How can the weights effect whether the clustering will be fine or coarse?

Edited by author 10-09-2004 09:34 PM
Intuitively, it seems pretty dependant on the weight you chose. How dependant is it ? Do they (Sanjoy...) have new results explaining why the average linkage initialization is more efficient. And, what is it for actually ? (If possible, I'd like something else than your scale stuff Andrew ;) )

I'm curious to know what kinds of vision applications has this been used with. Clustering, of course, would be useful for a variety of vision-based tasks, but I'm finding it hard to think of something that would need specific hierarchical clustering.

I think the value of this method depends a lot on how important the tree is to you. Often the tree is just an artifact of the clustering method (e.g., Wards). Typically, one is only interested in a few levels because near the root, the groupings are too diverse to be meaningful and near the leaves you start losing track of things you want to keep together. For example, if you have 20 identical somethings, you don't care at all that this group can theoretically be split down 19 more times.

Given that, I think it would have been good for the authors to compare their method to standard industry pratices for combining Wards and K-means. They're working with such small datasets (n<1000) that it's very feasible to first cluster by Wards, stop at some level, then improve the result with K-means. You'd lose the hierarchy, but as mentioned, that's often of little interest. Or, they could split those clusters divisely to recover a new lower-portion of the tree if they wanted it, using their same cost metric. I would have liked to see a comparison of their method with this type of standard practice.

- Robin

What exactly do they mean by "hillclimbing"?

I would like to know more about the "cost function" and what it measures. maybe you could explain this by telling us more about the "yeast data" experiment. What is it and what is it trying to achieve?

Edited by author 10-12-2004 01:58 PM
I agree with the view of Robin that typically we are not interested in whole range of k. How do we choose w(k) which reflects our prior preference about some particular range of k, considering that even if w(k) is uniform, more emphasis is on smaller values of k.

The present reordering scheme may not remain optimal for arbitrary choices of w(k) (except the example mentioned in paper), so it would be interesting to explore the family of w(k) for which efficient alternatives could be devised.

This question is not directly related to this paper.
From the image segmentation and scene understanding point of view, norm in the cost function used here will probably correspond to euclidean distances in some feature space. Has there been any work to accomodate the importance of clusters representing some semantically meaningful objects? E.g. an image segment representing a person may consist of features which are not necesarily close to each other but together they form a meaningful cluster.

Sanjeev,

This general topic is an interesting one. The wards-error term is a compactness measure, equivalent to moment of inertia in physical objects. There are some assumptions implicit in this - one being that feature dimensions are orthogonal, something that's often not true in practice.

You can, however, use other error measures, including non-metric ones, with many clustering methods. For example, you can use Shannon entropy within clusters as an error measure. What you want in this case is to minimize surprisal within your clusters. Although non-euclidean, this error measure will work with Wards method, since all you need is a way to measure the increase in total error with each agglomeration step. Like moment of inertia, information-content is a multiple-linkage similarity measure, so it tends to encourage compact (rather than stringy) clusters.

- Robin

I also agree with Robin, that a key question here is whether we suspect our data to be structured hierarchically (i.e., do we care about the tree); and if so, what is the appropriate number of clusters.

However, based on vague intuition, I think that if their method was compared to a method which combines a hierarchical approach with the flat k-means approach they would lose. For their procedure must maintain a hierarchical structure, whereas a combined approach is allowed to relax this constraint. Since the metric they use to compare methods is the k-means cost function, it seems that a method that is allowed to minimize this cost function directly without constraints during part of its procedure should beat their method.

When assigning non-uniform weights to preference a particular level of granularity, does the hierarchy provide a way to automatically identify "interesting" inherent levels of granularity?

Perhaps this would involve calculating where small weight-changes would have little vs major impact?

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