DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications

Convolutional Neural Networks (CNNs) are a cornerstone of the Deep Learning toolbox and have led to many breakthroughs in Artificial Intelligence. These networks have mostly been developed for regular Euclidean domains such as those supporting images, audio, or video. Because of their success, CNN-based methods are becoming increasingly popular in Cosmology. Cosmological data often comes as spherical maps, which make the use of the traditional CNNs more complicated. The commonly used pixelization scheme for spherical maps is the Hierarchical Equal Area isoLatitude Pixelisation (HEALPix). We present a spherical CNN for analysis of full and partial HEALPix maps, which we call DeepSphere. The spherical CNN is constructed by representing the sphere as a graph. Graphs are versatile data structures that can act as a discrete representation of a continuous manifold. Using the graph-based representation, we define many of the standard CNN operations, such as convolution and pooling. With filters restricted to being radial, our convolutions are equivariant to rotation on the sphere, and DeepSphere can be made invariant or equivariant to rotation. This way, DeepSphere is a special case of a graph CNN, tailored to the HEALPix sampling of the sphere. This approach is computationally more efficient than using spherical harmonics to perform convolutions. We demonstrate the method on a classification problem of weak lensing mass maps from two cosmological models and compare the performance of the CNN with that of two baseline classifiers. The results show that the performance of DeepSphere is always superior or equal to both of these baselines. For high noise levels and for data covering only a smaller fraction of the sphere, DeepSphere achieves typically 10% better classification accuracy than those baselines. Finally, we show how learned filters can be visualized to introspect the neural network.Comment: arXiv admin note: text overlap with arXiv:astro-ph/0409513 by other author

FMA: A Dataset For Music Analysis

We introduce the Free Music Archive (FMA), an open and easily accessible dataset suitable for evaluating several tasks in MIR, a field concerned with browsing, searching, and organizing large music collections. The community's growing interest in feature and end-to-end learning is however restrained by the limited availability of large audio datasets. The FMA aims to overcome this hurdle by providing 917 GiB and 343 days of Creative Commons-licensed audio from 106,574 tracks from 16,341 artists and 14,854 albums, arranged in a hierarchical taxonomy of 161 genres. It provides full-length and high-quality audio, pre-computed features, together with track- and user-level metadata, tags, and free-form text such as biographies. We here describe the dataset and how it was created, propose a train/validation/test split and three subsets, discuss some suitable MIR tasks, and evaluate some baselines for genre recognition. Code, data, and usage examples are available at https://github.com/mdeff/fmaComment: ISMIR 2017 camera-read

Structured Sequence Modeling with Graph Convolutional Recurrent Networks

This paper introduces Graph Convolutional Recurrent Network (GCRN), a deep learning model able to predict structured sequences of data. Precisely, GCRN is a generalization of classical recurrent neural networks (RNN) to data structured by an arbitrary graph. Such structured sequences can represent series of frames in videos, spatio-temporal measurements on a network of sensors, or random walks on a vocabulary graph for natural language modeling. The proposed model combines convolutional neural networks (CNN) on graphs to identify spatial structures and RNN to find dynamic patterns. We study two possible architectures of GCRN, and apply the models to two practical problems: predicting moving MNIST data, and modeling natural language with the Penn Treebank dataset. Experiments show that exploiting simultaneously graph spatial and dynamic information about data can improve both precision and learning speed

LiveMesh, a tool for real-time rendering of neuronal cells from morphologies

The project goal was to prove the feasibility of GPU-based tessellation to generate neuron membrane mesh representations from parametric descriptions of neurons. The developed prototype software produces a smooth, continuous and high-fidelity representation of neuron morphologies that can be used for scientific visualization. It is considered by the Blue Brain Project (BBP) visualization team as a replacement of their current offline mesh generation algorithm for real-time rendering. The implementation used C++, OpenGL and Qt

Graph-based Image Inpainting

The project goal was to explore the applications of spectral graph theory to address the inpainting problem of large missing chunks. We used a non-local patch graph representation of the image and proposed a structure detector which leverages the graph representation and influences the fill-order of our exemplar-based algorithm. Our method achieved state-of-the-art performances

MGCN: Semi-supervised Classification in Multi-layer Graphs with Graph Convolutional Networks

Graph embedding is an important approach for graph analysis tasks such as node classification and link prediction. The goal of graph embedding is to find a low dimensional representation of graph nodes that preserves the graph information. Recent methods like Graph Convolutional Network (GCN) try to consider node attributes (if available) besides node relations and learn node embeddings for unsupervised and semi-supervised tasks on graphs. On the other hand, multi-layer graph analysis has been received attention recently. However, the existing methods for multi-layer graph embedding cannot incorporate all available information (like node attributes). Moreover, most of them consider either type of nodes or type of edges, and they do not treat within and between layer edges differently. In this paper, we propose a method called MGCN that utilizes the GCN for multi-layer graphs. MGCN embeds nodes of multi-layer graphs using both within and between layers relations and nodes attributes. We evaluate our method on the semi-supervised node classification task. Experimental results demonstrate the superiority of the proposed method to other multi-layer and single-layer competitors and also show the positive effect of using cross-layer edges