We propose a genetic-based expectation-maximization (GA-EM) algorithm for learning Gaussian mixture models from multivariate data. This algorithm is capable of selecting the number of components of the model using the minimum description length (MDL) criterion. Our approach benefits from the properties of Genetic algorithms (GA) and the EM algorithm by combination of both into a single procedure. The population-based stochastic search of the GA explores the search space more thoroughly than the EM method. Therefore, our algorithm enables escaping from local optimal solutions since the algorithm becomes less sensitive to its initialization. The GA-EM algorithm is elitist which maintains the monotonic convergence property of the EM algorithm. The experiments on simulated and real data show that the GA-EM outperforms the EM method since: 1) We have obtained a better MDL score while using exactly the same termination condition for both algorithms. 2) Our approach identifies the number of components which were used to generate the underlying data more often than the EM algorithm.

Although nonnegative matrix factorization (NMF) favors a sparse and part-based representation of nonnegative data, there is no guarantee for this behavior. Several authors proposed NMF methods which enforce sparseness by constraining or penalizing the ℓ1normal-norm of the factor matrices. On the other hand, little work has been done using a more natural sparseness measure, the ℓ0normal-pseudonormal-norm. In this paper, we propose a framework for approximate NMF which constrains the ℓ0normal-norm of the basis matrix, or the coefficient matrix, respectively. For this purpose, techniques for unconstrained NMF can be easily incorporated, such as multiplicative update rules, or the alternating nonnegative least-squares scheme. In experiments we demonstrate the benefits of our methods, which compare to, or outperform existing approaches.

One of the central themes in Sum-Product networks (SPNs) is the interpretation of sum nodes as marginalized latent variables (LVs). This interpretation yields an increased syntactic or semantic structure, allows the application of the EM algorithm and to efficiently perform MPE inference. In literature, the LV interpretation was justified by explicitly introducing the indicator variables corresponding to the LVs' states. However, as pointed out in this paper, this approach is in conflict with the completeness condition in SPNs and does not fully specify the probabilistic model. We propose a remedy for this problem by modifying the original approach for introducing the LVs, which we call SPN augmentation. We discuss conditional independencies in augmented SPNs, formally establish the probabilistic interpretation of the sum-weights and give an interpretation of augmented SPNs as Bayesian networks. Based on these results, we find a sound derivation of the EM algorithm for SPNs. Furthermore, the Viterbi-style algorithm for MPE proposed in literature was never proven to be correct. We show that this is indeed a correct algorithm, when applied to selective SPNs, and in particular when applied to augmented SPNs. Our theoretical results are confirmed in experiments on synthetic data and 103 real-world datasets.

Purpose of ReviewSubstantial research exists focusing on the various aspects and domains of early human development. However, there is a clear blind spot in early postnatal development when dealing with neurodevelopmental disorders, especially those that manifest themselves clinically only in late infancy or even in childhood.Recent FindingsThis early developmental period may represent an important timeframe to study these disorders but has historically received far less research attention. We believe that only a comprehensive interdisciplinary approach will enable us to detect and delineate specific parameters for specific neurodevelopmental disorders at a very early age to improve early detection/diagnosis, enable prospective studies and eventually facilitate randomised trials of early intervention.SummaryIn this article, we propose a dynamic framework for characterising neurofunctional biomarkers associated with specific disorders in the development of infants and children. We have named this automated detection ‘Fingerprint Model’, suggesting one possible approach to accurately and early identify neurodevelopmental disorders.