Hi,

    K-mean is a clustering technique used to grouped similar petterns in given features. Kindly, let me know what type of dataset you have and what would you like to do from that dataset.

looking to hear from you.

regards

Muddsair

Dear Sarpras,

If you use just two features/attributes, then Amirehsan's answer is true. Otherwise, you can try Sammon Mapping for creating visualization that plot multiple attributes into two axis (2 dimesion). 

These articles and papers may be useful for you:

Sammon Mapping

• Simple Explanation (http://en.wikipedia.org/wiki/Sammon_mapping)
• Paul Henderson (http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/AV0910/henderson.pdf)

You can also try some tools to implement this visualization:

Sammon Mapping Tools

• Matlab: Fuzzy Clustering Toolbox (http://www.abonyilab.com/software-and-data/fclusttoolbox), also its documentation (http://www.abonyilab.com/software-and-data/fclusttoolbox/fuzzyclusteringtoolbox.pdf?attredirects=0)
• R Project (http://stat.ethz.ch/R-manual/R-devel/library/MASS/html/sammon.html)
• C# (http://www.codeproject.com/Articles/43123/Sammon-Projection)

Good luck

plotting your data points on an XY plane is only possible when you have 2 dimensional data samples, in which case it doesnt matter which dimension is represented by the X or Y axis as long as you are consistent. However, there is no theoretical limit to the the dimensionality of data K-means clustering can be used for (I have gone as high as 24,000 dimensions), which also means that unless you apply a dimension reduction  technique, you have to represent each dimension with an axis.

There are some interesting parallels between k-means and location analysis that makes the interpretation question you ask very clear / nice. Suppose the N cases have 2 attributes X and Y measured as Cartesian coordinates. In this special case where X and Y are for example from spatial coordinates -- sometimes called Easting and Northing, or you could use UTM coordinates, or state plane as the basis for your spatial coordinates; (be careful LAT and LON are not good; why? ... spherical coordinates).

Notice then that the distance between the points is a metric that matches your intuition that near points are more similar, and hence more likely to end up in the same cluster. Then the k-means represent points in this 2-space that are the centers of clusters of nodes -- with the characteristic that they minimize the sum of squared distance deviations of the points in each cluster from the assigned cluster "centroid."  You can make a reasonable location solution for k facilities using the k-means algorithm, provided you are careful with units, as well of course as being aware of the distinction between medians and centroids (another topic).

So how do we generalize --- the X and Y might be some other non-spatial attribute in which case we lose the spatial or geographical image but we still regard the centroids as representative of the points clustered or assigned to each cluster -- a diagram with X and Y and the clusters might still make sense.

If we have more than 2 dimensions, we may be able to do some reduction to recover a reasonable "map" of the points on a 2-D plot (there are multivariate statistical methods for this.) Check out the idea of "multidimensional scaling."

Thank you for such brief answer.

My data is mainly a time domain data. for better visualization i am attaching file.The Data file is detail of data i am try to cluster. I am trying to cluster cell with their time of spiking. In the graph i am showing result of k-means.

I want to know that what is the axis stand for?

How do i locate the cell 1-15 data point in that clustering graph, i.e which point is stand for cell?

The 2-D plot (on the right) is the projection of the points onto the PC1, PC2 plane.

Note that the clusters are still reasonable --- they separate out into bundles or clusters.... but there is one point at (4,30) which appears to have a symbol belonging to the right side cluster BUT in this projection appears to be closer to the other clusters. This is simply an artifact of trying to show 3-D points in 2-D.  It might be worth trying to plot the cluster means in 3-D. Your original question didn't mention 3-D?

There is a paper (by myself) on RG about the use of cluster for hub location -- with a bit of imagination I could see it having a temporal interpretation! The weights of the strength of the interaction could be a function of the time lag between them?

https://www.researchgate.net/publication/226692211_A_clustering_approach_to_the_planar_hub_location_problem

See especially Figure 1 of that paper which shows the cluster centroids ("means") and interprets the effect of a weighting on pull these centroids to new locations.

A related paper on spatial analysis and GIS (which has a cluster example), will be posted shortly at: https://www.researchgate.net/publication/263389755_Spatial_Analysis_and_GIS

Best wishes...

Article A Clustering Approach to the Planar Hub Location Problem

Chapter Spatial Analysis and GIS

Sarpras: By the way, thanks for your sample data which I am going to examine. Would I be correct in guessing that PC1 PC2, PC3 refers to principal component scores ?  i,e. have you already reduced the multiple cell measures to some key components? Sorry -- I am just guessing based on the names -- I do not know your field. Is there larger data series?

MOK

Morton E. O'Kelly: Thank You for the Advice. \Yes there are very large data series. Before making cluster i used PCA technique and then use k-means. All these done by Matlab programming. Some of my data are  like 30X1500 dimension, where 30 are cells and all monitored for 1500 sec. I want to cluster the cell as per their behavior with time response.

In fact, you could perform a k-means at once, and and perform a PCA to use the first 2 or 3 PC to visualize your data.

I'm not very clear here yet, you say large data, 30x1500 dimension, but then say 30 cells monitored for 1500 seconds. If you monitor each cell for 1 value then you have only 2 dimensional data, for each cell you have a value and a time - which is in your 'xls' file. You have 30 sets of 2-D data which is somewhat different from multi-dimensional data. (Obviously if you monitor more than one value in each cell you have more dimensions.)

You also say that you 'represent k-means graphically' - what does this mean? Which k-means outputs are you plotting?

What I think you are trying to do:

If you are trying to cluster cells that have similar values at a similar time, then try something like plotting time on the x-axis, cell value on the y-axis and you will visually see the groups. So what you want to do then is automatically group them using k-means clustering.

In that 2-D plot k-means will group data that is close into a cluster. (It will do the same with multi-dimensional data) thus, if something spikes in value at a particular time it will be far from those that didn't (higher up the y-axis)

The k-means output is a list of the cluster assigment for each data sample, row, of your input. To find which cells have similar values at a similar time you need to enter every reading as a cell value and a time per row, not as 30 cell values per row. In this way the data will appear on the plot (in the data space) in groups.

1. reshape your 'xls' data to 3 columns: cell reading, time, cell number.

2. Run k-means using the first two columns, cell reading and time - any similar readings at a similar time should be clustered

3. append the k-means 'idx' output to your data file and you have an array with the 4 columns, cell reading, time, cell number, cluster number.

4. cells which spike at the same time will be in the same cluster, plot the cluster number against the cell readings (or mean of cell readings within that cluster or something) and you should see which clusters have a high 'spike' value.

5. find all the data sample in that cluster and you have the cell number and time of all the samples in that cluster.

From there it is simple to trace any data sample you like.

If you do actually have multi-dimensional data then the principles are the same, but you will have more columns of cell readings, k-means will still return a cluster index list.

I think you might be over simplifying your problem if you want to cluster cells with their behavious in time, do you want all those that rise or fall at the same time to be clustered? all those that spike at a similar time? all those that change behaviour at a similar time etc... clustering only groups similar values in data space, you may still need to create that data space.

I'm also not really sure why you need to use clustering here, try this:

Plot the data, 1st image, and we see 2, or 3 traces have spikes.

Now calculate the differences in the data using the 'diff' command and plot, you get image 2.

The traces with 'large' values in the 'diff' array are the spikey traces.

To find the actual spike, look for the large values in the 'diff' array.

If you insist on using clustering, then cluster on the 'diff' array - put all the diff values in a single column and run your clustering the high values will group together, the low values will group together. Again, track which sample the k-means output applies to.

Hope that helps somewhat?

I had a look at your data, and I think you should be clear about how you intend to represent your cells. I 4hink your best option is to represent your cells with a vector of 29 dimensions. Each dimension will represent the spikes recorded at the respective time. I dont think you can visualise a 29 dimension data, but the clustering will be effective. Dont worry too much about visualisation but if it is important, you can apply a dimension reduction technique to reduce the dimension to 3 for visualisation.

For more than 2-D visualization, you may use a dimensional reduction, like PCA for instance

I agree with the previous answer. The goal of 2D visualization is to help the clusters interpretation. Then the visualization has to be in a well defined 2D subspace: PCA is a good candidate.

If you want to increase the importance of small distances (local neighborhood), you can build a graph of these neighbors (with a distance threshold) and visualise it through a unix command like "neato" provided by the "graphviz" package.

But the X and Y axes are less well-defined in that case.