Ma-chines (LSMs) are two major types of reservoir computing. In this paper we will refer to ESNs as reservoir computing.

Based on analysis of field data collected by NMS (Network Management Systems) of CMCC Heilongjiang Co.Ltd, this paper proposes to use reservoir computing for cell classifica-tion by traffic data as input and generate reliable cell classifica-tion results for network planning and optimization.

The remainder of the paper is structured as follows. Section II presents analysis of traffic data and introduces reservoir computing. In Section III, we describe the cell classification method with reservoir computing. The experiment results and discussion are presented in Section IV. We conclude in Section V.

II. PREREQUISITES

A. Traffic data analysis The raw data are collected by cells hourly including record

time, cell name, TCH traffic, etc. NMS generates a daily file with about 500,000 records. Traffic data is calculated by the unit Erlang. Traffic characteristics of cells can be obtained from traffic data. Traffic intensity always changes by day and week. Cells usually have higher traffic during daytime than nighttimes in a day. When it comes to a week, the changes are more complicated. Some cells have higher traffic during week-days than weekends or vice versa and some cells have no sig-nificant changes in weekdays and weekends. Moreover, several special factors (e.g., festivals, emergency) always cause traffic unusual changes.

Figure 1 shows an example of traffic intensity changes dur-ing Dec.3, 2008 (Thursday) to Dec.9, 2008 (Tuesday) with 24 measurements per one day. This cell has higher traffic during

This work is supported in part by a Grant (No. [2008]1891) from CMCC Heilongjiang Co. Ltd. and a Grant (No.20092302110013) from Ph.D. Programs Foundation of Ministry of Education of China.

978-1-4244-2833-5/10/$25.00 ©2010 IEEE

weekdays than weekends, and has higher traffic during daytime than nighttimes.

Figure 1. Mobile communication raffic data.

Due to the particular characteristics of mobile communica-tion, different characteristics of the covering region, the mo-bility of customers and other factors have led to the existence of different characteristics of traffic data. From the perspective of traffic forecasting, in order to ensure the forecasting accu-racy, appropriate forecasting model should be adopted accord-ing to the characteristics of traffic data. Manual classification and selection is difficult due to the large amount of data. Therefore, it is necessary to study the classification methods of cell by traffic data in order to provide supports for traffic forecasting.

B. Echo state networks Figure 2 shows a typical structure of ESNs which consist

of input units, dynamical reservoir (DR) and output units. ESNs with K input units, N dynamical reservoir processing elements and L output units can be described as:

in backx( +1) = f(W u( +1)+Wx( )+W y( ))n n n n (1)

out outy( +1) = f (W (u( +1),x( +1),y( )))n n n n (2)

In (1) and (2), x(n) = (x1(n) ,…, xN(n)), y(n) = (y1(n) ,…, yL(n)), u(n) = (u1(n) ,…, uK(n)) are activations of the DR proc-essing elements, output units and input units at time step n, respectively. The functions f = (f1 ,…, fN) are activation func-tions for DR processing elements (implemented as tanh func-tions in this paper). The functions out out out

1f = ( ,..., )Lf f are the output units’ output functions (implemented as identity func-tions in this paper). By an N×K input weight ma-trix in inW = ( )ijw , the input is tied to DR processing element. The DR processing elements are connected by an N×N matrix W = (wij). back backW = ( )ijw is an N×L matrix for the connec-tions that project back from the output to DR. And DR is tied to the output units by an L×(K+N+L) matrix out outW = ( )ijw . The term (u(n + 1), x(n + 1), y(n)) is the concatenation of the input, internal, and previous output activation vectors.

ESNs learning process can be briefly described as training suitable output weights to obtain the desired output from DR which is random, large and fixed in advance. DR has a large

number of neurons which are randomly and sparsely con-nected. Determination of optimal output weight matrix Wout is a linear regression task of mean-square error (MSE) minimiza-tion [9].

Figure 2. Scheme diagram of a typical structure of ESNs.

III. CELL CLASSIFICATION WITH ESNS

A. Feature Extraction Due to the high dimensional characteristic of traffic data

whose length is 168, feature extraction was adopted. 6 kinds of statistical values were calculated including maximum value, minimum value, mean value, median value, most frequent val-ue and standard deviation. The statistical features were adopted due to their simplicity. Moreover, feature selection could be beneficial to improve the results of the classification method which will be addressed by future work.

B. Experiment Design The ESNs classifier was input with the 6-dimension fea-

tures and trained to map the reservoir signals to a 1-of-4 style output. Each cell type was represented by an output channel which was +1 when trained with a feature of that type and -1 otherwise.

In this paper, the activation functions for DR processing elements were implemented as tanh functions and the output units’ output functions fout were implemented as identity func-tions. The connections denoted as dashed line in Figure 2 were not adopted. Therefore ESNs could be described as:

inx( +1) = tanh(W u( +1)+Wx( ))n n n (3)

outy( +1) = W x( +1)n n (4)

To evaluate the performance of the ESNs classifier for cell classification by traffic, we performed 2-fold cross validation classification experiments. We trained ESNs classifier and evaluated performance over a range of values of three model parameters as follows: (1) number of DR processing elements N, (2) ESNs reservoir spectral radius SR, (3) ESNs input scal-ing parameter IS.

The training of ESNs in this paper can be stated as:

• Obtain the statistical features of the traffic data as training samples.

• Set the parameters of ESNs including N, SR, IS.

• Initialize connection matrices Win and W using random weights.

• Collect x(n) by feeding training samples into (3).

• Calculate Wout with pseudo-inverse method by (4).

IV. RESULTS AND DISCUSSIONS Base on the data collected hourly during Dec.3, 2008 to

Dec.9, 2008 by NMS of CMCC Heilongjiang Co.Ltd, we did cell type classification experiments for 603 cells from four dif-ferent types.

The experiments explored the effects of number of DR processing elements N, ESNs reservoir spectral radius SR, and ESNs input scaling parameter IS. The ESNs classifiers were trained over combinations of the three model parameters within the following ranges : N∈[10, 200], SR∈[0.1, 0.99], and IS∈[0.01, 1]. And all the ranges were divided into 20 segments equally. The connectivity of the neurons in DR was set to 10/N.

In Figures 3 through 5, the average error rates of 10 repeti-tions of a 2-fold cross validation versus different parameters are showed. For each point plotted in the figure, the value is obtained by averaging the error rates over all the possible val-ues of the remaining parameters.

0 50 100 150 2000.3

0.32

0.34

0.36

0.38

0.4

0.42

0.44

N

Aver

age

erro

r rat

e

Figure 3. Average error rate vs. N.

Figure 3 shows that the number of DR processing elements N has great effect on the average error rate of the cell classifi-cation by traffic. The average error rate increases obviously outside the range of [40,100]. The lowest average error rate is obtained with N = 80.

The effect that ESNs reservoir spectral radius SR has on the average error rate is showed in Figure 4. The changes of SR only make minor changes on the classification perform-ance.

Figure 5 shows that input scaling parameter IS in ESNs in-fluences the classification performance greatly. The average

error rate is significantly lower when IS<0.2. The lowest aver-age error rate is obtained with IS=0.062.

0 0.2 0.4 0.6 0.8 10.35

0.355

0.36

0.365

SR

Aver

age

erro

r rat

e

Figure 4. Average error rate vs. SR.

0 0.2 0.4 0.6 0.8 10.1

0.2

0.3

0.4

0.5

IS

Aver

age

erro

r rat

e

Figure 5. Average error rate vs. IS.

The results in Figures 3 through 5 indicate that ESNs pa-rameter setting is of great importance to influence on error rate of the cell classification by traffic. In this paper, the best result of classification error rate with ESNs is 0.041.

To validate the performance of ESNs in cell classification by traffic, we also obtained results by experiments with two other traditional neural networks as classification methods: MLPs with BP training (BPNN) and RBF network (RBFNN). For BPNN, the number of hidden neurons is set to the range of [5, 55]. For RBFNN, the spread of radial basis functions is set to the range of [1, 40].

The best results of BPNN and RBFNN in our experiments are 0.116 and 0.192, respectively. The method adopting ESNs outperforms BPNN and RBFNN in error rate for cell classifi-cation by traffic. To compare with BPNN and RBFNN, the classification error rate decreases by 64.7% and 78.6%, re-spectively.

V. CONCLUSION This paper presented a method for cell classification by

traffic in mobile networks. We applied reservoir computing to field data collected by NMS of CMCC Heilongjiang Co.Ltd and achieved classification error rate 0.041. The method pro-posed in this paper is feasible and effective for cell classifica-tion by traffic for mobile networks. Furthermore, the method could be served as a support for network planning and optimi-zation.

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