In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

[Q]: Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data analysis. An important variant is the sparse NMF problem which arises when we explicitly require the learnt features to be sparse. A natural measure of sparsity is the L0 norm, however its optimization is NP-hard. Mixed norms, such as L1/L2 measure, have been shown to model sparsity robustly, based on intuitive attributes that such measures need to satisfy. This is in contrast to computationally cheaper alternatives such as the plain L1 norm. However, present algorithms designed for optimizing the mixed norm L1/L2 are slow and other formulations for sparse NMF have been proposed such as those based on L1 and L0 norms. Our proposed algorithm allows us to solve the mixed norm sparsity constraints while not sacrificing computation time. We present experimental evidence on real-world datasets that shows our new algorithm performs an order of magnitude faster compared to the current state-of-the-art solvers optimizing the mixed norm and is suitable for large-scale datasets.
[A]: Block Coordinate Descent for Sparse NMF


[Q]: Online learning aims to perform nearly as well as the best hypothesis in hindsight. For some hypothesis classes, though, even finding the best hypothesis offline is challenging. In such offline cases, local search techniques are often employed and only local optimality guaranteed. For online decision-making with such hypothesis classes, we introduce local regret, a generalization of regret that aims to perform nearly as well as only nearby hypotheses. We then present a general algorithm to minimize local regret with arbitrary locality graphs. We also show how the graph structure can be exploited to drastically speed learning. These algorithms are then demonstrated on a diverse set of online problems: online disjunct learning, online Max-SAT, and online decision tree learning.
[A]: On Local Regret


[Q]: In distributed classification, each learner observes its environment and deduces a classifier. As a learner has only a local view of its environment, classifiers can be exchanged among the learners and integrated, or merged, to improve accuracy. However, the operation of merging is not defined for most classifiers. Furthermore, the classifiers that have to be merged may be of different types in settings such as ad-hoc networks in which several generations of sensors may be creating classifiers. We introduce decision spaces as a framework for merging possibly different classifiers. We formally study the merging operation as an algebra, and prove that it satisfies a desirable set of properties. The impact of time is discussed for the two main data mining settings. Firstly, decision spaces can naturally be used with non-stationary distributions, such as the data collected by sensor networks, as the impact of a model decays over time. Secondly, we introduce an approach for stationary distributions, such as homogeneous databases partitioned over different learners, which ensures that all models have the same impact. We also present a method that uses storage flexibly to achieve different types of decay for non-stationary distributions. Finally, we show that the algebraic approach developed for merging can also be used to analyze the behaviour of other operators.
[A]:
An Algebra to Merge Heterogeneous Classifiers