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SVMs can generate a confidence score which is basically like a probability for a particular data item to belong to the particular class. I want to use this probability as a proxy for the 'distance' of the data-item from the cluster. The distance will be further used for estimating the class cohesiveness using the silhouette width.

I wanted to take the view of other experienced members if the approach of taking the probability generated by SVM will be correct as a proxy for the distance measure. I have generally seen gaussian functions being used for this purpose.

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If I understood your question correctly, you are performing multi-class classification with an SVM at hand, but, are calling/viewing this multi-class setting as clusters. Which then explains your use of the terms 'distance to the cluster (center)'.

"... 'distance' of the data-item from the cluster."

My answer to your question

if the approach of taking the probability generated by SVM will be correct as a proxy for the distance measure

is: No. Read on for the 'why' part.

In my opinion, to answer your question, briefly recounting SVMs as against clustering should help. SVMs work with separating hyperplanes, because it has the knowledge of the class-labels beforehand. On the contrary, any clustering technique, in absence of this knowledge, looks for cluster centers and hence is bothered about the distance of any data point from its corresponding cluster center. The hyperplane is nowhere giving you information about where this cluster center lies, so, it won't be correct to use the confidence measure from SVMs as a distance measure from the cluster center, certainly not for estimating the class cohesiveness. This could rather be done by visualizing the class/cluster if that is possible. Distances between data points can not be known from SVMs directly, all it can tell you is w.r.t. the learnt separating hyperplane -- which side of the hyperplane and how far from it.

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  • $\begingroup$ I am still not very clear as to why it (confidence score from SVM) wouldn't give a measure of how strongly does a datapoint belong to the given class. What else does the confidence score stand for? $\endgroup$ – TheBlueNotebook Sep 25 '14 at 3:12
  • $\begingroup$ The confidence score does give a measure of how strongly does a datapoint belong to the given class, but that is, as I said before, w.r.t. the hyperplane and not taking into account, explicitly, where the other data points lie. In other words, the distances between the data points are not considered. In the statement "won't be correct to use the confidence measure from SVMs as a distance measure from the cluster center", clearly, my answer is No for using it as such a distance measure from the cluster centre. Because, from SVM, you also don't have any information about the cluster center. $\endgroup$ – SPN Sep 25 '14 at 7:46
  • $\begingroup$ Visualizing with figures about what SVM does/tells you and what you wish to achieve will certainly help the discussion more. I could have done that but for want of time. Hopefully, I still managed to put forth my point. Last, if the answer is useful, may be you can +1 it! ;) $\endgroup$ – SPN Sep 25 '14 at 9:19
  • $\begingroup$ I would have loved to, but I do not have enough reputation on the stats SO, yet. $\endgroup$ – TheBlueNotebook Sep 25 '14 at 16:26
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Support Vectors are not "central" vectors of your data set.

Instead, they are borderline cases.

Similarly, the confidence score of SVM does not measure how typical an object is; but mostly how far away from the other class it is.

Consider this example from Wikipedia (https://commons.wikimedia.org/wiki/File:Linear-svm-scatterplot.svg):

https://commons.wikimedia.org/wiki/File:Linear-svm-scatterplot.svg

An object at (100,100) - way out of the picture - would have a 1.0 score for being in the "white" class. But that does not at all mean the object is "central" to that class. Only that is substantially far away from the other class.

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  • $\begingroup$ Got it. I was interpreting the term confidence score in an entirely different manner I guess. Thank you for clarifying. $\endgroup$ – TheBlueNotebook Sep 25 '14 at 16:29

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