In this paper, we propose doubly convolutional neural networks (DCNNs), which significantly improve the performance of CNNs by further exploring this idea. In stead of allocating a set of convolutional filters that are independently learned, a DCNN maintains groups of filters where filters within each group are translated versions of each other. Practically, a DCNN can be easily implemented by a two-step convolution procedure, which is supported by most modern deep learning libraries. We perform extensive experiments on three image classification benchmarks: CIFAR-10, CIFAR-100 and ImageNet, and show that DCNNs consistently outperform other competing architectures. We have also verified that replacing a convolutional layer with a doubly convolutional layer at any depth of a CNN can improve its performance.
Graph convolutional neural networks (GCNN) have numerous applications in different graph based learning tasks. Although the techniques obtain impressive results, they often fall short in accounting for the uncertainty associated with the underlying graph structure. In the recently proposed Bayesian GCNN (BGCN) framework, this issue is tackled by viewing the observed graph as a sample from a parametric random graph model and targeting joint inference of the graph and the GCNN weights. In this paper, we introduce an alternative generative model for graphs based on copying nodes and incorporate it within the BGCN framework. Our approach has the benefit that it uses information provided by the node features and training labels in the graph topology inference. Experiments show that the proposed algorithm compares favorably to the state-of-the-art in benchmark node classification tasks.
We present a novel class of convolutional neural networks (CNNs) for set functions, i.e., data indexed with the powerset of a finite set. The convolutions are derived as linear, shift-equivariant functions for various notions of shifts on set functions. The framework is fundamentally different from graph convolutions based on the Laplacian, as it provides not one but several basic shifts, one for each element in the ground set. Prototypical experiments with several set function classification tasks on synthetic datasets and on datasets derived from real-world hypergraphs demonstrate the potential of our new powerset CNNs. Papers published at the Neural Information Processing Systems Conference.
"The implementation part is very good and up-too the mark. The explanation step by step process is very good." (February 2018). "course done very well; everything is explained in detail; really satisfied!!!" (February 2018). "Difficult topics are simply illustrated and therefore easy to understand." (January 2018).
Throughout this article, I will discuss some of the more complex aspects of convolutional neural networks and how they related to specific tasks such as object detection and facial recognition. This article is a natural extension to my article titled: Simple Introductions to Neural Networks. I recommend looking at this before tackling the rest of this article if you are not well-versed in the idea and function of convolutional neural networks. Due to the excessive length of the original article, I have decided to leave out several topics related to object detection and facial recognition systems, as well as some of the more esoteric network architectures and practices currently being trialed in the research literature. I will likely discuss these in a future article related more specifically to the application of deep learning for computer vision.