K-means clustering

K-means Is one of the simplest unsupervised learning algorithms that solve the well known clustering problem. The k-means algorithm takes the inputs parameter, k, and partitions a set of n objects into k cluster so that the resulting intracluster similarity is high but the intercluster similarity is low. Cluster similarity is measured in regard to the mean value of the objects in a cluster, which can be viewed as the cluster’s centroid or center of gravity.

Given K, the k-means algorithm is implemented in four steps:

• Partition objects into k nonempty subsets
• Compute seed points as the centroids of the clusters of the current partition(the centroid is the center, i.e., mean point, of the cluster)
• Assign each object to the cluster with the nearest seed point
• Go back to step 2, stop when no more new assignment 

Finally this algorithm aims at minimizing an objective function, in this case a mean squared error function is calculated as:
\[E=\sum\limits_{i=0}^{k}{{{\sum }_{p\in {{c}_{i}}}}\left| p-{{m}_{i}} \right|}\]

where E is the sum of the square error for all objects in the data set; p is the point in space representing a given object; and mi is the mean of cluster Ci (both p and mi are multidimensional).

Algorithm: k-means.

The k-means algorithm for partitioning, where each cluster’s center is represented by the mean value of the objects in the cluster.

Input:

K: the number of clusters,  

D: a data set containing n objects.

Output: A set of k cluster

Advantages: with a large number of variables, k-means may be computationally faster than hierarchical clustering (if k is small). K-means may produce tighter cluster than hierarchical clustering, especially if the cluster are globular.

Disadvantages:

·         Difficult in comparing the quality of the clusters produced.

·         Applicable only when mean is defined.

·         Need to specify k, the number of clusters, in advance.

·         Unable to handle noisy data and outliers.  

·         Not suitable to discover clusters with non-convex shapes. 

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Research Methodology - Objectives and Motivation of research

Research is common parlance refers to a research for knowledge. Once can also define research as a scientific and systematic search for pertinent information on a specific topic. In fact, research is an art of scientific investigation. The advanced Learner’s Dictionary of current English lays down the meaning of research as a “careful investigation or inquiry specially through search for new facts in any branch of knowledge”. Redman and Mory define research as a “Systematized efforts to gain new knowledge” some people considered research as a movement, a movement from the known to the unknown. It is actually a voyage of discovery. We all possess the vital instinct of inquisitiveness for when the unknown conforms us we wonder and our inquisitiveness make us probe and attain full and fuller understanding of the unknown. This inquisitiveness is the mother of all knowledge and the mother which man employs for obtaining the knowledge of whatever the unknown, can be termed as research.

Research is an academic activity and as such the term should be used in a technical sense. According to Clifford Woody research comprises defining and redefining problems, formulating hypothesis or suggested solutions; collecting, organizing and evaluating data; making deductions and reaching conclusions; and at last carefully testing the conclusions to determine whether they fit the formulating hypothesis.

Objectives of Research:

The purpose of research is to discover answers to questions through the application of scientific procedures. The main aim of research is to find out the truth which is hidden and which has not been discovered as yet. Though each research study has its own specific purpose, we may think of research objectives as falling into a number of following broad groupings:

1. To gain familiarity with a phenomenon or to achieve new insights into it

2. To portray accurately the characteristics of a particular individual, situation or a group

3. To determine the frequency with which something occurs or with which it is associated with something else

4. To test a hypothesis of a causal relationship between variables.

Motivation in Research

What makes people to undertake research? This is a question of fundamental importance. The possible motives for doing research may be either one or more of the following:

1. Desire to get a research degree along with its consequential benefits;

2. Desire to face the challenge in solving the unsolved problems, i.e., concern over practical problems initiates research;

3. Desire to get intellectual joy of doing some creative work;

4. Desire to be of service to society;

5. Desire to get respectability.

However, this is not an exhaustive list of factors motivating people to undertake research studies. Many more factors such as directives of government, employment conditions, curiosity about new things, desire to understand causal relationships, social thinking and awakening, and the like may as well motivate (or at times compel) people to perform research operations.

Reference:

Kothari, C.K. (2006), Research Methodology, Prentice-Hall of India (P) Limited, New Delhi.

 

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