Given M vectors in N-dimensional attribute space, it is much easier to find M hyperplanes that separate each of the vectors from all the others than to solve M arbitrary linear dichotomies with approximately equal class memberships. An explanation of the rapid growth with M and N of the number of separable one-against-all linear halfplane dichotomies is proposed in terms of convex polyhedra in a hyperspherical shell. The counterintuitive surge is illustrated by averaged results on pseudo-random integer arrays obtained by Linear Programming and Neural Networks. Although the initial motivation arose from seemingly arbitrary rankings of scientists and universities, this project is not directed at any application.
Spectral signatures have been used with great success in computer vision to characterise the local and global topology of 3D meshes. In this paper, we propose to use two widely used spectral signatures, the Heat Kernel Signature and the Wave Kernel Signature, to create node embeddings able to capture local and global structural information for a given graph. For each node, we concatenate its structural embedding with the one-hot encoding vector of the node feature (if available) and we define a kernel between two input graphs in terms of the Wasserstein distance between the respective node embeddings. Experiments on standard graph classification benchmarks show that our kernel performs favourably when compared to widely used alternative kernels as well as graph neural networks.
Thousands of huge printed sheets depicting engineering drawings keep record of complex industrial structures from Oil & Gas facilities. Currently, there is a trend of digitising these drawings, having as final end the regeneration of the original computer-aided design (CAD) file, which can be better visualised and analysed through diverse computer applications. Most efforts in literature and commercial applications have focused on converting these sheets into CAD files in an automated way. Nonetheless, this needs to be a zero-error process; as the final CAD will always be verified by an engineer for integrity and inspection. In this paper, we present a method that, on the one hand, highlights which components in the CAD are most likely to have been incorrectly identified, and on the other hand, facilitates the engineer to search some groups of components in these huge assets. These techniques are based on graph embedding, computer neural networks and sub-graph matching.
We use coins in our daily life to pay for bus, metro tickets, vending machines, etc. However, the market for antique and historical coins is another place, where the quality of coins and their genuinity play a significant role. Hence, researchers have considered different methods in coin detection studies. In recent years 2-D and 3-D image processing approaches have been widely used in image-based coin detection. In this paper, we propose a method to detect counterfeit coins based on image content. We employed SIFT, SURF, and MSER to determine the similarity degree of our datasets. Then, we evaluate those descriptors by statistical analysis to see which one is the most effective criterion for counterfeit coin detection. According to experiments, SIFT was selected as the most reliable algorithm for the Danish coin image dataset. Then, we train an autoencoder to find anomalies in the coin images. The trained autoencoder receives a coin image as input and generates a new image. The output image is compared with a basic image using the selected criterion. If the similarity between these two images meets a threshold then the coin is genuine. Most counterfeit coin detection methods require fake data for training. This can be eliminated by our autoencoding-based anomaly method.
Convolutional neural networks (CNN) have enabled major advances in image classification through convolution and pooling. In particular, image pooling transforms a connected discrete grid into a reduced grid with the same connectivity and allows reduction functions to take into account all the pixels of an image. However, a pooling satisfying such properties does not exist for graphs. Indeed, some methods are based on a vertex selection step which induces an important loss of information. Other methods learn a fuzzy clustering of vertex sets which induces almost complete reduced graphs. We propose to overcome both problems using a new pooling method, named MIVSPool. This method is based on a selection of vertices called surviving vertices using a Maximal Independent Vertex Set (MIVS) and an assignment of the remaining vertices to the survivors. Consequently, our method does not discard any vertex information nor artificially increase the density of the graph. Experimental results show an increase in accuracy for graph classification on various standard datasets.
