On Filter Size in Graph Convolutional Networks

Recently, many researchers have been focusing on the definition of neural networks for graphs. The basic component for many of these approaches remains the graph convolution idea proposed almost a decade ago. In this paper, we extend this basic component, following an intuition derived from the well-known convolutional filters over multi-dimensional tensors. In particular, we derive a simple, efficient and effective way to introduce a hyper-parameter on graph convolutions that influences the filter size, i.e. its receptive field over the considered graph. We show with experimental results on real-world graph datasets that the proposed graph convolutional filter improves the predictive performance of Deep Graph Convolutional Networks.Comment: arXiv admin note: text overlap with arXiv:1811.0693

Tree Echo State Networks

In this paper we present the Tree Echo State Network (TreeESN) model, generalizing the paradigm of Reservoir Computing to tree structured data. TreeESNs exploit an untrained generalized recursive reservoir, exhibiting extreme efficiency for learning in structured domains. In addition, we highlight through the paper other characteristics of the approach: First, we discuss the Markovian characterization of reservoir dynamics, extended to the case of tree domains, that is implied by the contractive setting of the TreeESN state transition function. Second, we study two types of state mapping functions to map the tree structured state of TreeESN into a fixed-size feature representation for classification or regression tasks. The critical role of the relation between the choice of the state mapping function and the Markovian characterization of the task is analyzed and experimentally investigated on both artificial and real-world tasks. Finally, experimental results on benchmark and real-world tasks show that the TreeESN approach, in spite of its efficiency, can achieve comparable results with state-of-the-art, although more complex, neural and kernel based models for tree structured data

Learning nonsparse kernels by self-organizing maps for structured data

The development of neural network (NN) models able to encode structured input, and the more recent definition of kernels for structures, makes it possible to directly apply machine learning approaches to generic structured data. However, the effectiveness of a kernel can depend on its sparsity with respect to a specific data set. In fact, the accuracy of a kernel method typically reduces as the kernel sparsity increases. The sparsity problem is particularly common in structured domains involving discrete variables which may take on many different values. In this paper, we explore this issue on two well-known kernels for trees, and propose to face it by recurring to self-organizing maps (SOMs) for structures. Specifically, we show that a suitable combination of the two approaches, obtained by defining a new class of kernels based on the activation map of a SOM for structures, can be effective in avoiding the sparsity problem and results in a system that can be significantly more accurate for categorization tasks on structured data. The effectiveness of the proposed approach is demonstrated experimentally on two relatively large corpora of XML formatted data and a data set of user sessions extracted from Website logs

Learning Nonsparse Kernels by Self-Organizing Maps for Structured Data

The development of neural network (NN) models able to encode structured input, and the more recent definition of kernels for structures, makes it possible to directly apply machine learning approaches to generic structured data. However, the effectiveness of a kernel can depend on its sparsity with respect to a specific data set. In fact, the accuracy of a kernel method typically reduces as the kernel sparsity increases. The sparsity problem is particularly common in structured domains involving discrete variables which may take on many different values. In this paper, we explore this issue on two well-known kernels for trees, and propose to face it by recurring to self-organizing maps (SOMs) for structures. Specifically, we show that a suitable combination of the two approaches, obtained by defining a new class of kernels based on the activation map of a SOM for structures, can be effective in avoiding the sparsity problem and results in a system that can be significantly more accurate for categorization tasks on structured data. The effectiveness of the proposed approach is demonstrated experimentally on two relatively large corpora of XML formatted data and a data set of user sessions extracted from Website logs

Linear Models and Deep Learning: Learning in Sequential Domains

With the diffusion of cheap sensors, sensor-equipped devices (e.g., drones), and sensor networks (such as Internet of Things), as well as the development of inexpensive human-machine interaction interfaces, the ability to quickly and effectively process sequential data is becoming more and more important. There are many tasks that may benefit from advancement in this field, ranging from monitoring and classification of human behavior to prediction of future events. Most of the above tasks require pattern recognition and machine learning capabilities. There are many approaches that have been proposed in the past to learn in sequential domains, especially extensions in the field of Deep Learning. Deep Learning is based on highly nonlinear systems, which very often reach quite good classification/prediction performances, but at the expenses of a substantial computational burden. Actually, when facing learning in a sequential, or more in general structured domain, it is common practice to readily resort to nonlinear systems. Not always, however, the task really requires a nonlinear system. So the risk is to run into difficult and computational expensive training procedures to eventually get a solution that improves of an epsilon (if not at all) the performances that can be reached by a simple linear dynamical system involving simpler training procedures and a much lower computational effort. The aim of this thesis is to discuss about the role that linear dynamical systems may have in learning in sequential domains. On one hand, we like to point out that a linear dynamical system (LDS) is able, in many cases, to already provide good performances at a relatively low computational cost. On the other hand, when a linear dynamical system is not enough to provide a reasonable solution, we show that it can be used as a building block to construct more complex and powerful models, or how to resort to it to design quite effective pre-training techniques for nonlinear dynamical systems, such as Echo State Networks (ESNs) and simple Recurrent Neural Networks (RNNs). Specifically, in this thesis we consider the task of predicting the next event into a sequence of events. The datasets used to test various discussed models involve polyphonic music and contain quite long sequences. We start by introducing a simple state space LDS. Three different approaches to train the LDS are then considered. Then we introduce some brand new models that are inspired by the LDS and that have the aim to increase the prediction/classification capabilities of the simple linear models. We then move to study the most common nonlinear models. From this point of view, we considered the RNN models, which are significantly more computationally demanding. We experimentally show that, at least for the addressed prediction task and the considered datasets, the introduction of pre-training approaches involving linear systems leads to quite large improvements in prediction performances. Specifically, we introduce pre-training via linear Autoencoder, and an alternative based on Hidden Markov Models (HMMs). Experimental results suggest that linear models may play an important role for learning in sequential domains, both when used directly or indirectly (as basis for pre-training approaches): in fact, when used directly, linear models may by themselves return state-of-the-art performance, while requiring a much lower computational effort with respect to their nonlinear counterpart. Moreover, even when linear models do not perform well, it is always possible to successfully exploit them within pre-training approaches for nonlinear systems