The goal of cluster analysis in survival data is to identify clusters that are decidedly associated with the survival outcome. Previous research has explored this problem primarily in the medical domain with relatively small datasets, but the need for such a clustering methodology could arise in other domains with large datasets, such as social networks. Concretely, we wish to identify different survival classes in a social network by clustering the users based on their lifespan in the network. In this paper, we propose a decision tree based algorithm that uses a global normalization of @math -values to identify clusters with significantly different survival distributions. We evaluate the clusters from our model with the help of a simple survival prediction task and show that our model outperforms other competing methods.
In order to overcome this issue, Gaynor and Bair @cite_34 proposed supervised sparse clustering as a modification to the sparse clustering algorithm of Witten and Tibshirani @cite_31 . The sparse clustering algorithm uses an objective function similar to k-means but with the modification that each feature has a weight associated to it. Supervised sparse clustering @cite_34 initializes these feature weights depending on the feature's relation with the survival outcome and optimizes the same objective function. Once again, they use Cox scores @cite_19 to quantify the effect of each feature on the survival outcome. The authors show that this leads to a clustering that is relatively more linked to the survival outcome.
@cite_19 @cite_31 @cite_34
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The analysis of censored failure times is considered. It is assumed that on each individual arc available values of one or more explanatory variables. The hazard function (age-specific failure rate) is taken to be a function of the explanatory variables and unknown regression coefficients multiplied by an arbitrary and unknown function of time. A conditional likelihood is obtained, leading to inferences about the unknown regression coefficients. Some generalizations are outlined. We consider the problem of clustering observations using a potentially large set of features. One might expect that the true underlying clusters present in the data differ only with respect to a small fraction of the features, and will be missed if one clusters the observations using the full set of features. We propose a novel framework for sparse clustering, in which one clusters the observations using an adaptively chosen subset of the features. The method uses a lasso-type penalty to select the features. We use this framework to develop simple methods for sparse K-means and sparse hierarchical clustering. A single criterion governs both the selection of the features and the resulting clusters. These approaches are demonstrated on simulated and genomic data.