Page 230 - Special Topic Session (STS) - Volume 1

STS426 Tanuka C.
relative to Local Group Centroid with apex parameters ( ), Morphological

Type (T), Heliocentric Radial Velocity ( ), Amplitude of rotational velocity ( )

ℎ
adjusted to inclination (), HI line width ( ). They are used to study the
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properties of the coherent groups of galaxies, once identified. Also Star
Formation Efficiency parameter ( = /) has been computed for
studying the property of the groups.
Since we have used a reduced data set from an original data set of ?, it
requires a checking for completeness. For this purpose we have performed
/ test. The test was first used by ? for studying space distribution of a
complete sample of radio quasars from 3 catalogue. According to this test

let be the limiting flux of a survey data. Two colours () = 4 3 and

3 3
= 4 are defined where r is the radial distance and is the maximum

3
distance observed. If the distribution of object is uniform then V =Vmax is
uniformly distributed over [0,1], then < / > = 0.5. Accordingly we have
computed < / > of several significant parameters (e.g. , distance D,
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etc.) and they are all close to ~ 0.3 - 0.6 i.e. the present data set used is

complete up to an accuracy of 60% - 80%.

3. Overview of The Statistical Methods
Cluster Analysis (CA) is the art of finding homogeneous (in terms of some
parameters) groups that are already present in the data. It is to be noted that
according to physical notation we have denoted variables by parameters. We
start this section with a coherent review of K-means Cluster Analysis;
discussing its merits, demerits and why we choose not to use it in our present
work. Then we proceed to the extensive discussion on Model-Based Clustering
methods (MBC); the method that has been employed in the present study.

3.1 The K-Means Cluster Analysis
The K-Means Algorithm (?) is one of the simplest unsupervised learning
algorithms which tries to partition a given set of points/observations into
K clusters, such that the points within each of the clusters tend to be near
each other in term of some distance measure. Most commonly this
distance is taken to be the “Euclidean Distance" with either standardized
or non-standardized observations. K-Means has been used in many
disciplines. It is very much popular for Astronomical datasets as well.
The algorithm aims at minimizing an objective function, known as
Squared-Error Function given as follows:

2
= ∑ ∑ ∥ − ∥ (3)

=1 =1

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