Paper:
The goal of lifetime clustering is to develop an inductive model that maps subjects into K clusters according to their underlying (unobserved) lifetime distribution. We introduce a neural-network based lifetime clustering model that can find cluster assignments by directly maximizing the divergence between the empirical lifetime distributions of the clusters. Accordingly, we define a novel clustering loss function over the lifetime distributions (of entire clusters) based on a tight upper bound of the two-sample Kuiper test p-value. The resultant model is robust to the modeling issues associated with the unobservability of termination signals, and does not assume proportional hazards. Our results in real and synthetic datasets show significantly better lifetime clusters (as evaluated by C-index, Brier Score, Logrank score and adjusted Rand index) as compared to competing approaches.

Review:
The authors propose an approach to cluster subjects into K clusters according to their underlying, often unknown, life distribution. The loss function to the neural-network-based approach is based on a tight upper bound to the two-sample Kuiper test. Experiments are conducted on artificial and two real life datasets.
I enjoyed reading the paper, the authors propose an approach to address an important yet relatively under-explored problem in survival analysis.
It is not entirely clear how to handle the case when after the model is trained, H^(u) for a new subject u is larger than t_max when the model is trained. In such case, \Chi^(u) will be negative, thus what happens with \beta^(u)(W_2)?
When the termination signals are not available (friendster data) termination signals are set artificially when training and evaluation, thus, is the model learning artificially set termination signals and thus artificial survival functions? what is the point of doing this? Moreover, if the termination signals are artificial, what is the point of calculating C-Index and Integrated Brier score? I understand the motivation to compare to existing methods, it is really not clear how meaningful they are at evaluating performance.
In general, using C-Index and Brier scores in the context of the presented application may be misleading (or non-applicable) because these metrics are usually applied to survival analysis scenarios where one seeks to estimate likelihood of survival or time to event (over a usually infinite time horizon). Here, \beta^(u)(W_2) is a function of \Chi^(u) which is known (also not comparable to survival analysis), artificially tied to a pre-specified time-horizon t_max, and not dependent on covariates as in survival analysis. Further, SSC-Bair and SSC-Gaynor are clustering models, how are survival estimates obtained for these?
In practice, how is K selected? based on the friendster results for K=2,3,4,5 they all seem to produce distinct clusters, so which one should be used? This raises a question: how are the clusters, their members or the number of clusters informing the use case? In the MIMIC III experiment, where events are observed, the model finds two clusters without strikingly different survival functions (relative to friendster). Can one really consider S_2 as the high-risk group? Can one get higher risk clusters with larger K?
Minor:
- A_i^(u) is missing from the definition in the training data.
- In Section 3.2, if \xi^(u) is shared, why the superscript indicating that is subject specific?