1,721,034 research outputs found
Metric Learning for Prototype-Based Classification
Full text linkBiehl M, Hammer B, Schneider P, Villmann T. Metric learning for prototype based classification. In: Bianchini M, Maggini M, Scarselli F, eds. Innovations in Neural Information – Paradigms and Applications. Studies in Computational Intelligence, 247. Berlin: Springer; 2009: 183-199
Implementation of the PaperRank and AuthorRank indices in the Scopus database
Full text linkWe implement the PaperRank and AuthorRank indices introduced in [Amodio & Brugnano, 2014] in the Scopus database, in order to highlight quantitative and qualitative information that the bare number of citations and/or the h-index of an author are unable to provide. In addition to this, the new indices can be cheaply updated in Scopus, since this has a cost comparable to that of updating the number of citations. Some examples are reported to provide insight in their potentialities, as well as possible extensions
On the complexity of neural network classifiers: a comparison between shallow and deep architectures
No full textRecently, researchers in the artificial neural network field have focused their attention on connectionist models composed by several hidden layers. In fact, experimental results and heuristic considerations suggest that deep architectures are more suitable than shallow ones for modern applications, facing very complex problems, e.g., vision and human language understanding. However, the actual theoretical results supporting such a claim are still few and incomplete. In this paper, we propose a new approach to study how the depth of feedforward neural networks impacts on their ability in implementing high complexity functions. First, a new measure based on topological concepts is introduced, aimed at evaluating the complexity of the function implemented by a neural network, used for classification purposes. Then, deep and shallow neural architectures with common sigmoidal activation functions are compared, by deriving upper and lower bounds on their complexity, and studying how the complexity depends on the number of hidden units and the used activation function. The obtained results seem to support the idea that deep networks actually implements functions of higher complexity, so that they are able, with the same number of resources, to address more difficult problems
Are multilayer perceptrons adequate for pattern recognition and verification?
No full textThis paper discusses the ability of multilayer perceptrons (MLPs) to model the probability distribution of data in typical pattern recognition and verification problems. It is proven that multilayer perceptrons with sigmoidal units and a number of hidden units less or equal than the number of inputs are unable to model patterns distributed in typical clusters, since these networks draw open separation surfaces in the pattern space. When using more hidden units than inputs, the separation surfaces can be closed but, unfortunately, it is proven that determining whether or not an MLP draws closed separation surfaces in the pattern space is NP-hard. The major conclusion of this paper is somewhat opposite to what is believed and reported in many application papers: MLPs are definitely not adequate for applications of pattern recognition requiring a reliable rejection and, especially, they are not adequate for pattern verification tasks
Artificial Neural Networks for Processing Graphs with Applications to Image Understanding: A Survey
No full textIn graphical pattern recognition, each data is represented as an arrangement of elements, that encodes both the properties of each element and the relations among them. Hence, patterns are modelled as labelled graphs where, in general, labels can be attached to both nodes and edges. Artificial neural networks able to process graphs are a powerful tool for addressing a great variety of real-world problems, where the information is naturally organized in entities and relationships among entities and, in fact, they have been widely used in computer vision, f.i. in logo recognition, in similarity retrieval, and for object detection. In this chapter, we propose a survey of neural network models able to process structured information, with a particular focus on those architectures tailored to address image understanding applications. Starting from the original recursive model (RNNs), we subsequently present different ways to represent images – by trees, forests of trees, multiresolution trees, directed acyclic graphs with labelled edges, general graphs – and, correspondingly, neural network architectures appropriate to process such structures
Processing directed acyclic graphs with recursive neural networks
No full textRecursive neural networks are conceived for processing graphs and extend the well-known recurrent model for processing sequences. In the previous literature, recursive neural networks can deal only with directed ordered acyclic graphs (DOAGs), in which the children of any given node are ordered. While this assumption is reasonable in some applications, it introduces unnecessary constraints in others. In this paper, it is shown that the constraint on the ordering can be relaxed by using an appropriate weight sharing, that guarantees the independence of the network output with respect to the permutations of the arcs leaving from each node. The method can be used with graphs having low connectivity and, in particular, few outcoming arcs.
Some theoretical properties of the proposed architecture are given. They guarantee that the approximation capabilities are maintained, despite the weight sharing
Which classes of functions can a given multilayer perceptron approximate?
No full textGiven a multilayer perceptron (MLP), there are functions that can be approximated up to any degree of accuracy by the MLP without having to increase the number of the hidden nodes. Those functions belong to the closure F̄ of the set F of the maps realizable by the MLP. In the paper, we give a list of maps with this property. In particular, it is proven that rationales belongs to F̄ for networks with arctangent activation function and exponentials belongs to F̄ for networks with sigmoid activation function. Moreover, for a restricted class of MLPs, we prove that the list is complete and give an analytic definition of F̄
Recursive Processing of Cyclic Graphs
No full textRecursive neural networks are a powerful tool for processing structured data. According to the recursive learning paradigm, the information to be processed consists of directed positional acyclic graphs (DPAGs). In fact, recursive networks are fed following the partial order defined by the links of the graph. Unfortunately, the hypothesis of processing DPAGs is sometimes too restrictive, being the nature of some real-world problems intrinsically disordered and cyclic. In the paper, a methodology is proposed which allows us to map any cyclic directed graph into a "recursive-equivalent" tree. Therefore, the computational power of recursive networks is definitely established, also clarifying the underlying limitations of the model
On the closure of the set of functions that can be realized by a given multilayer perceptron
No full textGiven a multilayer perceptron (MLP) with a fixed architecture, there are functions that can be approximated up to any degree of accuracy, without having to increase the number of the hidden nodes. Those functions belong to the closure F̄ of the set F of the maps realizable by the MLP. In this paper, we give a list of maps with this property. In particular, it is proven that 1) rational functions belongs to F̄ for networks with inverse tangent activation function and 2) products of polynomials and exponentials belongs to F̄ for networks with sigmoid activation function. Moreover, for a restricted class of MLP's, we prove that the list is complete and give an analytic definition of F̄. © 1998 IEEE
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