2017 |
Vasileios Charisopoulos, Petros Maragos Morphological perceptrons: Geometry and training algorithms Conference Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 10225 LNCS , 2017, ISSN: 16113349. Abstract | BibTeX | Links: [PDF] @conference{346, title = {Morphological perceptrons: Geometry and training algorithms}, author = { Vasileios Charisopoulos and Petros Maragos}, url = {http://robotics.ntua.gr/wp-content/uploads/publications/CharisopoulosMaragos_MorphologPerceptGeometryTrainAlgor_ISMM17.pdf}, doi = {10.1007/978-3-319-57240-6_1}, issn = {16113349}, year = {2017}, date = {2017-01-01}, booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)}, volume = {10225 LNCS}, pages = {3--15}, abstract = {Neural networks have traditionally relied on mostly linear models, such as the multiply-accumulate architecture of a linear perceptron that remains the dominant paradigm of neuronal computation. However, from a biological standpoint, neuron activity may as well involve inherently nonlinear and competitive operations. Mathematical morphology and minimax algebra provide the necessary background in the study of neural networks made up from these kinds of nonlinear units. This paper deals with such a model, called the morphological perceptron. We study some of its geometrical properties and introduce a training algorithm for binary classification. We point out the relationship between morphological classifiers and the recent field of tropical geometry, which enables us to obtain a precise bound on the number of linear regions of the maxout unit, a popular choice for deep neural networks introduced recently. Finally, we present some relevant numerical results.}, keywords = {}, pubstate = {published}, tppubtype = {conference} } Neural networks have traditionally relied on mostly linear models, such as the multiply-accumulate architecture of a linear perceptron that remains the dominant paradigm of neuronal computation. However, from a biological standpoint, neuron activity may as well involve inherently nonlinear and competitive operations. Mathematical morphology and minimax algebra provide the necessary background in the study of neural networks made up from these kinds of nonlinear units. This paper deals with such a model, called the morphological perceptron. We study some of its geometrical properties and introduce a training algorithm for binary classification. We point out the relationship between morphological classifiers and the recent field of tropical geometry, which enables us to obtain a precise bound on the number of linear regions of the maxout unit, a popular choice for deep neural networks introduced recently. Finally, we present some relevant numerical results. |
2000 |
H F C Pessoa, Petros Maragos Neural networks with hybrid morphological / rank / linear nodes : a unifying framework with applications to handwritten character recognition ଝ Journal Article Pattern Recognition, 33 , 2000. @article{111, title = {Neural networks with hybrid morphological / rank / linear nodes : a unifying framework with applications to handwritten character recognition ଝ}, author = {H F C Pessoa and Petros Maragos}, url = {http://robotics.ntua.gr/wp-content/uploads/publications/PessoaMaragos_MRLNNet_PatRecogn2000.pdf}, year = {2000}, date = {2000-01-01}, journal = {Pattern Recognition}, volume = {33}, keywords = {}, pubstate = {published}, tppubtype = {article} } |
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