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\title{A Survey on Clustering Techniques for Multi-Valued Data Sets}
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             \author[1]{Lnc. Prakash  K}

             \affil[1]{  Annamacharya institute of technology and sciences}

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\date{\small \em Received: 10 December 2015 Accepted: 5 January 2016 Published: 15 January 2016}

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\begin{abstract}
        


The complexity of the attributes in some particular domain is high when compare to the standard domain, the reason for this is its internal variation and the structure .their representation needs more complex data called multi-valued data which is introduced in this paper. Because of this reason it is needed to extend the data examination techniques (for example characterization, discrimination, association analysis, classification, clustering, outlier analysis, evaluation analysis) to multi-valued data so that we get more exact and consolidated multi-valued data sets. We say that multi-valued data analysis is an expansion of the standard data analysis techniques. The objects of multi-valued data sets are represented by multi-valued attributes and they contain more than one value for one entry in the data base. An example for this type of attribute is ?languages known? .this attribute may contain more than one value for the corresponding objects because one person may be known more than one language.

\end{abstract}


\keywords{}

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\let\tabcellsep& 	 	 		 
\section[{I. Introduction}]{I. Introduction}\par
Analysis to such objects, called multi-valued Data analysis. 
\section[{II. Input to Multi-Valued Data Analysis Algorithms}]{II. Input to Multi-Valued Data Analysis Algorithms}\par
In general Columns of the source data table are variables (attributes) and rows (objects) are multi-valued descriptions. Each cell of this multi-valued data table may contain data of different types as given bellow.\par
? The sell may contain a quantitative value for example. If "height" is an attribute and a is a unit then height (a)=2.4 . ? The sell may contain discrete value, for instance, consider "village" is a variable and a is a unit then village (a) = Raja pet. ? The sell may contain Multi-valued, for example, in the quantitative case: height (a) =(3 .2, 4 .1,5\par
)which means that the weight of a maybe 3 .2 or 4 .1 or 5 . In the discrete case, language (a) = (Telugu, Hindi, Tamil) means that the language of a may be Telugu or Hindi or Tamil. Here it is clear that the above two are special cases of this case. ? The sell may contain Interval valued data: for instance height (a) = \hyperref[b10]{[12,}\hyperref[b13]{15]}, which tells that the height of a varies in the interval \hyperref[b10]{[12,}\hyperref[b13]{15]}. Some other types of variables may also exist with Multi valued weights, Taxonomic, Hierarchically dependent, logically dependent. 
\section[{III. Result of Multi-Valued Data Analysis Algorithms}]{III. Result of Multi-Valued Data Analysis Algorithms}\par
The output of any data analysis depending on the type of the data mining task. If the task is characterization it represents the nature of data and its character. When the task is association we can find the frequent items and then form the association rules. If the task is classification we can find the different classes that are associated with the data. If the task is clustering we can partition the data into different similar groups depending on the similarity measure. 
\section[{IV. Source of Multi-Valued Data}]{IV. Source of Multi-Valued Data}\par
Multi-valued data is formed from the tables that are integrated from different sources so this type of data is summarized and concise so the requirement of consolidation of different huge data sets causes multivalued data sets. The result from several probability 43 Year 2016 
\section[{( ) C}]{( ) C}\par
Abstract-The complexity of the attributes in some particular domain is high when compare to the standard domain, the reason for this is its internal variation and the structure .their representation needs more complex data called multi-valued data which is introduced in this paper. Because of this reason it is needed to extend the data examination techniques (for example characterization, discrimination, association analysis, classification, clustering, outlier analysis, evaluation analysis) to multi-valued data so that we get more exact and consolidated multi-valued data sets. We say that multi-valued data analysis is an expansion of the standard data analysis techniques. The objects of multi-valued data sets are represented by multi-valued attributes and they contain more than one value for one entry in the data base. An example for this type of attribute is "languages known" .this attribute may contain more than one value for the corresponding objects because one person may be known more than one language. n the process of making more general surveys the persons are permitted to give more than one answer for a particular question. The answer may be a set of categorical values or a set of numerical values or sometimes it may be the combination of both. Now a days the data base is going on increasing and it is needed the integration of different data bases as a result a very lengthy databases are formed. The data bases that are formed in this way may contain the same objects that are repeated many times with different values .the increasing importance is to reduce the data base size by summarizing the data without loss of the information that is used for analysis. This can be achieved by introducing the concept of multi-valued attributes in the data bases. Because the cells of such data may contain not only single numerical or categorical values, but much more multifaceted information, such as subsets of categorical variable values, intervals of ordinal variable values, dependencies and need rules to be specified. These new statistical units are called multi-valued objects and there is a need for an extension of standard Data in order to answer to a query that is applied on different relational data bases form the multi-valued data sets. Multi-valued data can also be generated from Data Analysis (functional analysis, clustering, associations, neural networks . . .) of standard databases, from expert knowledge (scenario of traffic accidents, type of employed . . .), from time series (in the intervals of time), from private data (in the view of hiding the initial data by less precision), etc.  
\section[{Table c}]{Table c}\par
There are some approaches like ribeiro95 [1] and Thompson 91 \hyperref[b16]{[5]} identify the knowledge directly from domains that are structured. The most straight forward way to form a linear file is joining of related tables. the above table-c is the result of both of the tables table-a and table-b. Table-c is obtained by applying the natural join to both of the tables table-a and table-b which has the problem that a single object cannot be identified unique, that means a single object can be represented by more than one row. The problem as a unique object even though an object is identified by more than one tuple.\par
So, Therefore this construction between a structure database and linear file is understood by many analysis frame works in efficiently This paper introduces a data mining framework and a information discovery to deal with this drawback of the previous linear file representations and we finally concentrate on the issues of structured database and discovery of a set of queries that describe the features of objects in the database. To overcome from this problem mentioned above it is needed to develop a better illustration procedure which with this type of representation is most of the data mining and machine learning algorithms identify each row represents information for objects that are co-related with other objects. One simple solution to solve the problem is to combine the associated objects into a single object by applying some aggregate operations. The issue in this concept is the selection of aggregate function that can be applied and minimizing the Loss of technical information because of the aggregate function so finally there forms a cluster of related objects that represent a set of objects as a single object. To solve the same problem another technique is introduction of multivalued attributes for the objects. The generalization of this type of linear file arrangement is as multi-valued data set. in this types of data bases the values of multivalued attribute are either a single value or a bin of values these bin of values represent the data that associate with the object with respect to the multi-valued attribute. Table-d consists the multi-valued data that is generated from the two tables table-a and table-b, in this table product type, purchase place and purchase amount are multi-valued attributes, the objects have a set of values in between braces in the corresponding cells of these multi-valued attributes, if there is no any value we represent it by null or if there is a single value we put that value as it is. Now table-d contains the unique tuples for representing the data of one person which is different from the data that is denoted by table-c. So a useful set of queries can be applied to this type of data for implementing data mining tasks, because of multivalued attributes are existed in the data base the following problems are encountered during this process.\par
? It is needed to identify the set of queries that access the features of objects in the database. ? Applying the data mining techniques to the database that consists of multi-valued attributes.\par
Most of the data mining techniques that are existed cannot work properly on the multi-value datasets which consists of a set of values because they are developed for applying on single valued attributes. So the need is to develop the techniques that can be applied on multi valued attributes.\par
Multi-valued Datasets that are available in UCI machine learning repository are given in the bellow table. 
\section[{Name of the Dataset}]{Name of the Dataset} 
\section[{Number of classes}]{Number of classes} 
\section[{Number of normal attributes}]{Number of normal attributes} 
\section[{Number of multivalued attributes}]{Number of multivalued attributes} 
\section[{Number of binary attributes}]{Number of binary attributes}\par
"Promoter" "Hayes-Roth" "Breast cancer" "Monks-1" "Monks-2" "Monks-3" "Balance" "Soya large" "Tic-tac-toe" "Car" "DNA" "Mushroom" "Nursery"  In general the categorization of two types of attributes in the data bases are quantitative attributes and qualitative attributes to apply data mining tasks on these databases we are needed to find the similarity measures among these type of attributes .\par
VI. Qualitative Type \hyperref[b4]{Tversky (1977)} proposed a contrast model and ratio model that is implemented by generalizing a several set of theoretical similarity models .Tversky described the objects as sets of features as a replacement of geometric points in a geometric space. To demonstrate his models, let a and b are two objects, and X and Y indicate the sets of features associated with the objects x and y respectively. Tversky proposed the following family of proximity measures which is called the contrast model:S(x, y) = ? n (X?Y) -? n(X -Y) -? n(X -Y)\par
For some ?, ?, ? ? 0; n is usually the cardinality of the set. In the previous models, the proximity between objects was determined only by their common features, or only by their distinctive features. In the contrast model, the proximity of a pair of objects is represented as a linear combination of the measures of the common and the distinctive features. The contrast model denotes proximity between objects as a weighted difference of the measures for their common and distinctive features. The given bellow family of similarity measures denotes the ratio model:S(x, y) = n (X?Y) / [n( X?Y) + ? n(X -Y) + ? n(Y-X)], ?, ? ? 0\par
In the ratio model, the proximity value is normalized to a value range of 0 and 1. In Tversky's set theoretic similarity models, a feature usually denotes a value of a binary attribute or a nominal attribute but it 
\section[{VII. Attributes That are Quantitative Type}]{VII. Attributes That are Quantitative Type}\par
To find the proximity within the group when the attributes are multi-valued type we use group mean for the particular attribute with respect to the object by using Euclidean distance like measures but the problem with this method is it should not consider the cardinality of the elements in a group. Another approach towards this is group average which can be used to calculate inter-group proximity. In this approach group similarity is calculated by taking the average of all the inter-object measures for those pairs of objects from which each object of a pair is in diverse groups.\par
For example, the average dissimilarity between group P and Q can be defined as given bellowD (P, Q) = ? ??(??, ??)/?? ?? ??=1\par
),  where n is the cardinality of object-pairs, d (a, b) is the variation metric for the i th pair of objects p and q where p? P And q ? Q . In calculating group similarity using on group average, decision on whether we compute the average for every probable pair of similarity or the average for a subset of possible pairs of similarity is required. 
\section[{VIII. Algorithms for Clustering}]{VIII. Algorithms for Clustering}\par
IX. 
\section[{Partitioning Algorithms for Clustering}]{Partitioning Algorithms for Clustering}\par
The data objects in these types of methods are initially considered as a single cluster and this can be partitioned into different clusters depending on the number of clusters required. The objects are assigned into partitions by iteratively placing the points between the partitions. There are different re arrangement schemes that iteratively reassign the points among the pre defined number of clusters not like hierarchical methods clusters not allowed revisiting the previously formed clusters. These algorithms Progressively develop the quality of clusters.\par
In all of the partitioning algorithms the number of clusters is decided initially, if we want to find the number of clusters automatically we can think data comes from the mixture of various probability distributions .the major advantage of probabilistic approach is interpretability of the clusters that are formed. The summarized cluster representation can be done by allowing the measures of intra cluster similarity, an another approach to measure the quality of clustering is the definition of objective function . in general partitioning algorithms constructs the clusters in non-convex shape.\par
Some partitioning algorithms for clustering are K\textunderscore means, K\textunderscore modes, K\textunderscore medoids (PAM, CLARA, CLARANS, and FCM). Partition based algorithms can found clusters of Non convex shapes. The pros and cons of partitioning clustering methods are described bellow. 
\section[{Advantages:}]{Advantages:}\par
? Comparatively scalable and simple.\par
? These algorithms are suitable for the datasets which forms spherical shaped clusters that are wellseparated Disadvantages:\par
? These algorithms causes efficiency degradation in the high dimensional spaces because almost all pairs of points are at a distance of its average the reason for this is the distance between points in high dimensional spaces is not defined properly. ? The description of cluster is less explained by these algorithms.\par
? User needs to specify the number of clusters in advance.\par
? These are in efficient to deal with non-convex shaped clusters of unreliable size and density. 
\section[{X. Hierarchical Algorithms for Clustering}]{X. Hierarchical Algorithms for Clustering}\par
Hierarchical clustering algorithms are of two types they are Agglomerative (top-bottom) and Divisive (bottom-top). In Agglomerative Hierarchical clustering initially one object is selected and the other objects are embedded consecutively to form bigger clusters the merging of objects depends on the distance like maximum, minimum and average .this procedure is repeated number of times until to form desired number of clusters. some Hierarchical algorithms for clustering are BIRCH, CURE, ROCK, Chameleon, Wards, SNN, GRIDCLUST, CACTUS in which clusters of Non convex shaped and, Arbitrary Hyper rectangular are produced. Some times to find the proximity between sub sets it is needed to generalize the proximity between individual points. Such proximity measure is called linkage metric. This is also the case when the data base consists of multi-valued data. This type of metric impacts the Hierarchical clustering algorithms because it impacts the closeness and relation of connectivity among the attributes without considering its structure.\par
Mostly used inter-cluster linkage metrics are single link, average\textunderscore  link, and complete link. The principal proximity of dissimilarity measure (usually distance) is computed for every pair of points with one point in the first set and another point in the second set. A specific functional operation such as minimum Average or maximum is applied to pair-wise proximity of dissimilarity measures an example for such functional operation is given bellow:D (C 1 , C 2 ) = functional operation \{d (x,y)/ x? C 1, y? C 1 \}\par
The pros and cons of partitioning clustering methods are described bellow Advantages:\par
These algorithms are flexible with respect to the level of granularity. similarity or distance proximities are easily managed. These algorithms can be applicable to any types of attributes. 
\section[{Disadvantages:}]{Disadvantages:}\par
It is difficult to identify the termination point. Most of the hierarchical algorithms cannot be repeated if once constructed. Clusters are formed depending on the reason of their improvement.\par
47 Year 2016 
\section[{( ) C}]{( ) C}\par
In density based methods the set of points which are in the space of Euclidean are partitioned into a set of ? More sensitive to initialization phase that means final results depends on the clusters that are formed at initial, also sensitive to noise and outliers.\par
points depending on the density among the points, connectivity between each pair of points and the boundary of the points that are grouped. In density based clusters each point in the cluster closely related to its adjacent neighbor, the clusters are formed in any direction that the density of the points in one cluster should be maximum. Because of this reason the cluster that depends on density are of arbitrary shaped as a result it provides a good security against outliers. These algorithms classify the data objects into core\textunderscore points, border\textunderscore points and noise points to form dense regions. The clusters are formed by connecting the core points together. So there may be a chance of forming non spherical or arbitrary shaped clusters. Some well known density based algorithms for clustering are "DBSCAN", "OPTICS","DBCLASD", "GDBSCAN" ," DENCLUE" and "SUBCLUE". When the data is of numeric type then only density based and partition based methods give results efficiently but grid based techniques perform well for the attributes with different data types along with multivalued data. For better performance the density based method "DENCLUE" initially uses grid structure. To structure real clusters Grid based algorithms uses subspace and hierarchical techniques for clustering. When compare to all Clustering algorithms Grid algorithms are very speedy and efficient processing algorithms. Arbitrary shaped clusters are formed by Adaptive grid algorithms such as MAFIA and AMR by using the grid cells. 
\section[{XV. Model Clustering Algorithms}]{XV. Model Clustering Algorithms}\par
A model is hypothesized for each of the clusters and tries to find Set of data points are related together based on different strategies like conceptual methods and statistical methods. For model based algorithms the well known approaches are one is neural network approach and another one is statistical approach. Algorithms such as "EM", "CLASSIT", "COBWEB SOM", and "SLINK" are some Model based clustering algorithms. 
\section[{XVI. Research Challenges}]{XVI. Research Challenges}\par
We have previously discussed that the problem of clustering becomes very demanding,attractive and at the same time challenging, when the data is of type categorical attributes and multi-valued attributed. The number of algorithms for the discovery of groups in such data is restricted, confined and limited, compared to the research devoted on data sets with numerical data. Further, few algorithms deal with mixtures of values, i.e., attributes of numerical and categorical The methods that partition the space into different cells or segments are called grid-based methods. Here each segment is related to a single value or a group of values (if the data is multi-valued data) is considered as a unit, as a result the concentration is turned on to the partition space. The partition is based on the characteristics of the grid that is formed from the data. The advantage of this type of arrangement of data in the form of grids is it does not depend on the order of the points that are arranged in the form of grids. 
\section[{Global}]{Global} 
\section[{XVII. Summary and Conclusion}]{XVII. Summary and Conclusion}\par
In this paper, we analyzed the difficulty of generating single flat file arrangement to represent Data sets that have been generated from structured databases, and pointed out its inappropriate representation to represent related information, a fact that has been frequently overlooked by recent data mining investigation. To overcome these difficulties, we used a better representation scheme, called multi-valued data set, which allows attributes of an object to have a set of values, and studied how existing similarity measures for single-valued attributes could be applied to measure group similarity for multi-valued data sets in clustering.We also proposed a unified framework for proximity Once the target database is grouped into clusters with similar properties, the discriminate query detection system, MASSON can find out useful characteristic information for a set of objects that fit in to a cluster. We claim that the planned representation scheme is suitable to cope with related information and that it is more communicative than the traditional single flat file format.\par
More prominently, the relationship information in a structured database is actually considered in clustering procedure.\begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}1 C}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-3.png}
\caption{\label{fig_1}Figure 1}\end{figure}
   \begin{figure}[htbp]
\noindent\textbf{ab} \par 
\begin{longtable}{P{0.10479452054794519\textwidth}P{0.2328767123287671\textwidth}P{0.23520547945205478\textwidth}P{0.15835616438356165\textwidth}P{0.11876712328767124\textwidth}}
pan number\tabcellsep City\tabcellsep Mode of payment\tabcellsep Date of payment\tabcellsep Amount in Rs\\
11231\tabcellsep Visakhapatnam(V)\tabcellsep Physical cash\tabcellsep 1/06/13\tabcellsep 500.00\\
11231\tabcellsep Hyderabad(H)\tabcellsep Credit to bank\tabcellsep 10/07/13\tabcellsep 80.00\\
11231\tabcellsep Nellore(N)\tabcellsep Check\tabcellsep 11/07/13\tabcellsep 100.00\\
14561\tabcellsep Visakhapatnam(V)\tabcellsep Physical cash\tabcellsep 19/08/13\tabcellsep 400.00\\
14561\tabcellsep Anakapalli(A)\tabcellsep Credit to bank\tabcellsep 20/08/13\tabcellsep 200.00\\
17891\tabcellsep Anakapalli(A)\tabcellsep Credit to bank\tabcellsep 5/09/13\tabcellsep 50.00\\
11011\tabcellsep Vizianagaram(Vz)\tabcellsep Physical cash\tabcellsep 8/09/13\tabcellsep 25.00\end{longtable} \par
 
\caption{\label{tab_0}Table a Table b}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{d} \par 
\begin{longtable}{P{0.09956616052060738\textwidth}P{0.03503253796095445\textwidth}P{0.28394793926247286\textwidth}P{0.02950108459869848\textwidth}P{0.26366594360086765\textwidth}P{0.13828633405639912\textwidth}}
Name\tabcellsep Age\tabcellsep \multicolumn{2}{l}{Product type category}\tabcellsep Purchase place\tabcellsep Purchase amount\\
A.Ajay kumar\tabcellsep 21.0\tabcellsep \{physical cash,credit to bank,check\}\tabcellsep Male\tabcellsep \{Visakhapatnam(V),Hyderabad(H), Nellore(N)\}\tabcellsep \{500.00,80.00,100.00\}\\
A.Vijay kumar\tabcellsep 22.0\tabcellsep bank \} \{ cash, credit to physical\tabcellsep Male\tabcellsep \{Visakhapatnam(V),anakapally(A)\}\tabcellsep \{400.00,200.00\}\\
A.Arun kumar\tabcellsep 23.0\tabcellsep \{Credit credit to bank\}\tabcellsep Male\tabcellsep Anakapally(A)\tabcellsep 50.00\\
A.Varun kumar\tabcellsep 24.0\tabcellsep bank \} \{ cash, credit to physical\tabcellsep Male\tabcellsep \{vizianagaram(Vz),Visakhapatnam(V)\}\tabcellsep \{25.00,50.00\}\end{longtable} \par
 
\caption{\label{tab_2}Table d :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{e} \par 
\begin{longtable}{}
\end{longtable} \par
  {\small\itshape [Note: . Similarity Measures for Multi-Valued Data Sets]} 
\caption{\label{tab_4}Table e V}\end{figure}
 		 		\backmatter  			 
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