Learning shape correspondence with anisotropic convolutional neural networks

Establishing correspondence between shapes is a fundamental problem in geometry processing, arising in a wide variety of applications. The problem is especially difficult in the setting of non-isometric deformations, as well as in the presence of topological noise and missing parts, mainly due to the limited capability to model such deformations axiomatically. Several recent works showed that invariance to complex shape transformations can be learned from examples. In this paper, we introduce an intrinsic convolutional neural network architecture based on anisotropic diffusion kernels, which we term Anisotropic Convolutional Neural Network (ACNN). In our construction, we generalize convolutions to non-Euclidean domains by constructing a set of oriented anisotropic diffusion kernels, creating in this way a local intrinsic polar representation of the data (`patch'), which is then correlated with a filter. Several cascades of such filters, linear, and non-linear operators are stacked to form a deep neural network whose parameters are learned by minimizing a task-specific cost. We use ACNNs to effectively learn intrinsic dense correspondences between deformable shapes in very challenging settings, achieving state-of-the-art results on some of the most difficult recent correspondence benchmarks

Applicability of semi-supervised learning assumptions for gene ontology terms prediction

Gene Ontology (GO) is one of the most important resources in bioinformatics, aiming to provide a unified framework for the biological annotation of genes and proteins across all species. Predicting GO terms is an essential task for bioinformatics, but the number of available labelled proteins is in several cases insufficient for training reliable machine learning classifiers. Semi-supervised learning methods arise as a powerful solution that explodes the information contained in unlabelled data in order to improve the estimations of traditional supervised approaches. However, semi-supervised learning methods have to make strong assumptions about the nature of the training data and thus, the performance of the predictor is highly dependent on these assumptions. This paper presents an analysis of the applicability of semi-supervised learning assumptions over the specific task of GO terms prediction, focused on providing judgment elements that allow choosing the most suitable tools for specific GO terms. The results show that semi-supervised approaches significantly outperform the traditional supervised methods and that the highest performances are reached when applying the cluster assumption. Besides, it is experimentally demonstrated that cluster and manifold assumptions are complimentary to each other and an analysis of which GO terms can be more prone to be correctly predicted with each assumption, is provided.Postprint (published version

Distributional Feature Mapping in Data Classification

Performance of a machine learning algorithm depends on the representation of the input data. In computer vision problems, histogram based feature representation has significantly improved the classification tasks. L1 normalized histograms can be modelled by Dirichlet and related distributions to transform input space to feature space. We propose a mapping technique that contains prior knowledge about the distribution of the data and increases the discriminative power of the classifiers in supervised learning such as Support Vector Machine (SVM). The mapping technique for proportional data which is based on Dirichlet, Generalized Dirichlet, Beta Liouville, scaled Dirichlet and shifted scaled Dirichlet distributions can be incorporated with traditional kernels to improve the base kernels accuracy. Experimental results show that the proposed technique for proportional data increases accuracy for machine vision tasks such as natural scene recognition, satellite image classification, gender classification, facial expression recognition and human action recognition in videos. In addition, in object tracking, learning parametric features of the target object using Dirichlet and related distributions may help to capture representations invariant to noise. This further motivated our study of such distributions in object tracking. We propose a framework for feature representation on probability simplex for proportional data utilizing the histogram representation of the target object at initial frame. A set of parameter vectors determine the appearance features of the target object in the subsequent frames. Motivated by the success of distribution based feature mapping for proportional data, we extend this technique for semi-bounded data utilizing inverted Dirichlet, generalized inverted Dirichlet and inverted Beta Liouville distributions. Similar approach is taken into account for count data where Dirichlet multinomial and generalized Dirichlet multinomial distributions are used to map density features with input features

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field