FEMa: a finite element machine for fast learning

Machine learning has played an essential role in the past decades and has been in lockstep with the main advances in computer technology. Given the massive amount of data generated daily, there is a need for even faster and more effective machine learning algorithms that can provide updated models for real-time applications and on-demand tools. This paper presents FEMa—a finite element machine classifier—for supervised learning problems, where each training sample is the center of a basis function, and the whole training set is modeled as a probabilistic manifold for classification purposes. FEMa has its theoretical basis in the finite element method, which is widely used for numeral analysis in engineering problems. It is shown FEMa is parameterless and has a quadratic complexity for both training and classification phases when basis functions are used that satisfy certain properties. The proposed classifier yields very competitive results when compared to some state-of-the-art supervised pattern recognition techniques.

[1]  Francesco Carlo Morabito,et al.  Deep Learning Representation from Electroencephalography of Early-Stage Creutzfeldt-Jakob Disease and Features for Differentiation from Rapidly Progressive Dementia , 2017, Int. J. Neural Syst..

[2]  Don Coppersmith,et al.  Matrix multiplication via arithmetic progressions , 1987, STOC.

[3]  H. Adeli,et al.  OBJECT-ORIENTED FINITE ELEMENT ANALYSIS USING EER MODEL , 1993 .

[4]  Chin-Teng Lin,et al.  An Improved Polynomial Neural Network Classifier Using Real-Coded Genetic Algorithm , 2015, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[5]  Andrés Ortiz,et al.  Ensembles of Deep Learning Architectures for the Early Diagnosis of the Alzheimer's Disease , 2016, Int. J. Neural Syst..

[6]  Hojjat Adeli,et al.  FUZZY-WAVELET RBFNN MODEL FOR FREEWAY INCIDENT DETECTION , 2000 .

[7]  Malek Adjouadi,et al.  A Cross-Correlated Delay Shift Supervised Learning Method for Spiking Neurons with Application to Interictal Spike Detection in Epilepsy , 2017, Int. J. Neural Syst..

[8]  D. Shepard.  A two-dimensional interpolation function for irregularly-spaced data , 1968, ACM National Conference.

[9]  Hojjat Adeli,et al.  A novel machine learning‐based algorithm to detect damage in high‐rise building structures , 2017 .

[10]  Hojjat Adeli,et al.  Probabilistic neural networks for diagnosis of Alzheimer's disease using conventional and wavelet coherence , 2011, Journal of Neuroscience Methods.

[11]  Hojjat Adeli,et al.  Distributed Finite-Element Analysis on Network of Workstations—Implementation and Applications , 1995 .

[12]  João Paulo Papa,et al.  Efficient supervised optimum-path forest classification for large datasets , 2012, Pattern Recognit..

[13]  Chih-Min Lin,et al.  Autolanding Control Using Recurrent Wavelet Elman Neural Network , 2015, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[14]  A Karim,et al.  COMPARISON OF THE FUZZY–WAVELET RBFNN FREEWAY INCIDENT DETECTION MODEL WITH THE CALIFORNIA ALGORITHM , 2002 .

[15]  Hojjat Adeli,et al.  Parallel backpropagation learning algorithms on CRAY Y-MP8/864 supercomputer , 1993, Neurocomputing.

[16]  João Paulo Papa,et al.  EEG signal classification for epilepsy diagnosis via optimum path forest - A systematic assessment , 2014, Neurocomputing.

[17]  Boguslaw Cyganek,et al.  Image recognition with deep neural networks in presence of noise - Dealing with and taking advantage of distortions , 2017, Integr. Comput. Aided Eng..

[18]  Hojjat Adeli,et al.  Comparison of fuzzy-wavelet radial basis function neural network freeway incident detection model with California algorithm , 2002 .

[19]  Ezequiel López-Rubio,et al.  Learning Topologies with the Growing Neural Forest , 2016, Int. J. Neural Syst..

[20]  Zhigang Zeng,et al.  Multistability of Recurrent Neural Networks With Nonmonotonic Activation Functions and Mixed Time Delays , 2016, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[21]  Donald F. Specht,et al.  Probabilistic neural networks , 1990, Neural Networks.

[22]  Hojjat Adeli,et al.  An adaptive conjugate gradient learning algorithm for efficient training of neural networks , 1994 .

[23]  F. Wilcoxon.  Individual Comparisons by Ranking Methods , 1945 .

[24]  R. Samworth.  Optimal weighted nearest neighbour classifiers , 2011, 1101.5783.

[25]  Hongzhe Dai,et al.  A Wavelet Support Vector Machine‐Based Neural Network Metamodel for Structural Reliability Assessment , 2017, Comput. Aided Civ. Infrastructure Eng..

[26]  Hojjat Adeli,et al.  Enhanced probabilistic neural network with local decision circles: A robust classifier , 2010, Integr. Comput. Aided Eng..

[27]  Hojjat Adeli,et al.  Computer-Aided Diagnosis of Parkinson’s Disease Using Enhanced Probabilistic Neural Network , 2015, Journal of Medical Systems.

[28]  Corinna Cortes,et al.  Support-Vector Networks , 1995, Machine Learning.

[29]  Jaakko Lehtinen,et al.  A meshless hierarchical representation for light transport , 2008, ACM Trans. Graph..

[30]  Jui-Sheng Chou,et al.  Smart Artificial Firefly Colony Algorithm‐Based Support Vector Regression for Enhanced Forecasting in Civil Engineering , 2015, Comput. Aided Civ. Infrastructure Eng..

[31]  Hojjat Adeli,et al.  RADIAL BASIS FUNCTION NEURAL NETWORK FOR WORK ZONE CAPACITY AND QUEUE ESTIMATION , 2003 .

[32]  Hojjat Adeli,et al.  Machine Learning: Neural Networks, Genetic Algorithms, and Fuzzy Systems , 1994 .

[33]  Leonardo Franco,et al.  Layer multiplexing FPGA implementation for deep back-propagation learning , 2017, Integr. Comput. Aided Eng..

[34]  Alexandre X. Falcão,et al.  Data clustering as an optimum‐path forest problem with applications in image analysis , 2009, Int. J. Imaging Syst. Technol..

[35]  Rodrigo Nakamura,et al.  Toward Satellite-Based Land Cover Classification Through Optimum-Path Forest , 2014, IEEE Transactions on Geoscience and Remote Sensing.

[36]  Yi-Zhou Lin,et al.  Structural Damage Detection with Automatic Feature‐Extraction through Deep Learning , 2017, Comput. Aided Civ. Infrastructure Eng..

[37]  ChaYoung-Jin,et al.  Deep Learning-Based Crack Damage Detection Using Convolutional Neural Networks , 2017 .

[38]  Hojjat Adeli,et al.  Supervised Deep Restricted Boltzmann Machine for Estimation of Concrete , 2017 .

[39]  Hojjat Adeli,et al.  A Concurrent Adaptive Conjugate Gradient Learning Algorithm On Mimd Shared-Memory Machines , 1993, Int. J. High Perform. Comput. Appl..

[40]  Robert J. Holt,et al.  Rational parametrizations of nonsingular real cubic surfaces , 1998, TOGS.

[41]  Guigang Zhang,et al.  Deep Learning , 2016, Int. J. Semantic Comput..

[42]  Mohammed Bennamoun,et al.  A Novel Adaptive Kernel for the RBF Neural Networks , 2016, Circuits, Systems, and Signal Processing.

[43]  João Paulo Papa,et al.  Optimum-Path Forest based on k-connectivity: Theory and applications , 2017, Pattern Recognit. Lett..

[44]  Yang Liu,et al.  Automated Pixel‐Level Pavement Crack Detection on 3D Asphalt Surfaces Using a Deep‐Learning Network , 2017, Comput. Aided Civ. Infrastructure Eng..

[45]  Hojjat Adeli,et al.  Distributed Finite-Element Analysis on Network of Workstations—Algorithms , 1995 .

[46]  Mohammad Hossein Rafiei,et al.  A Novel Machine Learning Model for Estimation of Sale Prices of Real Estate Units , 2016 .

[47]  Oral Büyüköztürk,et al.  Deep Learning‐Based Crack Damage Detection Using Convolutional Neural Networks , 2017, Comput. Aided Civ. Infrastructure Eng..

[48]  João Paulo Papa,et al.  Supervised pattern classification based on optimum‐path forest , 2009, Int. J. Imaging Syst. Technol..