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With the abundance of data, machine learning applications engaged increased attention in the last decade. An attractive approach to robustify the statistical analysis is to preprocess the data through clustering. This paper develops a low-complexity Riemannian optimization framework for solving optimization problems on the set of positive semidefinite stochastic matrices. The low-complexity feature of the proposed algorithms stems from the factorization of the optimization variable $\mathbf {X}=\mathbf {Y}\mathbf {Y}^{\mathrm{T}}$ X = Y Y T and deriving conditions on the number of columns of $\mathbf {Y}$ Y under which the factorization yields a satisfactory solution. The paper further investigates the embedded and quotient geometries of the resulting Riemannian manifolds. In particular, the paper explicitly derives the tangent space, Riemannian gradients and Hessians, and a retraction operator allowing the design of efficient first and second-order optimization methods for the graph-based clustering applications of interest. The numerical results reveal that the resulting algorithms present a clear complexity advantage as compared with state-of-the-art euclidean and Riemannian approaches for graph clustering applications. [ABSTRACT FROM AUTHOR]

$k$ k -means method using Lloyd heuristic is a traditional clustering method which has played a key role in multiple downstream tasks of machine learning because of its simplicity. However, Lloyd heuristic always finds a bad local minimum, i.e., the bad local minimum makes objective function value not small enough, which limits the performance of $k$ k -means. In this paper, we use coordinate descent (CD) method to solve the problem. First, we show that the $k$ k -means minimization problem can be reformulated as a trace maximization problem, then a simple and efficient coordinate descent scheme is proposed to solve the maximization problem. Two interesting findings through theory are that Lloyd cannot decrease the objective function value of $k$ k -means produced by our CD further, and our proposed method CD to solve $k$ k -means problem can avoid produce empty clusters. In addition, according to the computational complexity analysis, it is verified CD has the same time complexity with original $k$ k -means method. Extensive experiments including statistical hypothesis testing, on several real-world datasets with varying number of clusters, varying number of samples and varying number of dimensions show that CD performs better compared to Lloyd, i.e., lower objective value, better local minimum and fewer iterations. And CD is more robust to initialization than Lloyd whether the initialization strategy is random or initialization of $k$ k -means++. [ABSTRACT FROM AUTHOR]

In this paper, we use shape grammars (SGs) for facade parsing, which amounts to segmenting 2D building facades into balconies, walls, windows, and doors in an architecturally meaningful manner. The main thrust of our work is the introduction of reinforcement learning (RL) techniques to deal with the computational complexity of the problem. RL provides us with techniques such as Q-learning and state aggregation which we exploit to efficiently solve facade parsing. We initially phrase the 1D parsing problem in terms of a Markov Decision Process, paving the way for the application of RL-based tools. We then develop novel techniques for the 2D shape parsing problem that take into account the specificities of the facade parsing problem. Specifically, we use state aggregation to enforce the symmetry of facade floors and demonstrate how to use RL to exploit bottom-up, image-based guidance during optimization. We provide systematic results on the Paris building dataset and obtain state-of-the-art results in a fraction of the time required by previous methods. We validate our method under diverse imaging conditions and make our software and results available online. [ABSTRACT FROM AUTHOR]

Visual Question Answering (VQA) is a task to answer natural language questions tied to the content of visual images. Most recent VQA approaches usually apply attention mechanism to focus on the relevant visual objects and/or consider the relations between objects via off-the-shelf methods in visual relation reasoning. However, they still suffer from several drawbacks. First, they mostly model the simple relations between objects, which results in many complicated questions cannot be answered correctly, because of failing to provide sufficient knowledge. Second, they seldom leverage the harmony cooperation of visual appearance feature and relation feature. To solve these problems, we propose a novel end-to-end VQA model, termed Multi-modal Relation Attention Network (MRA-Net). The proposed model explores both textual and visual relations to improve performance and interpretability. In specific, we devise 1) a self-guided word relation attention scheme, which explore the latent semantic relations between words; 2) two question-adaptive visual relation attention modules that can extract not only the fine-grained and precise binary relations between objects but also the more sophisticated trinary relations. Both kinds of question-related visual relations provide more and deeper visual semantics, thereby improving the visual reasoning ability of question answering. Furthermore, the proposed model also combines appearance feature with relation feature to reconcile the two types of features effectively. Extensive experiments on five large benchmark datasets, VQA-1.0, VQA-2.0, COCO-QA, VQA-CP v2, and TDIUC, demonstrate that our proposed model outperforms state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a high-dimensional Bayesian posterior with a simpler variational distribution by solving an optimization problem. This approach has been successfully applied to various models and large-scale applications. In this review, we give an overview of recent trends in variational inference. We first introduce standard mean field variational inference, then review recent advances focusing on the following aspects: (a) scalable VI, which includes stochastic approximations, (b) generic VI, which extends the applicability of VI to a large class of otherwise intractable models, such as non-conjugate models, (c) accurate VI, which includes variational models beyond the mean field approximation or with atypical divergences, and (d) amortized VI, which implements the inference over local latent variables with inference networks. Finally, we provide a summary of promising future research directions. [ABSTRACT FROM AUTHOR]