A Clustering Method For Electromagnetic Interference Signals Based On Particle Swarm Optimization

This paper proposes a method which clusters EMI signals based on particle swarm optimization. And the advantages of this method compared to other clustering algorithms are present in this paper. From the clustering experiments on 158 sets of data and comparison with other classical algorithms, the clustering algorithm proposed has certain accuracy and feasibility.


Introduction
With the rapidly increase of electronic devices such as mobile phones, the electromagnetic interference (EMI) has become more and more urgent, considering its huge interference to normal electronic communication and signal analysis.It is therefore for of great significance to analyze unknown EMI source signals.
The current state-of-the-art technologies to address this problem include the fast independent component analysis (Fast ICA) [1][2], wavelet transform [2][3], the fast Fourier transform (FFT) [4][5].An indispensable procedure of these techniques is the clustering step.
Existing clustering method are K-means [12], fuzzy clustering [13], wavelet analysis [3,14], Fourier analysis [5].K-means is an intuitive method, and easy to implemented, so that it is one of the most widely used clustering approach.However, it also has obvious defects, that it can only handle numeric attributes and is sensitive to initialization.It also require the number of cluster centroids beforehand, and could only obtain a local optimal clustering results [6].Similar to K-means, Fuzzy c-means could not overcome the local minimum, and the sensitivity to initialization.Moreover, it is hard to select an appropriate weighting parameter M, which has a significant influence on the clustering performance.Wavelet analysis and Fourier analysis are limited to dimension reduction clustering processing of signal in the time domain.
Due to the high dimension that EMI signals have and its non-linear characteristic [15][16][17], it's necessary to reduce the dimension of the data in a proper way.In addition, to avoid problems like local minimum discussed above, we decided to use PSO based clustering algorithm which can handle this task well.Therefore, this paper proposes a new algorithm procedure for extracting electromagnetic interference characteristics to reduce the dimension of the data, and uses PSO based clustering algorithm to cluster the low dimensional data.Through the experiments, this algorithm has a good performance on accuracy and efficiency in signal processing and clustering.
The rest of this paper is organized as follows: in the second section, we a feature extraction method for electromagnetic inference signals.Subsequently, we propose the clustering algorithm based on PSO.Section 4 shows comparison experimental results.Finally, we draw a conclusion in the last section.

A low dimensional representation of EMI signals
In this section, we propose a powerful representation of EMI signals with low dimensionality.
EMI signals usually contain thousands of discrete point whether in time domain or frequency domain.Original EMI signal data usually has high dimensions that is from hundreds to thousands.EMI signals we handled in this paper have more than 6000 dimensions.In addition, EMI signal data value changes dramatically.The intensity of EMI signal data is also a significant feature we interested in.
High dimensional data will make cluster algorithm hard to converge and result in deadly problems like dimension crisis.On the other hand, high dimensional data will cost algorithm much more calculation and spend more time.
Because EMI signals have their special characteristics, we need special features to describe them.In this paper, we present a new method to reduce data dimension.EMI signal data are extracted into five aspects of feature: exception, variance, bandwidth, number of thorns and the number of peaks and troughs.Exception value is a macroscopic feature describing the data value on average.And variance describes degree of dispersion on data value.We use bandwidth to show the volatile of the signal.Signal has larger bandwidth may contain more energy.The number of thorns reflects the instability of the signal and represent the number of the extreme values.Values in extreme prominent will be recognized as thorns.The number of peaks and troughs shows the overall trend of the signal.This describe the shape of the signal which contains trend information.By doing feature extraction, all information we interested is extracted.And through these features we can discriminate different EMI signals in appropriate time.

EMI signal cluster
In this section, we will introduce the PSO clustering algorithm, and describe our proposed method.

PSO cluster algorithm
In 2002, Omran et al. [10] proposed a swarm optimization based unsupervised image classification algorithm.This is the earliest PSO based clustering algorithm in literature.Most of the PSO clustering algorithms follow the basic framework of this algorithm, where the number of clustering centroids is user defined.Each particle in the swarm contains a vector representing a candidate of cluster centres.The whole particle swarm contains variety of partition of data set.Firstly, a set of random cluster centre is assigned to each particle.For each particle, data are clustered according to the nearest candidate centre.Subsequently, the algorithm utilizes the PSO algorithm to find the optimal particle, of which the positon is an approximate optimal partition on a data set.
Based on Omran's work, Merwe et al. proposed basic PSO clustering algorithm for the clustering to general data set [7].Fitness function of this PSO clustering algorithm is ‫ܬ‬ .
ܰ --dimension of the data; ܰ --number of cluster; ‫ݖ‬ --data vectors; ݊ --number of samples in set ‫ܥ‬ ; ݉ --mean(centre) of set ‫ܥ‬ ; The outline of the basic PSO clustering algorithm is as follows [7]: Algorithm 1 PSO Clustering Algorithm Input: normalized data vectors ‫ݖ‬ Output: the optimal particle ‫ݖ‬ that contains best cluster centre 1: Randomly chosen cluster centre and assigned to each particle, randomly generated particle velocity.2: Divide each particle on minimum distance principle, and calculate each particle's fitness value by (1) and update individual extreme value.3: According to each particle's extreme value, find the global extreme value and its position.
4: Based on the PSO velocity formula, update each particle's velocity, and limit it in VMAX.5: Based on the PSO position formula, update each particle's position.6: Jump to step 2 until satisfy some condition 7: Output the position of the optimum particle ‫ݖ‬ , which contains the optimal ܰ cluster centre.
The basic PSO clustering algorithm provides an effective way to solve the problems of many traditional clustering algorithms.Traditional hierarchical methods need to search and estimate large amount of objects or clusters.This results in bad scalability.In addition, these methods may be hard to deal with overlapping clusters.On the other hand, partition methods like K-means can only divide spherical clusters.And it's easy to get in local optimum.However, PSO clustering algorithm can solve these problems.

The proposed algorithm
Here, we will present out method.Firstly, we extract a low dimensional feature from source EMI signals, and standardize the extracted features as follows: where ‫ݔ‬ is the j-th component of the i-th vector, ൫‫ݔ‬ ൯ , ሺ‫ݔ‬ ሻ are the maximum and minimum values for the j-th component of all vectors, respectively.
After extraction, all the EMI signal data is presented as vectors as follows: Where i is the serial number of the data; n is the dimension of data after feature extraction; For each particle ‫‬ , it is an ݊ ൈ ܰ matrices, representing the positions of N_c clustering centres, where At the beginning, the positions and velocities of particles are randomly initialized.As described in subsection 3.1, we then divide every particle with the minimum distance principle, calculate the fitness and update the individual optimal value as follows Whereܰ is the dimension of data; ܰ is the number of clusters; ‫ݖ‬ is the data vector; ݊ denotes the number of samples in ‫ܥ‬ ; ݉ stands for centres of samples in ‫ܥ‬ .
Based on the individual optimal position, we search for a global optimal particle together with its position.According to the velocity formula [11] as below, we update the velocity of particles with a limited maximum value ‫ݒ‬ ௫ .
Where ‫ݒ‬ ௗ ሺ‫ݐ‬ሻ is the velocity of the particle i in the t-th iteration; ‫ݔ‬ ௗ ሺ‫ݐ‬ሻ is the position of the particle i in the t tth iteration; Ȧ is the inertia weight; and non-negative c1 and c2 are learning factors; r1 and r2 are independent random functions obeying uniform distribution in the range of [0, 1].
The termination condition can be set as a maximum iteration number, or the residual error.
At last, the optimal position of each particle is output as a cluster centre.
The overall outline of the proposed algorithm is shown in Figure 1.

Data format and other clustering algorithm
The original electromagnetic signal data used in this paper is the frequency domain information in two dimension--frequency (in ascending order) and voltage.We have totally 158 groups of categorized data and each group contains 2431 to 3069 two-dimensional vectors.
For other different mixed electromagnetic signals, such as time domain signals or mixed signals, they can also be used as the input to our method.When the signals are mixed, this method can cluster closely related signal together, which will be helpful for further separation and analysis.
For some commonly used clustering algorithm, PSO algorithm has obvious advantages.Compare to methods based on neural networks, PSO clustering algorithm has a more simple structure, which means it is easy to converge.In addition, PSO clustering algorithm is not sensitive on initialization, and it has a better scalability.

Parameter settings
In all our experiments, the number of particles N is set as 85. c1 and c2 are set to 1.2, while the inertia weight range WMAX is chosen as 0.9, and WMIN is set to 0.4. the maximum iteration M is 200.Finally, we set the number of clusters K as 7.

Groups of samples clustering
Here, we first demonstrate the low dimensional feature extracted by using the method described in section 2, as shown in Table 1.We then normalize the feature, and conduct clustering by suing PSO clustering algorithm.The result is shown in Table 2.

Start
Extract signal feature and standardize them Assign position and velocity for each particle randomly Based on the individual optimal position, find the global optimal particle and its position.
According to the velocity formula, update the velocity of particles and limit them within VMAX  The final output clustering centres can be seen in Table 3.According to the comparison with original data images (see Figure 2), we can draw the conclusion that the algorithm has good effect on clustering.
Acquiring the clustering centre, we can compare each feature's difference between two classifications based on their clustering centre.For example, the first class and the second class are similar in bandwidth and the number of thorns, but are different in exception and variance.Furthermore, we can also calculate the difference accurately.
For the same data, this paper also carried on comparison experimental by using the SOM.The results are as follows: The final clustering result is as shown in Table 4: 3,4,9,10,12 As can be seen from the result, by using SOM, data 1 and data 7 are divided into the same class.Data 2 and 8 are divided into different classes.According to the classification label, PSO clustering algorithm has a better solution that data 1 and 2 are divided together and data 7 and 8 are in the same class (see Figure 2).
Besides, the result of SOM clustering is influenced by subjective factors.On the contrary, PSO clustering can draw a clear clustering results and output each classes' clustering center so as to quantitatively reflect the difference between each category.

Comparison of 158 groups of data clustering algorithms
Here we use 158 groups of categorized EMI signal data as test data.To present the advantages of our method, we use 4 other common clustering algorithms as comparison.
To show the significance of dimension reduction, we also use original data as input vector as a comparison.During experiment, it spends hours of time to calculate.After doing the same number of recursion, results are disappointing.Clusters are hard to converge, which means almost all the signal are divided into a same class.
The comparison clustering results by using different approaches are shown in Table 5.

Conclusion
In order to separate interference factor from the system signal and use clustering to find out typical electromagnetic interference factor, this paper presents a method for feature extraction and clustering of electromagnetic signal data by PSO

APOP
and describe the advantages of this method compared to traditional clustering algorithms such as K-means, SOM, FCM, which show that our method outperforms the comparison approaches, and require less running time.

Figure 1 .
Figure 1.Caption of the Figure 1.Below the figure.

Figure 2 .
Figure 2. Curves of the original EMI signal data.

Table 1 .
Data after feature extraction.

Table 2 .
Cluster result by using the low dimensional feature and PSO clustering algorithm.

Table 3 .
Output centres using the proposed method.

Table 4 .
Clustering result by using SOM.

Table 5 .
Comparison results by using different approaches.for clustering, as can be seen, the algorithm proposed in this paper has high accuracy and efficiency in electromagnetic signal clustering.However, compared to SOM network, this algorithm requires the number of clustering, which is one disadvantage of the algorithm.