Fuzzy-Neural Clustering Comparison for Outlier Detection

International Journal of Computer Engineering and Technology (IJCET), ISSN 0976-
6367(Print), ISSN 0976 – 6375(Online) Volume 4, Issue 4, July-August (2013), © IAEME
422
COMPARISON OF FUZZY - NEURAL CLUSTERING BASED OUTLIER
DETECTION TECHNIQUES
Nilam Upasani
Research Scholar, Computer Engineering, Indian School of Mines, Dhanbad, India
Hari Om
Computer Engineering, Indian School of Mines, Dhanbad, India
ABSTRACT
Fuzzy logic can be used to reason like humans and can deal with uncertainty other than
randomness. Ability to learn, adapt, fault tolerance and reason with available knowledge, are the
distinguished features of neural networks. Outlier detection is a difficult task to be performed, due to
uncertainty involved in it. The outlier itself is a fuzzy concept and difficult to determine in a
deterministic way. The hybridization of fuzzy and neural soft computing system is very promising,
since they exactly tackle the situation associated with outliers. This paper provides a detailed
comparison of fuzzy and/or neural approaches used for outlier detection by discussing their pros and
cons. Thus this is a very helpful document for naive researchers in this field.
Keywords: outlier detection; fuzzy logic; neural nerwork; data mining
I. INTRODUCTION
Business Intelligence is a de-facto standard that uses Data Mining techniques to manage and
plan businesses. Mined knowledge is in the form of rules, association among the patterns, current and
future customer trends. But there is a serious issue concerning with data mining, called outliers. In
literature different definitions of outlier exist: the most commonly referred are [1]:
- “An outlier is an observation that deviates so much from other observations as to arouse
suspicions that is was generated by a different mechanism “ (Hawkins, 1980).
- “An outlier is an observation (or subset of observations) which appear to be inconsistent with
the remainder of the dataset” (Barnet & Lewis, 1994).
- “An outlier is an observation that lies outside the overall pattern of a distribution” (Moore
and McCabe, 1999).
- “Outliers are those data records that do not follow any pattern in an application” (Chen and
al., 2002).
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- “An outlier in a set of data is an observation or a point that is considerably dissimilar or
inconsistent with the remainder of the data” (Ramasmawy at al., 2000).
Outlier may occur due to data error, noise, anomaly, improper sensors or typo error. Outliers
may cause incorrect knowledge discovery and obstruct the process of data mining and thus may badly
affect the business profit. Recently, many application domains have recognized the direct mapping
between the outliers in data and real world anomalies that are of great interest to data analyst. The
outlier detection is searching for objects in the database that do not obey laws valid for the major part
of the data. Outlier detection is an important pre-processing task [2]. It has several realistic
applications in areas such as, image processing [3], remote sensing [4], fraud detection [5], identifying
computer network intrusions and bottlenecks [6], criminal activities in e-commerce and detecting
suspicious activities [7], Satellite image analysis, etc.
For any outlier detection technique, there are two ways to report the outliers which are scores
and labels [8]. In scoring techniques, outlier score is assigned to each instance in the test data
depending on the degree to which that instance is considered an outlier. Thus the output of such
techniques is a ranked list of outliers. An analyst may choose to either analyze top few outliers or use
a cut-off threshold to select the outliers. In label techniques, a label (normal or anomalous) is assigned
to each test instance.
Outlier detection and clustering analysis are two greatly interconnected tasks, although they
serve different purposes. Clustering locates the majority patterns in a data set and categorizes data
accordingly, whereas outlier detection tries to capture those exceptional cases that deviate
substantially from the majority patterns. Without intrinsic clustering in the data, no natural outliers
will exist. Clustering is an important tool for outlier analysis. A number of clustering-based outlier
detection techniques have been developed, most of which rely on the key assumption that normal
objects belong to large and dense clusters, while outliers form very small clusters [9, 10].
Outlier detection methods are derived from three fields of computing which are statistics
(proximity-based, parametric, non-parametric and semi-parametric), neural networks (supervised and
unsupervised) and machine learning. The main advantage of statistical models is they are
mathematically justified. They are commonly appropriate to quantitative real-valued data sets. In case
of least quantitative ordinal data distributions, the ordinal data should be transformed to suitable
numerical values for statistical (numerical) processing. This restricts their applicability and in case of
complex data transformations it also increases the processing time. Much outlier detection has only
focused on continuous real-valued data attributes whereas Machine Learning has mainly centered on
categorical data. Machine learning techniques are robust, do not suffer the Curse of Dimensionality,
work well on noisy data and have simple class boundaries compared with the complex class
boundaries. Neural Network approaches are normally non-parametric and model based. They
generalize well to unseen patterns, capable of learning complex class boundaries and have better
reasoning ability along with fault tolerance. Much of the pattern recognition task is now implemented
using fuzzy logic as it can be used to reason in imprecise situations and can handle uncertainty. If we
hybridize fuzzy logic with the neural networks, it combines advantages of both. Such a hybrid system
can also be used for Outlier Detection. As outlier detection and clustering analysis are two greatly
interconnected tasks, this survey aims at providing an overview of the outlier detection techniques
involving fuzzy and/or neural network approaches based on clustering, by focusing on their strengths
and weaknesses.
This paper is organized as follows. Section II and III gives a comprehensive overview of the
fuzzy clustering based outlier detection and neural network based outlier detection techniques.
Advantages and disadvantages of these two approaches are discussed in Section IV. Section V points
towards some hybridized fuzzy neural network approaches effectively used for pattern recognition,
which can also be used for the task of outlier detection. Conclusions are given in section VI and
references are cited at the end.

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II. FUZZY CLUSTERING BASED OUTLIER DETECTION
Crisp set can be used to handle structured data which is generally free from outlier points.
But it is difficult to handle unstructured natural data which often contain outlier data points. Fuzzy
set (introduced by Zadeh [11]) is different from its crisp counterpart, as it allows the elements to have
a degree of membership. Thus, to handle unstructured natural data which is qualitative and imprecise
in nature, many of the data mining techniques are integrated with fuzzy logic [12]. In traditional
clustering approaches each pattern belongs to one and only one cluster [13]. In case of fuzzy
clustering, the membership function associates each pattern with all the clusters. Thus fuzzy clusters
grow in their natural shapes. In this section some fuzzy clustering outlier detection techniques are
analyzed.
A. Fuzzy C-Means algorithm (FCM) [14]:
FCM is one of the well known fuzzy clustering algorithms, and used in a wide variety of
applications, such as medical imaging, remote sensing, data mining and pattern recognition
[15,16,17,18,19]. Chiu, Yager & Filev have proposed Fuzzy c-means data clustering algorithm in
which each data point belongs to a clustering to a degree specified by a membership grade [20].
Fuzzy c-means clustering has two processes: the calculation of cluster centers and the assignment of
points to these centers using a form of Euclidian distance. This process is repeated until the cluster
centers are stabilized. FCM partitions a collection of data points into fuzzy groups. Unlike k-means
where data point must exclusively belong to one cluster center, FCM finds a cluster center in each
group in order to minimize the objective function of the dissimilarity measure. FCM employs fuzzy
partitioning so that a given data point can belong to several groups with the degree of belongingness
specified by membership grades between 0 and 1. The membership of each data point corresponding
to each cluster center will be calculated on the basis of distance between the cluster center and the
data point, using exp. [1],
………. [1]
where
µj(xi) : is the membership of xi in the jth
cluster
dji : is the distance of xi in cluster cj
m : is the fuzzification parameter
p : is the number of specified clusters
dki : is the distance of xi in cluster Ck
The new cluster centers are calculated with these membership values using the exp. [2].
………. [2]
where
Cj : is the center of the jth
cluster
xi : is the ith
data point
µj : the function which returns the membership
m : is the fuzzification parameter

425
More the data is near to the cluster center more is its membership towards the particular
cluster center. Clearly, summation of membership of each data point should be equal to one. After
each iteration, the membership and cluster centers are updated.
Good characteristics of this algorithm are, it is simple to implement, robust in behavior, can
handle multidimensional data, gives best result for overlapped data set and can model uncertainty
within the data. The main drawback of this algorithm is that it is unable to handle outlier points
effectively because of the restriction that the sum of membership values of a data point in all the
clusters must be one. This tends to give high membership values for the outlier points. It is also
incapable to calculate the membership value if the distance of a data point is zero. We get better
result but at the cost of more number of iteration
B. Fuzzy clustering based algorithm proposed by Binu Thomas and Raju Ghave [21]:
They have proposed a novel fuzzy clustering method in which they have modified the
membership function proposed by Fuzzy C-Means algorithm. In this method a very low membership
value is assigned to the outlier points to handle unstructured natural data.
In FCM, many limitations arise because the membership of a point in a cluster is calculated based
on its membership in other clusters. In this method, the membership of a point in a cluster depends
only on its distance in that cluster calculated by a simple expression exp. [3].
………. [3]
Where
µj(xi) : is the membership of xi in the jth
cluster
dji : is the distance of xi in cluster cj
Max(dj) : is the maximum distance in the cluster cj
With this it is possible to calculate the membership value if the distance of a data point is zero
which is the limitation of FCM. It is more proficient in handling the natural data with outlier points
by allocating very low membership values to the outlier points. It is far better in the calculation of
new cluster centers. This method has limitations in exploring highly structured crisp data which is
free from outlier points.
C. Fuzzy clustering based algorithm proposed by Moh'd Belal et.al. [22]:
Moh'd Belal Al-Zoubi, Ali Al-Dahoud, Abdelfatah A. Yahya proposed an efficient method
for outlier detection based on fuzzy clustering techniques. This technique is based on the key
assumption that normal objects belong to large and dense clusters, whereas outliers form very small
clusters. Here a small cluster is a cluster with fewer points than half the average number of points in
the other clusters.
In this approach, FCM algorithm is performed first to produce a set of k clusters as well as
the objective function (OF) and Compute the threshold (T) to determine outliers. Then small clusters
are determined and the points that belong to these clusters are considered as outliers. After this if any
outliers are left then those would be detected in the remaining clusters by temporary removing a
point from the data set and re-calculating the objective function. If a noticeable change is observed in
the Objective Function (OF), the point is considered an outlier. This approach is efficient to locate
the outliers when applied to different data sets. However, the proposed method is very time
consuming because the FCM algorithm has to run multiple times.

426
III. NEURAL NETWORK BASED OUTLIER DETECTION
Neural networks serve to learn, process, and predict the information using layers of
interconnected units resembling the neurons that comprise the nervous system of the human brain.
Neural networks have the advantage of powerful modeling ability. Neural network does not involve
the complex process and has the advantage of requiring poor or no a priori assumption on the
considered data. There are many outlier detection techniques based on neural networks.
A. Outlier Detection Using Replicator Neural Networks[23]
Hawkins S., H. X. Williams, G.J. and Baxter R.A. have proposed replicator neural network
(RNN) based technique to find outliers in large multivariate databases. Earlier Replicator Neural
Network was used for its data compression capabilities in several applications of image and speech
processing [24, 25]. RNNs have a flexible, non-parametric representation of clusters and hence they
have used it as a powerful tool for outlier detection [26]. In this approach, a feed-forward multi-layer
neural network is used with three hidden layers sandwiched between the input and output layers
which have n units each, corresponding to the n features of the training data. In order to minimize the
average reconstruction error, the number of units in the three hidden layers is chosen experimentally
across all training patterns. To develop a compressed and implicit model of the data during training,
the input variables are also the output variables. A measure of outlyingness (called the Outlier Factor)
of individuals is then developed as the reconstruction error of individual data points. The Outlier
Factor of the ith
data record OFi as the measure of outlyingness is defined by the average
reconstruction error over all features (variables) as given in exp. [4].
………. [4]
where, n is the number of features, xij is the input value and Oij is the input value. The OF is
evaluated for all data records using the trained RNN.
Instead of the usual sigmoid activation function for the middle hidden layer a staircase-like
function with parameters N (number of activation levels) and a3 (transition rate from one level to the
next) are employed. This activation function provides the data compression as it continuously divides
distributed data points into a number of discrete valued vectors. The mapping to discrete categories
naturally places the data points into a number of clusters which is essential for outlier detection. For
scalability the RNN is trained with a smaller training set and then applied to all the data to calculate
their outlyingness. Neural Network methods often have difficulty with such smaller datasets, though
RNN performs satisfactory for both small and large datasets. But its performance degrades with
datasets containing radial outliers and so it is not suggested for this type of dataset.
B. Multiple Outlier Detection in Multivariate Data Using Self-Organizing Maps Title [27]
Nag A.K., Mitra A. and Mitra S. proposed an artificial intelligence technique of self-
organizing map (SOM) based non-parametric method for outlier detection. It can be used to detect
outliers from large multidimensional datasets and also provides information about the entire outlier
neighborhood.
SOM is a feed forward neural network that uses an unsupervised training algorithm, and
through a process called self-organization, configures the output units into a topological
representation of the original data (Kohonen 1997). SOM produces a topology-preserving mapping of
the multidimensional data cloud onto lower dimensional visualizable plane and hence provides an
easy way of detection of multidimensional outliers in the data, at respective levels of influence.

427
The outcome of the SOM algorithm is the set of weight vectors which are used to connect the
multidimensional input vector space and the output grid. A trained weight vector associated with a
grid on the output layer gives a unique identification of that unit. First the training process of winner
selection and weight updation is done. Then the appropriate visualization of the topology of map is
done and the outliers are detected by interpreting the results. Advantage includes the easy
implementation as it does not require any priori assumption on the variable.
C. Subtractive Clustering Based RBF Neural Network Model for Outlier Detection [28]
Peng Yang, Qingsheng Zhu and Xun Zhong proposed a RBF neural network model using
subtractive clustering algorithm for selecting the hidden node centers, which can achieve faster
training speed. This method has adopted the Subtractive Clustering (SC) to determine the hidden node
centers in RBF network since it allows a scatter input-output space partitioning, which can lead to a
proper network structure and achieve computation efficiency. Accurate prediction is achieved by
minimizing the variances of the nodes in the hidden layer. An RBF network is a three-layer feed
forward neural network which consists of an input layer, a hidden layer and an output layer. The
network is trained to implement a desired input-output mapping by producing incremental changes of
the weights of the network.
Finally, according to the degree of outlier for each input instance candidate outliers can be
obtained. Advantage of this method is that it can perform more accurate prediction with lower false
positive rate and higher detection rate and it can be an effective solution for detecting outliers.
IV. ADVANTAGES AND DISADVANTAGES OF FUZZY - NEURAL CLUSTERING BASED
TECHNIQUES
A. Advantages and disadvantages of fuzzy based techniques
• The use of a fuzzy set approach to pattern classification inherently provides degree of
membership information that is extremely useful in higher level decision making.
• Fuzzy logic is capable of supporting, to a reasonable extent, human type reasoning in natural
form by allowing partial membership for data items in fuzzy subsets [29].
• Fuzzy logic can handle uncertainty at various stages.
• With this approach knowledge can be expressed in terms of If–THEN rules.
• Disadvantage of fuzzy clustering is that with a growing number of objects the amount of
output of the results becomes huge, so that the information received often cannot be worked
up.
B. Advantages and disadvantages of neural networks based techniques
• Neural networks have an adaptive capability of learning new patterns and refine existing ones.
• These techniques are capable of learning complex class boundaries and have ability to learn
complex nonlinear input-output relationships
• As neural networks are massively parallel in nature, Complex computational task can be
performed in great speed.
• They are nonparametric that is it can work without any prior information available.
• Neural network have disadvantages such as lower detection precision in case of small learning
sample size, weaker detection stability.

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V. HYBRID APPROACHES INVOLVING BOTH FUZZY LOGIC AND NEURAL
NETWORKS FOR PATTERN RECOGNITION
We have surveyed that the variations of fuzzy logic and neural network are best suitable for
classification and clustering. This hybrid approach is used for speaker identification, real time heart
diseases detection, face recognition, etc [30, 31, 32, 33]. However, not much work is done for using
this hybrid approach for the outlier detection.
Wang G., Jinxing Hao, Jian Ma, Lihua Huang have proposed a novel approach for Intrusion
Detection System to solve network security problems based on the hybrid approach [34]. The
technique is called Fuzzy Clustering Artificial Neural Network (FC-ANN). The basic objective was
to enhance the detection precision for low-frequent attacks and detection stability.
The general procedure of FC-ANN approach has three major stages. In the first stage, they
have used one of the popular soft clustering techniques, fuzzy c-means clustering to divide the
training data into several subsets. In the second stage, based on different training sets, different
neural networks are trained. They have used classic feed-forward neural networks trained with the
back-propagation algorithm for training. In the third stage, to eliminate the errors of different ANNs,
a meta-learner, fuzzy aggregation module is used to learn again and combine the results of different
ANN’s.
This method has employed divide and conquer approach. Fuzzy clustering is used to divide
the whole training set into subsets which have less number and lower complexity. Thus the ANN can
learn each subset more quickly, robustly and precisely so that low-frequent attacks can also be
detected. The proposed technique is found better in performance compared to BPNN and other well-
known methods such as decision tree, the naïve Bayes in terms of detection precision and detection
stability.
VI. CONCLUSION AND FUTURE DIRECTIONS
In this survey we have discussed different ways in which the problem of cluster based outlier
detection has been formulated in literature, and we attempted to provide an overview of the huge
literature on different techniques. Different outlier detection algorithms are available which are based
on fuzzy logic and neural network, which have their own advantages and disadvantages.
Some researchers have used hybrid approach, based on fuzzy logic and neural network to
combine the advantages and to overcome the disadvantages of both the techniques for various
domains which are mentioned in section V. But very few have used this hybrid approach for outlier
detection. Thus, there is still a wide scope to apply modern fuzzy-neural techniques in this area to
improve the quality and required time of outlier detection process.
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