This paper explores the recently proposed Graph Convolutional Network architecture proposed in (Kipf & Welling, 2016) The key points of their work is summarized and their results are reproduced. Graph regularization and alternative graph convolution approaches are explored. I find that explicit graph regularization was correctly rejected by (Kipf & Welling, 2016). I attempt to improve the perfo...

Regularization plays a critical role in modern statistical research, especially in high dimensional variable selection problems. Existing Bayesian methods usually assume independence between variables a priori. In this article, we propose a novel Bayesian approach, which explicitly models the dependence structure through a graph Laplacian matrix. We also generalize the graph Laplacian to allow ...

In this letter, we introduce a semi-supervised manifold regularization framework for human pose estimation. We utilize the unlabeled data to compensate for the complexities in the input space and model the underlying manifold by a nearest neighbor graph. We argue that the optimal graph is a subgraph of the k nearest neighbors (k-NN) graph. Then, we estimate distances in the output space to appr...

Graph smoothness objectives have achieved great success in semi-supervised learning but have not yet been applied extensively to unsupervised generative models. We define a new class of entropic graph-based posterior regularizers that augment a probabilistic model by encouraging pairs of nearby variables in a regularization graph to have similar posterior distributions. We present a three-way a...

A graph is regularizable if it is possible to assign weights to its edges so that all nodes have the same degree. Weights can be positive, nonnegative or arbitrary as soon as the regularization degree is not null. Positive and nonnegative regularizable graphs have been thoroughly investigated in the literature. In this work, we propose and study arbitrarily regularizable graphs. In particular, ...

Several techniques have recently aimed to improve the performance of deep learning models for Scene Graph Generation (SGG) by incorporating background knowledge. State-of-the-art can be divided into two families: one where knowledge is incorporated model in a subsymbolic fashion, and another which maintained symbolic form. Despite promising results, both families face several shortcomings: firs...

Novel Monte Carlo estimators are proposed to solve both the Tikhonov regularization (TR) and interpolation problems on graphs. These based random spanning forests (RSF), theoretical properties of which enable analyze estimators' mean variance. We also show how perform hyperparameter tuning for these RSF-based estimators. TR is a component in many well-known algorithms, we can be easily adapted ...

`-Graph has been proven to be effective in data clustering, which partitions the data space by using the sparse representation of the data as the similarity measure. However, the sparse representation is performed for each datum separately without taking into account the geometric structure of the data. Motivated by `-Graph and manifold leaning, we propose Laplacian Regularized `-Graph (LR`-Gra...

An efficient spatial regularization method using superpixel segmentation and graph Laplacian is proposed for the sparse hyperspectral unmixing method. Since it likely to find spectrally similar pixels in a homogeneous region, we use algorithm extract regions by considering image boundaries. We first regions, which are called superpixels, then, weighted each constructed selecting <inline-formula...