Current approaches to game design improvements rely on time-consuming gameplay testing processes, which rely on highly subjective feedback from a target audience. In this paper, we propose a generalizable approach for building predictive models of players’ emotional reactions across different games and game genres, as well as other forms of digital stimuli. Our input agnostic approach relies on the following steps: (a) collecting players' physiologically-inferred emotional states during actual gameplay sessions, (b) extrapolating the causal relations between changes in players' emotional states and recorded game events, and (c) building hierarchical cluster models of players' emotional reactions that can later be used to infer individual player models via fuzzy cluster membership vectors. We expect this work to benefit game designers by accelerating the affective play-testing process through the offline simulation of players' reactions to game design adaptations, as well as to contribute towards individually-tailored affective gaming.

Regression mixture models are widely studied in statistics, machine learning and data analysis. Fitting regression mixtures is challenging and is usually performed by maximum likelihood by using the expectation-maximization (EM) algorithm. However, it is well-known that the initialization is crucial for EM. If the initialization is inappropriately performed, the EM algorithm may lead to unsatisfactory results. The EM algorithm also requires the number of clusters to be given a priori; the problem of selecting the number of mixture components requires using model selection criteria to choose one from a set of pre-estimated candidate models. We propose a new fully unsupervised algorithm to learn regression mixture models with unknown number of components. The developed unsupervised learning approach consists in a penalized maximum likelihood estimation carried out by a robust expectation-maximization (EM) algorithm for fitting polynomial, spline and B-spline regressions mixtures. The proposed learning approach is fully unsupervised: 1) it simultaneously infers the model parameters and the optimal number of the regression mixture components from the data as the learning proceeds, rather than in a two-fold scheme as in standard model-based clustering using afterward model selection criteria, and 2) it does not require accurate initialization unlike the standard EM for regression mixtures. The developed approach is applied to curve clustering problems. Numerical experiments on simulated data show that the proposed robust EM algorithm performs well and provides accurate results in terms of robustness with regard initialization and retrieving the optimal partition with the actual number of clusters. An application to real data in the framework of functional data clustering, confirms the benefit of the proposed approach for practical applications.

The Infinite Relational Model (IRM) is a probabilistic model for relational data clustering that partitions objects into clusters based on observed relationships. This paper presents Averaged CVB (ACVB) solutions for IRM, convergence-guaranteed and practically useful fast Collapsed Variational Bayes (CVB) inferences. We first derive ordinary CVB and CVB0 for IRM based on the lower bound maximization. CVB solutions yield deterministic iterative procedures for inferring IRM given the truncated number of clusters. Our proposal includes CVB0 updates of hyperparameters including the concentration parameter of the Dirichlet Process, which has not been studied in the literature. To make the CVB more practically useful, we further study the CVB inference in two aspects. First, we study the convergence issues and develop a convergence-guaranteed algorithm for any CVB-based inferences called ACVB, which enables automatic convergence detection and frees non-expert practitioners from difficult and costly manual monitoring of inference processes. Second, we present a few techniques for speeding up IRM inferences. In particular, we describe the linear time inference of CVB0, allowing the IRM for larger relational data uses. The ACVB solutions of IRM showed comparable or better performance compared to existing inference methods in experiments, and provide deterministic, faster, and easier convergence detection.

We consider point clouds obtained as random samples of a measure on a Euclidean domain. A graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points they connect. Our goal is to develop mathematical tools needed to study the consistency, as the number of available data points increases, of graph-based machine learning algorithms for tasks such as clustering. In particular, we study when is the cut capacity, and more generally total variation, on these graphs a good approximation of the perimeter (total variation) in the continuum setting. We address this question in the setting of $\Gamma$-convergence. We obtain almost optimal conditions on the scaling, as number of points increases, of the size of the neighborhood over which the points are connected by an edge for the $\Gamma$-convergence to hold. Taking the limit is enabled by a transportation based metric which allows to suitably compare functionals defined on different point clouds.

We consider a problem of grouping multiple graphs into several clusters using singular value thesholding and non-negative factorization. We derive a model selection information criterion to estimate the number of clusters. We demonstrate our approach using "Swimmer data set" as well as simulated data set, and compare its performance with two standard clustering algorithms.

As a well-known clustering algorithm, Fuzzy C-Means (FCM) allows each input sample to belong to more than one cluster, providing more flexibility than non-fuzzy clustering methods. However, the accuracy of FCM is subject to false detections caused by noisy records, weak feature selection and low certainty of the algorithm in some cases. The false detections are very important in some decision-making application domains like network security and medical diagnosis, where weak decisions based on such false detections may lead to catastrophic outcomes. They are mainly emerged from making decisions about a subset of records that do not provide enough evidence to make a good decision. In this paper, we propose a method for detecting such ambiguous records in FCM by introducing a certainty factor to decrease invalid detections. This approach enables us to send the detected ambiguous records to another discrimination method for a deeper investigation, thus increasing the accuracy by lowering the error rate. Most of the records are still processed quickly and with low error rate which prevents performance loss compared to similar hybrid methods. Experimental results of applying the proposed method on several datasets from different domains show a significant decrease in error rate as well as improved sensitivity of the algorithm.

Spectral clustering is a standard approach to label nodes on a graph by studying the (largest or lowest) eigenvalues of a symmetric real matrix such as e.g. the adjacency or the Laplacian. Recently, it has been argued that using instead a more complicated, non-symmetric and higher dimensional operator, related to the non-backtracking walk on the graph, leads to improved performance in detecting clusters, and even to optimal performance for the stochastic block model. Here, we propose to use instead a simpler object, a symmetric real matrix known as the Bethe Hessian operator, or deformed Laplacian. We show that this approach combines the performances of the non-backtracking operator, thus detecting clusters all the way down to the theoretical limit in the stochastic block model, with the computational, theoretical and memory advantages of real symmetric matrices.

Intratumor heterogeneity is often manifested by vascular compartments with distinct pharmacokinetics that cannot be resolved directly by in vivo dynamic imaging. We developed tissue-specific compartment modeling (TSCM), an unsupervised computational method of deconvolving dynamic imaging series from heterogeneous tumors that can improve vascular phenotyping in many biological contexts. Applying TSCM to dynamic contrast-enhanced MRI of breast cancers revealed characteristic intratumor vascular heterogeneity and therapeutic responses that were otherwise undetectable.

This paper considers networks where relationships between nodes are represented by directed dissimilarities. The goal is to study methods for the determination of hierarchical clusters, i.e., a family of nested partitions indexed by a connectivity parameter, induced by the given dissimilarity structures. Our construction of hierarchical clustering methods is based on defining admissible methods to be those methods that abide by the axioms of value - nodes in a network with two nodes are clustered together at the maximum of the two dissimilarities between them - and transformation - when dissimilarities are reduced, the network may become more clustered but not less. Several admissible methods are constructed and two particular methods, termed reciprocal and nonreciprocal clustering, are shown to provide upper and lower bounds in the space of admissible methods. Alternative clustering methodologies and axioms are further considered. Allowing the outcome of hierarchical clustering to be asymmetric, so that it matches the asymmetry of the original data, leads to the inception of quasi-clustering methods. The existence of a unique quasi-clustering method is shown. Allowing clustering in a two-node network to proceed at the minimum of the two dissimilarities generates an alternative axiomatic construction. There is a unique clustering method in this case too. The paper also develops algorithms for the computation of hierarchical clusters using matrix powers on a min-max dioid algebra and studies the stability of the methods proposed. We proved that most of the methods introduced in this paper are such that similar networks yield similar hierarchical clustering results. Algorithms are exemplified through their application to networks describing internal migration within states of the United States (U.S.) and the interrelation between sectors of the U.S. economy.

We use a semisupervised learning algorithm based on a topological data analysis approach to assign functional categories to yeast proteins using similarity graphs. This new approach to analyzing biological networks yields results that are as good as or better than state of the art existing approaches.