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. |
Copyright Notice:
Some material presented is available for download to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author’s copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
The work already published by the IEEE is under its copyright. Personal use of such material is permitted. However, permission to reprint/republish the material for advertising or promotional purposes, or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of the work in other works must be obtained from the IEEE.