Hi Alaa,

k-means clustering partitions data into k number of mutually exclusive clusters. These techniques assign each observation to a cluster by minimizing the distance from the data point to the mean or median location of its assigned cluster, respectively. 

In MATLAB, it is on instruction (kmeans), as shown in example: 

idx = kmeans(X,k)

performs k-means clustering to partition the observations of the n-by-p data matrix X into k clusters, and returns an n-by-1 vector (idx) containing cluster indices of each observation. Rows of X correspond to points and columns correspond to variables.

refer to like http://www.mathworks.com/help/stats/kmeans.html#bue6nb7-1

for more details.

Best Wishes

Salam

Thank you Mr. Salam Ismaeel,,

I have one question if you don't mind, can we use k-means to find the "k" itself? In other word, if the researcher does not known the best number of clusters that gather the observations, can k-means find it for him?

Hi,

no, you have to determine the number of clusters before using k-means. There is a lot of research (and even more discussion) on the issue of finding the "correct" number of clusters. It also depends on the software package you use. For example, SPSS tries to find the optimal number of clusters for you. In R, you can use different packages to find the optimal number of clusters. For example, the NbClust package provides several indices for this.

You can find a nice introduction into clustering (and classification) here: Rupp, A. A. (2013). Clustering and classification. In Little, T. (Ed.), The Oxford handbook of quantitative methods (pp. 517-550). New York: Oxford University Press.

And example of how clustering is used in educational research can be found here: Bahr, P. R., Bielby, R., & House, E. (2011). The use of cluster analysis in typological research on community college students. New Directions for Institutional Research, 2011(S1), 67–81. http://doi.org/10.1002/ir.417

One last comment: You write that "I don't like to know the statistical equations and complex algorithms involved in K-Means, I just want to use it, as education researcher."

This is legitimate to say, but you will only come so far without at least some basic understanding of how k-means works and what this means to data selection and preparation, and to the results you get from k-means.

Thank you Mr. Björn Fisseler,,

Your comment is very helpful and I am going to read the articles you mentioned!

By the way, I am a computer engineer before being an educational researcher :)

When I said, "I don't like to know the statistical equations and complex algorithms involved in K-Means" that does not mean I wont know the logical concepts of selecting the observations in K-means. I should definitely learn "how" and "when" to use such tool.

Anyway, your comment is appreciated and I am happy to hear more.

An easy way to select k is to make a loop for different values of k and select the min. error. e.g. 

for loop = 2: NumberOfClusters

      [idx, C, sumd, D] = kmeans(X,loop);

      S(Color, loop) = sumsqr(sumd);

end

and I got the fig. 

Yes, you could go for WSS and BSS, but there are several other methods to do this. Doug Steinley has published several papers on clusterings with k-means:

https://psychology.missouri.edu/steinleyd

Take a look at his paper on choosing the correct k:

Steinley, D., & Brusco, M. J. (2011). Testing for validity and choosing the number of clusters in K-means clustering. Psychological Methods, 16, 285-297.

It is not clear, why and where you want to use exactly this approach? It looks that it is not typically. For what? Have some specific problem? For data confidence assessment, for model validation or other?

Hello Mr. Egils Ginters,,

That what I am asking for, "What" and "When".

I heard about k-means years ago and I thought it would be good to consider this tool for educational statistics, along with other tools like regressions and Bayesian classification modeling.

It seems I should read a lot before answering these questions. However, for the first glance, I may say that k-means can be useful in model validation and I would like to learn this area in specific.

Aims are Aims and Tools are Tools, Mr. Stefan Sversky,,

When one come to study new field, he will surely try to make a connection between previous field and the new one. In most cases, the researchers in the old field will find this annoying, bothersome, troublesome and useless interruption. However, and in fact, this will enrich, fertilize and capitalize the old field. After a while, the old researchers will see the value of such tools, learn it and use it.

K-means clustering is just a tool, one may not use this tool in his course of research because his research does not need it. However, if the research, in fact, was best done by such tool, how would he use it if he don't know it??

I always say to myself, learn something new; you will need it one day.

Hi Alaa,

Many interesting research paper can be found here: Marković, M., Kostić Kovačević, I., Nikolić, O. and Nikolić, B. (2015), INSOS—educational system for teaching intelligent systems. Comput. Appl. Eng. Educ., 23: 268–276. doi: 10.1002/cae.21595

Best Wishes,

Kristijan

Many thanks Mr. Kristijan Kuk. I will read your recommended article.

Keep in mind that there is also fuzzy K-means algorythm :)