The classification of time series data is a challenge common to all data-driven fields. However, there is no agreement about which are the most efficient techniques to group unlabeled time-ordered data. This is because a successful classification of time series patterns depends on the goal and the domain of interest, i.e. it is application-dependent. In this article, we study free-to-play game data. In this domain, clustering similar time series information is increasingly important due to the large amount of data collected by current mobile and web applications. We evaluate which methods cluster accurately time series of mobile games, focusing on player behavior data. We identify and validate several aspects of the clustering: the similarity measures and the representation techniques to reduce the high dimensionality of time series. As a robustness test, we compare various temporal datasets of player activity from two free-to-play video-games. With these techniques we extract temporal patterns of player behavior relevant for the evaluation of game events and game-business diagnosis. Our experiments provide intuitive visualizations to validate the results of the clustering and to determine the optimal number of clusters. Additionally, we assess the common characteristics of the players belonging to the same group. This study allows us to improve the understanding of player dynamics and churn behavior.

Reducing user attrition, i.e. churn, is a broad challenge faced by several industries. In mobile social games, decreasing churn is decisive to increase player retention and rise revenues. Churn prediction models allow to understand player loyalty and to anticipate when they will stop playing a game. Thanks to these predictions, several initiatives can be taken to retain those players who are more likely to churn. Survival analysis focuses on predicting the time of occurrence of a certain event, churn in our case. Classical methods, like regressions, could be applied only when all players have left the game. The challenge arises for datasets with incomplete churning information for all players, as most of them still connect to the game. This is called a censored data problem and is in the nature of churn. Censoring is commonly dealt with survival analysis techniques, but due to the inflexibility of the survival statistical algorithms, the accuracy achieved is often poor. In contrast, novel ensemble learning techniques, increasingly popular in a variety of scientific fields, provide high-class prediction results. In this work, we develop, for the first time in the social games domain, a survival ensemble model which provides a comprehensive analysis together with an accurate prediction of churn. For each player, we predict the probability of churning as function of time, which permits to distinguish various levels of loyalty profiles. Additionally, we assess the risk factors that explain the predicted player survival times. Our results show that churn prediction by survival ensembles significantly improves the accuracy and robustness of traditional analyses, like Cox regression.

In this paper we study nonconvex and nonsmooth multi-block optimization over Riemannian manifolds with coupled linear constraints. Such optimization problems naturally arise from machine learning, statistical learning, compressive sensing, image processing, and tensor PCA, among others. We develop an ADMM-like primal-dual approach based on decoupled solvable subroutines such as linearized proximal mappings. First, we introduce the optimality conditions for the afore-mentioned optimization models. Then, the notion of $\epsilon$-stationary solutions is introduced as a result. The main part of the paper is to show that the proposed algorithms enjoy an iteration complexity of $O(1/\epsilon^2)$ to reach an $\epsilon$-stationary solution. For prohibitively large-size tensor or machine learning models, we present a sampling-based stochastic algorithm with the same iteration complexity bound in expectation. In case the subproblems are not analytically solvable, a feasible curvilinear line-search variant of the algorithm based on retraction operators is proposed. Finally, we show specifically how the algorithms can be implemented to solve a variety of practical problems such as the NP-hard maximum bisection problem, the $\ell_q$ regularized sparse tensor principal component analysis and the community detection problem. Our preliminary numerical results show great potentials of the proposed methods.

Background: A universal unanswered question in neuroscience and machine learning is whether computers can decode the patterns of the human brain. Multi-Voxels Pattern Analysis (MVPA) is a critical tool for addressing this question. However, there are two challenges in the previous MVPA methods, which include decreasing sparsity and noise in the extracted features and increasing the performance of prediction. Methods: In overcoming mentioned challenges, this paper proposes Anatomical Pattern Analysis (APA) for decoding visual stimuli in the human brain. This framework develops a novel anatomical feature extraction method and a new imbalance AdaBoost algorithm for binary classification. Further, it utilizes an Error-Correcting Output Codes (ECOC) method for multiclass prediction. APA can automatically detect active regions for each category of the visual stimuli. Moreover, it enables us to combine homogeneous datasets for applying advanced classification. Results and Conclusions: Experimental studies on 4 visual categories (words, consonants, objects and scrambled photos) demonstrate that the proposed approach achieves superior performance to state-of-the-art methods.

In this paper, we have derived a set of sufficient conditions for reliable clustering of data produced by Bernoulli Mixture Models (BMM), when the number of clusters is unknown. A BMM refers to a random binary vector whose components are independent Bernoulli trials with cluster-specific frequencies. The problem of clustering BMM data arises in many real-world applications, most notably in population genetics where researchers aim at inferring the population structure from multilocus genotype data. Our findings stipulate a minimum dataset size and a minimum number of Bernoulli trials (or genotyped loci) per sample, such that the existence of a clustering algorithm with a sufficient accuracy is guaranteed. Moreover, the mathematical intuitions and tools behind our work can help researchers in designing more effective and theoretically-plausible heuristic methods for similar problems.

Understanding player behavior is fundamental in game data science. Video games evolve as players interact with the game, so being able to foresee player experience would help to ensure a successful game development. In particular, game developers need to evaluate beforehand the impact of in-game events. Simulation optimization of these events is crucial to increase player engagement and maximize monetization. We present an experimental analysis of several methods to forecast game-related variables, with two main aims: to obtain accurate predictions of in-app purchases and playtime in an operational production environment, and to perform simulations of in-game events in order to maximize sales and playtime. Our ultimate purpose is to take a step towards the data-driven development of games. The results suggest that, even though the performance of traditional approaches such as ARIMA is still better, the outcomes of state-of-the-art techniques like deep learning are promising. Deep learning comes up as a well-suited general model that could be used to forecast a variety of time series with different dynamic behaviors.

Radiomics aims to extract and analyze large numbers of quantitative features from medical images and is highly promising in staging, diagnosing, and predicting outcomes of cancer treatments. Nevertheless, several challenges need to be addressed to construct an optimal radiomics predictive model. First, the predictive performance of the model may be reduced when features extracted from an individual imaging modality are blindly combined into a single predictive model. Second, because many different types of classifiers are available to construct a predictive model, selecting an optimal classifier for a particular application is still challenging. In this work, we developed multi-modality and multi-classifier radiomics predictive models that address the aforementioned issues in currently available models. Specifically, a new reliable classifier fusion strategy was proposed to optimally combine output from different modalities and classifiers. In this strategy, modality-specific classifiers were first trained, and an analytic evidential reasoning (ER) rule was developed to fuse the output score from each modality to construct an optimal predictive model. One public data set and two clinical case studies were performed to validate model performance. The experimental results indicated that the proposed ER rule based radiomics models outperformed the traditional models that rely on a single classifier or simply use combined features from different modalities.

By exploiting the property that the RBM log-likelihood function is the difference of convex functions, we formulate a stochastic variant of the difference of convex functions (DC) programming to minimize the negative log-likelihood. Interestingly, the traditional contrastive divergence algorithm is a special case of the above formulation and the hyperparameters of the two algorithms can be chosen such that the amount of computation per mini-batch is identical. We show that for a given computational budget the proposed algorithm almost always reaches a higher log-likelihood more rapidly, compared to the standard contrastive divergence algorithm. Further, we modify this algorithm to use the centered gradients and show that it is more efficient and effective compared to the standard centered gradient algorithm on benchmark datasets.

The methodology of community detection can be divided into two principles: imposing a network model on a given graph, or optimizing a designed objective function. The former provides guarantees on theoretical detectability but falls short when the graph is inconsistent with the underlying model. The latter is model-free but fails to provide quality assurance for the detected communities. In this paper, we propose a novel unified framework to combine the advantages of these two principles. The presented method, SGC-GEN, not only considers the detection error caused by the corresponding model mismatch to a given graph, but also yields a theoretical guarantee on community detectability by analyzing Spectral Graph Clustering (SGC) under GENerative community models (GCMs). SGC-GEN incorporates the predictability on correct community detection with a measure of community fitness to GCMs. It resembles the formulation of supervised learning problems by enabling various community detection loss functions and model mismatch metrics. We further establish a theoretical condition for correct community detection using the normalized graph Laplacian matrix under a GCM, which provides a novel data-driven loss function for SGC-GEN. In addition, we present an effective algorithm to implement SGC-GEN, and show that the computational complexity of SGC-GEN is comparable to the baseline methods. Our experiments on 18 real-world datasets demonstrate that SGC-GEN possesses superior and robust performance compared to 6 baseline methods under 7 representative clustering metrics.

Plain vanilla K-means clustering is prone to produce unbalanced clusters and suffers from outlier sensitivity. To mitigate both shortcomings, we formulate a joint outlier detection and clustering problem, which assigns a prescribed number of datapoints to an auxiliary outlier cluster and performs cardinality-constrained K-means clustering on the residual dataset. We cast this problem as a mixed-integer linear program (MILP) that admits tractable semidefinite and linear programming relaxations. We propose deterministic rounding schemes that transform the relaxed solutions to feasible solutions for the MILP. We also prove that these solutions are optimal in the MILP if a cluster separation condition holds.