Customer lifetime value (LTV) is crucial to companies who are intending to adopt personalized promoting strategies to optimize the profits. However, LTV prediction in the scenario of online App advertising usually suffers from label sparsity issue, towards which existing methods designed complex model structures but ignored the information contained in intermediate user behaviors. Moreover, previous works mainly focus on fitting the overall LTV distribution, overlooking the fact that LTV in online App advertising consists of sources with diverse data distributions and thus resulting in sub-optimal solutions. In this paper, we propose a novel Progressive Tasks guided Multi-Source Network (PTMSN) to tackle the aforementioned problems. Specifically, a Cascaded Sub-task Module (CSM) is introduced to alleviate data sparsity by modeling reliance between explicit interactions and implicit monetization. In addition, as the overall LTV is assembled from multiple sources, we propose a divide-and-conquer scheme named Multi-source Integrating Module (MIM) to disentangle the original single target into several source distributions and model in a fine-grained manner. Extensive offline experiments on real-world industrial datasets compared to state-of-the-art baseline models validate the effectiveness of our approach. PTMSN has been successfully deployed in industrial online advertising system, serving various business scenarios and acquiring 2.97% absolute ROI gains.

K-Means algorithm is a popular clustering method. However, it has two limitations: 1) it gets stuck easily in spurious local minima, and 2) the number of clusters$k$has to be given a priori. To solve these two issues, a multi-prototypes convex merging based K-Means clustering algorithm (MCKM) is presented. First, based on the structure of the spurious local minima of the K-Means problem, a multi-prototypes sampling (MPS) is designed to select the appropriate number of multi-prototypes for data with arbitrary shapes. Then, a merging technique, called convex merging (CM), merges the multi-prototypes to get a better local minima without$k$being given a priori. Specifically, CM can obtain the optimal merging and estimate the correct$k$. By integrating these two techniques with K-Means algorithm, the proposed MCKM is an efficient and explainable clustering algorithm for escaping the undesirable local minima of K-Means problem without given$k$first. Two theoretical proofs are given to guarantee that the cost of MCKM (MPS+CM) can achieve a constant factor approximation to the optimal cost of the K-Means problem. Experimental results performed on synthetic and real-world data sets have verified the effectiveness of the proposed algorithm.