Localized Data Fusion for Kernel k-Means Clustering with Application to Cancer Biology
In many modern applications from, for example, bioinformatics and computer vision, samples have multiple feature representations coming from different data sources. Multiview learning algorithms try to exploit all these available information to obtain a better learner in such scenarios. In this paper, we propose a novel multiple kernel learning algorithm that extends kernel k-means clustering to the multiview setting, which combines kernels calculated on the views in a localized way to better capture sample-specific characteristics of the data. We demonstrate the better performance of our localized data fusion approach on a human colon and rectal cancer data set by clustering patients. Our method finds more relevant prognostic patient groups than global data fusion methods when we evaluate the results with respect to three commonly used clinical biomarkers.
This paper generalizes multi-kernel k-means clustering (solved via relaxation) to the case where each clustered item (here, a person) gets an item-specific set of weights over the multiple kernels, rather than the traditional, shared, global weighting of the kernels. Using TCGA (cancer) data, with 3 modalities, they demonstrate that this generalization yields better clusterings than the traditional (global approach), when measured against 3 "bronze standard" clusterings arising from known clinical clusters.The writing is clear, making for an easy read.Although this is a somewhat incremental-seeming tweak, I think it was clever, with the potential to actually be used (rather than lost in the NIPS archives), and therefore of some significance. Other comments:In the introduction you mention that k-means is susceptible to local minima, and then use this to motivate the relaxation approach. However, as described on p3, even the relaxation approach ends up using k-means clustering, so this is a little puzzling to the reader.Following on my previous comment, it would seem that your approach is sensitive to initialization, and susceptible to local minima. Please make clear if this is true or not, and if it is, please explain how you deal with this issue (in your, and the other algorithms) in the experimental section.Also, why not use a naturally continuous-valued clustering like mixture of Gaussians, rather than the hard version of it of k-means? On p. 5 you discuss "computational effort" and doing things "more efficiently". Please give the time complexity for the various algorithms being discussed so that the reader can appreciate these points. Similarly, you mention the notion of time complexity in the Discussion, but not any actual time complexities.Following on the last point, what is the largest data set you expect to be able to handle with the current algorithm. 204 patients is rather small for current genomics data sets (and other data sets).  As a point of reference, please give a timing for your experiments.Concluding the success of the algorithm on the basis of one experiment, while not unusual for NIPS, is a little weak. Would be great if you could add in further experiments, not to mention some with a ground truth for objective comparison, if possible.You use always only 2 clusters, but it would be interesting to know if your model is just as amenable to model selection (i.e. # of clusters) as other methods. Presumably so, but would be good to know.p. 6 "aligned to each other"--slightly odd phrasing, but I eventually understood by looking at the figures. Similarly so the "nine biomarker-metric pairs".p.7 would be good if you annotated the tie with non-bold (maybe with a *), as I was confused for a while about where the 8/9 things were, until I realized there was a tie.