M43016571

Karthikeyan.P et al Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 3( Version 1), March 2014, pp.65-71
www.ijera.com 65|P a g e
High Dimensional Data Clustering Using Fast Cluster Based
Feature Selection
Karthikeyan.P1
, Saravanan.P2
, Vanitha.E3
1
PG Scholar, Department of Computer & Communication Engineering, PTR CET, Madurai, Tamil Nadu
2
Assistant Professor, Department of Computer Science Engineering, PTR CET, Madurai, Tamil Nadu
3
Assistant Professor, Department of Computer Science Engineering, PTR CET, Madurai, Tamil Nadu
ABSTRACT
Feature selection involves identifying a subset of the most useful features that produces compatible results as the
original entire set of features. A feature selection algorithm may be evaluated from both the efficiency and
effectiveness points of view. While the efficiency concerns the time required to find a subset of features, the
effectiveness is related to the quality of the subset of features. Based on these criteria, a fast clustering-based
feature selection algorithm (FAST) is proposed and experimentally evaluated in this paper. The FAST algorithm
works in two steps. In the first step, features are divided into clusters by using graph-theoretic clustering
methods. In the second step, the most representative feature that is strongly related to target classes is selected
from each cluster to form a subset of features. Features in different clusters are relatively independent; the
clustering-based strategy of FAST has a high probability of producing a subset of useful and independent
features. To ensure the efficiency of FAST, we adopt the efficient minimum-spanning tree (MST) using the
Kruskal‟s Algorithm clustering method. The efficiency and effectiveness of the FAST algorithm are evaluated
through an empirical study.
Index Terms—Feature subset selection, filter method, feature clustering, graph-based clustering
I. INTRODUCTION
CLASSIFICATION
Data mining refers to "using a variety of
techniques to identify nuggets of information or
decision-making knowledge in bodies of data, and
extracting these in such a way that they can be put to
use in the areas such as decision support, prediction,
forecasting and estimation. The data is often
voluminous, but as it stands of low value as no direct
use can be made of it; it is the hidden information in
the data that is useful”. Data mine tools have to infer
a model from the database, and in the case of
supervised learning this requires the user to define
one or more classes.
The database contains one or more attributes
that denote the class of a tuple and these are known as
predicted attributes whereas the remaining attributes
are called predicting attributes. A combination of
values for the predicted attributes defines a class.
When learning classification rules the system has to
find the rules that predict the class from the
predicting attributes so firstly the user has to define
conditions for each class, the data mine system then
constructs descriptions for the classes. Basically the
system should given a case or tuple with certain
known attribute values be able to predict what class
this case belongs to, once classes are defined the
system should infer rules that govern the
classification therefore the system should be able to
find the description of each class.
With the aim of choosing a subset of good
features with respect to the target concepts, feature
subset selection is an effective way for reducing
dimensionality, removing irrelevant data, increasing
learning accuracy and improving result
comprehensibility.Many feature subset selection
methods have been proposed and studied for machine
learning applications. They can be divided into four
broad categories: the Embedded, Wrapper, Filter, and
Hybrid approaches. The embedded methods
incorporate feature selections a part of the training
process and are usually specific to given learning
algorithms, and therefore maybe more efficient than
the other three categories. Traditional machine
learning algorithms like decision trees or artificial
neural networks are examples of embedded
approaches.
The wrapper methods use the predictive
accuracy of a predetermined learning algorithm to
determine the goodness of the selected subsets, the
accuracy of the learning algorithms is usually high.
However, the generality of the selected features is
limited and the computational complexity is large.
The filter methods are independent of learning
algorithms, with good generality. Their
computational complexity is low, but the accuracy of
the learning algorithms is not guaranteed the hybrid
RESEARCH ARTICLE OPEN ACCESS

methods area combination of filter and wrapper
methods by using a filter method to reduce search
space that will be considered by the subsequent
wrapper. They mainly focus on combining filter and
wrapper methods to achieve the best possible
performance with a particular learning algorithm with
similar time complexity of the filter methods.
The wrapper methods are computationally
expensive and tend to overfit on small training sets.
The filter methods, in addition to their generality, are
usually a good choice when the number of features is
very large. Thus, we will focus on the filter method in
this paper.
1.1 System Architecture
Fig 1Architecture of Proposed Method
II. CLUSTERING
Clustering and segmentation are the
processes of creating a partition so that all the
members of each set of the partition are similar
according to some metric. A cluster is a set of objects
grouped together because of their similarity or
proximity. Objects are often decomposed into an
exhaustive and/or mutually exclusive set of clusters.
Clustering according to similarity is a very powerful
technique, the key to it being to translate some
intuitive measure of similarity into a quantitative
measure. When learning is unsupervised then the
system has to discover its own classes i.e. the system
clusters the data in the database. The system has to
discover subsets of related objects in the training set
and then it has to find descriptions that describe each
of these subsets. There are a number of approaches
for forming clusters. One approach is to form rules
which dictate membership in the same group based
on the level of similarity between members. Another
approach is to build set functions that measure some
property of partitions as functions of some parameter
of the partition.
III. FEATURE SELECTION
It is widely recognized that a large number
of features can adversely affect the performance of
inductive learning algorithms, and clustering is not an
exception. However, while there exists a large body
of literature devoted to this problem for supervised
learning task, feature selection for clustering has been
rarely addressed. The problem appears to be a
difficult one given that it inherits all the uncertainties
that surround this type of inductive learning.
Particularly, that there is not a single performance
measure widely accepted for this task and the lack of
supervision available.
In machine learning and statistics, feature
selection, also known as variable selection, attribute
selection or variable subset selection, is the process of
selecting a subset of relevant features for use in
model construction. The central assumption when
using a feature selection technique is that the data
contains many redundant or irrelevant features.
Redundant features are those which provide no more
information than the currently selected features, and
irrelevant features provide no useful information in
any context. Feature selection techniques are a subset
of the more general field of feature extraction.
Feature extraction creates new features from
functions of the original features, whereas feature
selection returns a subset of the features. Feature
selection techniques are often used in domains where
there are many features and comparatively few
samples (or data points). The archetypal case is the
use of feature selection in analyzing DNA
microarrays, where there are many thousands of
features, and a few tens to hundreds of samples.
Feature selection techniques provide three main
benefits when constructing predictive models
 Improved model interpretability,
 Shorter training times,
 Enhanced generalization by reducing over fitting.
Feature selection is also useful as part of the
data analysis process, as shows which features are
important for prediction, and how these features are
related. With such an aim of choosing a subset of
good features with respect to the target concepts,
feature subset selection is an effective way for
reducing dimensionality, removing irrelevant data,
increasing learning accuracy, and improving result
comprehensibility. Irrelevant features, along with

redundant features, severely affect the accuracy of the
learning machines. Thus, feature subset selection
should be able to identify and remove as much of the
irrelevant and redundant information as possible.
Moreover, “good feature subsets contain features
highly correlated with (predictive of) the class, yet
uncorrelated with (not predictive of) each
other.”Many feature subset selection methods have
been proposed and studied for machine learning
applications. They can be divided into four broad
categories: the Embedded, Wrapper, Filter, and
Hybrid approaches
3.1 Wrapper Filter
Wrapper methods are widely recognized as a
superior alternative in supervised learning problems,
since by employing the inductive algorithm to
evaluate alternatives they have into account the
particular biases of the algorithm. How- ever, even
for algorithms that exhibit a moderate complexity, the
number of executions that the search process requires
results in a high computational cost, especially as we
shift to more exhaustive search strategies. The
wrapper methods use the predictive accuracy of a
predetermined learning algorithm to determine the
goodness of the selected subsets, the accuracy of the
learning algorithms is usually high. However, the
generality of the selected features is limited and the
computational complexity is large. The filter methods
are independent of learning algorithms, with good
generality. Their computational complexity is low,
but the accuracy of the learning algorithms is not
guaranteed
3.2 Hybrid Approach
The hybrid methods are a combination of
filter and wrapper methods by using a filter method to
reduce search space that will be considered by the
subsequent wrapper. They mainly focus on
combining filter and wrapper methods to achieve the
best possible performance with a particular learning
algorithm with similar time complexity of the filter
methods.
In cluster analysis, graph-theoretic methods
have been well studied and used in many
applications. Their results have, sometimes, the best
agreement with human performance. The general
graph-theoretic clustering is simple: compute a
neighborhood graph of instances, then delete any
edge in the graph that is much longer/shorter
(according to some criterion) than its neighbors. The
result is a forest and each tree in the forest represents
a cluster. In our study, we apply graph-theoretic
clustering methods to features. In particular, we adopt
the minimum spanning tree (MST)-based clustering
algorithms, because they do not assume that data
points are grouped around centers or separated by a
regular geometric curve and have been widely used in
practice.
Based on the MST method, we propose a
Fast clustering based feature Selection algorithm
(FAST). The FAST algorithm works in two steps. In
the first step, features are divided into clusters by
using graph-theoretic clustering methods. In the
second step, the most representative feature that is
strongly related to target classes is selected from each
cluster to form the final subset of features.Features in
different clusters are relatively independent; the
clustering based strategy of FAST has a high
probability of producing a subset of useful and
independent features. The proposed feature subset
selection algorithm FAST was tested various
numerical data sets. The experimental results show
that, compared with other five different types of
feature subset selection algorithms, the proposed
algorithm not only reduces the number of features,
but also improves the classification accuracy.
3.3 Using Mutual Information for Selecting
Features in Supervised Neural Net Learning
Investigates the application of the mutual in
for “criterion to evaluate a set of candidate features
and to select an informative subset to be used as input
data for a neural network classifier. Because the
mutual information measures arbitrary dependencies
between random variables, it is suitable for assessing
the “information content” of features in complex
classification tasks, where methods bases on linear
relations (like the correlation) are prone to mistakes.
The fact that the mutual information is
independent of the coordinates chosen permits a
robust estimation. Nonetheless, the use of the mutual
information for tasks characterized by high input
dimensionality requires suitable approximations
because of the prohibitive demands on computation
and samples. An algorithm is proposed that is based
on a “greedy” selection of the features and that takes
both the mutual information with respect to the output
class and with respect to the already-selected features
into account. Finally the results of a series of
experiments are discussed.
During “preprocessing” stage, where an
appropriate number of relevant features are extracted
from the raw data, has a crucial impact both on the
complexity of the learning phase and on the
achievable generalization performance. While it is
essential that the information contained in the input
vector is sufficient to determine the output class, the
presence of too many input features can burden the
training process and can produce a neural network
with more connection weights that those required by
the problem

A major weakness of these methods is that
they are not invariant under a transformation of the
variables. For example a linear scaling of the input
variables (that may be caused by a change of units for
the measurements) is sufficient to modify the PCA
results. Feature selection methods that are sufficient
for simple distributions of the patterns belonging to
different classes can fail in classification tasks with
complex decision boundaries. In addition, methods
based on a linear dependence (like the correlation)
cannot take care of arbitrary relations between the
pattern coordinates and the different classes. On the
contrary, the mutual information can measure
arbitrary relations between variables and it does not
depend on transformations acting on the different
variables.
Our objective was less ambitious, because
only the first of the above options was considered
(leaving the second for the capabilities of the neural
net to build complex features from simple ones). We
assumed that a set of candidate features with globally
sufficient information is available and that the
problem is that of extracting from this set a suitable
subset that is sufficient for the task, thereby reducing
the processing times in the operational phase and,
possibly, the training times and the cardinality of the
example set needed for a good generalization.
In particular we were interested in the
applicability of the mutual information measure. For
this reason we considered the estimation of the MI
from a finite set of samples, showing that the MI for
different features is over-estimated in approximately
the same way. This estimation is the building block of
the MIFS algorithm, where the features are selected
in a “greedy” manner, ranking them according to
their MI with respect to the class discounted by a
term that takes the mutual dependencies into account.
3.4 On Feature Selection through Clustering
The algorithm for feature selection that
clusters attributes using a special metric and then
makes use of the dendrogram of the resulting cluster
hierarchy to choose the most relevant attributes. The
main interest of our technique resides in the improved
understanding of the structure of the analyzed data
and of the relative importance of the at-tributes for
the selection process.
The performance, robustness, and usefulness
of classification algorithms are improved when
relatively few features are involved in the
classification. Thus, selecting relevant features for the
construction of classifiers has received a great deal of
attention. The central idea of this work is to introduce
an algorithm for feature selection that clusters
attributes using a special metric and, then uses a
hierarchical clustering for feature selection.
Hierarchical algorithms generate clusters that are
placed in a cluster tree, which i s commonly known
as a dendrogram. Clustering‟s are obtained by
extracting t hose clusters that are situated at a given
height in this tree. It shows that good classifiers can
be built by using a small number of attributes located
at the centers of the clusters identified in the
dendrogram. This type of data compression can be
achieved with little or no penalty in terms of the
accuracy of the classifier produced and highlights the
relative importance of attributes.
Clustering‟s were extracted from the tree
produced by the algorithm by cutting the tree at
various heights starting with the maximum height of
the tree created above (corresponding t o a single
cluster) and working down t o a height of 0 (which
consists of single-attribute clusters). A
„representative‟ attribute was created for each cluster
as the attribute that has the minimum total distance to
the other members of the cluster, again using the
Barth élemyMontjardet distance. A similar study
was undertaken f or the zoo database, after
eliminating the attribute animal which determines
uniquely the type of the animal. These results suggest
that this method has comparable accuracy to the
wrapper method and CSF. However, the tree of
attributes helps to understand the relationships
between attributes and their relative importance.
Attribute clustering help to build classifiers
in a semi-supervised manner allowing analysts a
certain degree of choice in the s election of the
features that may be considered by classifiers, and
illuminating relationships between attributes and their
relative importance for classification. With the
increased interest of data miners in n bio-computing
in n general, and in microarray data in particular,
classification problems that involve thousands of
features and relatively few examples came t o t he
fore. We intend to apply our techniques to this type of
data.
IV. IRRELEVANT FEATURES
REMOVAL
Irrelevant features, along with redundant
features, severely affect the accuracy of the learning
machines. Thus, feature subset selection should be
able to identify and remove as much of the irrelevant
and redundant information as possible. Moreover,
“good feature subsets contain features highly
correlated with (predictive of) the class, yet
uncorrelated with (not predictive of) each other.”
Keeping these in mind, we develop a novel algorithm
which can efficiently and effectively deal with both
irrelevant and redundant features, and obtain a good
feature subset. We achieve this through a new feature
selection framework which composed of the two

connected components of irrelevant feature removal
and redundant feature elimination. The former
obtains features relevant to the target concept by
eliminating irrelevant ones, and the latter removes
redundant features from relevant ones via choosing
representatives from different feature clusters, and
thus produces the final subset.
The irrelevant feature removal is
straightforward once the right relevance measure is
defined or selected, while the redundant feature
elimination is a bit of sophisticated. In our proposed
FAST algorithm, it involves 1) the construction of the
minimum spanning tree from a weighted complete
graph; 2) the partitioning of the MST into a forest
with each tree representing a cluster; and 3) the
selection of representative features from the clusters.
4.1 Load Data and Classify
Load the data into the process. The data has
to be preprocessed for removing missing values,
noise and outliers. Then the given dataset must be
converted into the arff format which is the standard
format for WEKA toolkit. From the arff format, only
the attributes and the values are extracted and stored
into the database. By considering the last column of
the dataset as the class attribute and select the distinct
class labels from that and classify the entire dataset
with respect to class labels.
4.2 Information Gain Computation
Relevant features have strong correlation
with target concept so are always necessary for a best
subset, while redundant features are not because their
values are completely correlated with each other.
Thus, notions of feature redundancy and feature
relevance are normally in terms of feature correlation
and feature-target concept correlation.
To find the relevance of each attribute with
the class label, Information gain is computed in this
module. This is also said to be Mutual Information
measure. Mutual information measures how much the
distribution of the feature values and target classes
differ from statistical independence. This is a
nonlinear estimation of correlation between feature
values or feature values and target classes. The
symmetric uncertainty (SU) is derived from the
mutual information by normalizing it to the entropies
of feature values or feature values and target classes,
and has been used to evaluate the goodness of
features for classification
The symmetric uncertainty is defined as follows:
𝐺𝑎𝑖𝑛 𝑋 𝑌 = 𝐻 𝑋 − 𝐻 𝑋 𝑌
= 𝐻(𝑌) − 𝐻(𝑌│𝑋)
To calculate gain, we need to find the entropy and
conditional entropy values. The equations for that are
given below:
𝐻 𝑋 = − 𝑝 𝑥 𝑙𝑜𝑔2 𝑝(𝑥)
𝑥∈𝑋
𝐻 𝑋 𝑌 = − 𝑝 𝑦 𝑝 𝑥 𝑦
𝑥𝜖𝑋𝑦𝜖𝑌
𝑙𝑜𝑔2 𝑝(𝑥|𝑦)
Where p(x) is the probability density function and p
(x|y) is the conditional probability density function.
4.3 T-Relevance Calculation
The relevance between the feature Fi € F and the
target concept C is referred to as the T-Relevance of
Fi and C, and denoted by SU(Fi,C). If SU(Fi,C) is
greater than a predetermined threshold, we say that Fi
is a strong T-Relevance feature.
𝑆𝑈 𝑋, 𝑌 =
2 × 𝐺𝑎𝑖𝑛 𝑋 𝑌
𝐻 𝑋 + 𝐻 𝑌
After finding the relevance value, the redundant
attributes will be removed with respect to the
threshold value.
4.4 F-Correlation Calculation
The correlation between any pair of features Fi
and Fj (Fi,Fj € ^ F ^ i ≠ j) is called the F-Correlation
of Fi and Fj, and denoted by SU(Fi, Fj). The equation
symmetric uncertainty which is used for finding the
relevance between the attribute and the class is again
applied to find the similarity between two attributes
with respect to each label.
4.5 MST Construction
With the F-Correlation value computed above,
the Minimum Spanning tree is constructed. For that,
we use Kruskal‟s algorithm which form MST
effectively.
Kruskal's algorithm is a greedy algorithm in
graph theory that finds a minimum spanning tree for a
connected weighted graph. This means it finds a
subset of the edges that forms a tree that includes
every vertex, where the total weight of all the edges
in the tree is minimized. If the graph is not connected,
then it finds a minimum spanning forest (a minimum
spanning tree for each connected component).
Description:
1. Create a forest F (a set of trees), where each
vertex in the graph is a separate tree.
2. Create a set S containing all the edges in the
graph
3. While S is nonempty and F is not yet spanning
 Remove an edge with minimum weight from S
 If that edge connects two different trees, then add
it to the forest, combining two trees into a single
tree

 Otherwise discard that edge.
At the termination of the algorithm, the
forest forms a minimum spanning forest of the graph.
If the graph is connected, the forest has a single
component and forms a minimum spanning tree. The
sample tree is as follows,
Fig 2. Correlations
ALGORITHM
_________________
inputs: D( 𝐹1, 𝐹2, ..., 𝐹𝑚, 𝐶) - the given data set
𝜃- the T-Relevance threshold.
output: S - selected feature subset .
//==== Part 1 : Irrelevant Feature Removal ====
1 for i = 1 to m do
2 T-Relevance = SU ( 𝐹𝑖, 𝐶)
3 if T-Relevance > 𝜃then
4 S = S ∪ { 𝐹𝑖};
//==== Part 2: Minimum Spanning Tree
Construction ====
5 G = NULL; //G is a complete graph
6 for each pair of features { 𝐹′ 𝑖, 𝐹′ 𝑗} ⊂ S do
7 F-Correlation = SU ( 𝐹′, 𝐹′ 𝑗)
8 𝐴𝑑𝑑𝐹′ 𝑖𝑎𝑛𝑑/ 𝑜𝑟𝐹′ 𝑗𝑡𝑜𝐺𝑤𝑖𝑡𝑕F-Correlation
𝑎𝑠𝑡𝑕𝑒𝑤𝑒𝑖𝑔𝑕𝑡𝑜𝑓𝑡𝑕𝑒𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔𝑒𝑑𝑔𝑒;
9 minSpanTree = KRUSKALS(G); //Using
KRUSKALS Algorithm to generate theminimum
spanning tree
//==== Part 3: Tree Partition and
Representative Feature Selection ====
10 Forest = minSpanTree
11 for each edge ∈Forest do
12 if
SU( 𝐹′ 𝑖, 𝐹′ 𝑗) <SU( 𝐹′ 𝑖, 𝐶) ∧SU( 𝐹′ 𝑖, 𝐹′ 𝑗) <SU( 𝐹′ 𝑗, 𝐶)
then
13 Forest = Forest − 𝐸𝑖𝑗
14 S = 𝜙
15 for each tree ∈Forest do
16 𝐹𝑗 𝑅= argmax 𝐹′ 𝑘∈𝑇𝑖SU( 𝐹′ 𝑘, 𝐶)
17 S = S ∪ { 𝐹𝑗𝑅};
18 returnS
In this tree, the vertices represent the
relevance value and the edges represent the F-
Correlation value. The complete graph G reflects the
correlations among all the target-relevant features.
Unfortunately, graph G has k vertices and k(k-1)/2
edges. For high-dimensional data, it is heavily dense
and the edges with different weights are strongly
interwoven. Moreover, the decomposition of
complete graph is NP-hard. Thus for graph G, we
build an MST, which connects all vertices such that
the sum of the weights of the edges is the minimum,
using the well knownKruskal algorithm. The weight
of edge (Fi`,Fj`) is F-Correlation SU(Fi`,Fj`).
4.6 Cluster Formation
After building the MST, in the third step, we first
remove the edges whose weights are smaller than
both of the T-Relevance SU(Fi`, C) and SU(Fj`, C),
from the MST. After removing all the unnecessary
edges, a forest Forest is obtained. Each tree Tj €
Forest represents a cluster that is denoted as V (Tj),
which is the vertex set of Tj as well. As illustrated
above, the features in each cluster are redundant, so
for each cluster V (Tj) we choose a representative
feature Fj R who‟s T-Relevance SU(Fj R,C) is the
greatest.
V. EXPERIMENTAL RESULTS
Fig 3.Dataset Loading
Fig 4. Dataset Conversion
Fig 5. Entropy & Gain Values

Fig 6. F- Correlation & Relevance
VI. CONCLUSION AND FUTURE
WORK
In this Project present a FAST clustering-
based feature subset selection algorithm for high
dimensional data. The algorithm involves 1)
removing irrelevant features, 2) constructing a
minimum spanning tree from relative ones, and 3)
partitioning the MST and selecting representative
features. In the proposed algorithm, a cluster consists
of features. Each cluster is treated as a single feature
and thus dimensionality is drastically reduced. The
text data from the four different aspects of the
proportion of selected features, run time,
classification accuracy of a given
classifier.Clustering-based feature subset selection
algorithm for high dimensional data. For the future
work, we plan to explore different types of
correlation measures, and study some formal
properties of feature space. In feature we are going to
classify the high dimensional data.
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