Top

Neural Processing Letters

Published in:

19-04-2019

A New Complex-Valued Polynomial Model

Authors: Bin Yang, Yuehui Chen

Published in: Neural Processing Letters | Issue 3/2019

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

This paper presents a novel complex-valued polynomial model (CPM) for real-valued prediction and classification problems. In a CPM, function, independent variables and dependent variables are complex-valued. Before CPM optimization, real-valued data need to be converted into complex values. As the linear version of additive tree model, additive expression tree is proposed to optimize the complex-valued structure of CPM. Real parts and imaginary parts of the complex-valued coefficients are encoded into a chromosome and brain storm optimization is utilized to evolve the complex-valued coefficients of CPM. CPM is utilized to predict three financial datasets and classify n-class problems. The prediction results show that CPM presents higher forecasting accuracy than real-valued polynomial model, other real-valued neural networks and ordinary differential equation. The classification performance of CPM is compared with existing methods on IRIS, Liver and Ionosphere datasets. And the results reveal that CPM performs better than well-established and newly proposed real-valued classifiers.

previous article No-Reference Video Quality Assessment Based on the Temporal Pooling of Deep Features

next article Generalizing the Convolution Operator in Convolutional Neural Networks

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Wilson RG (1985) Potential for using weed seed content in the soil to predict future weed problems. Weed Sci 33(2):171–175CrossRef

Borg JAMVD, Netto WJ, Planta DJU (1991) Behavioural testing of dogs in animal shelters to predict problem behavior. Appl Anim Behav Sci 32(2–3):237–251CrossRef

Crowley RS, Medvedeva O (2006) An intelligent tutoring system for visual classification problem solving. Artif Intell Med 36(1):85–117CrossRef

Vakil AC (1997) Confronting the classification problem: toward a taxonomy of NGOs. World Dev 25(12):2057–2070MathSciNetCrossRef

Angeline PJ, Saunders GM, Pollack JB (1994) An evolutionary algorithm that constructs recurrent neural networks. IEEE Trans Neural Netw 5:54–65CrossRef

Yao X (1999) Evolving artificial neural networks. Proc IEEE 87:1423–1447CrossRef

Ding J, Ding F, Liu XP, Liu GJ (2011) Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data. IEEE Trans Autom Control 56(11):2677–2683MathSciNetMATHCrossRef

Kandpal M, Kalyan CM, Samavedham L (2013) Genetic programming-based approach to elucidate biochemical interaction networks from data. IET Syst Biol 7(1):18–25CrossRef

Chen YH, Yang J, Zhang Y, Dong JW (2005) Evolving additive tree models for system identification. Int J Comput Cogn 3(2):19–26

10.

Muttil N, Lee JHW (2005) Genetic programming for analysis and real-time prediction of coastal algal blooms. Ecol Model 189(3):363–376CrossRef

11.

Azzawi H, Hou J, Xiang Y, Alanni R (2016) Lung cancer prediction from microarray data by gene expression programming. IET Syst Biol 10(5):168–178CrossRef

12.

Ma X, Liu ZB (2016) Predicting the oil well production based on multi expression programming. Open Pet Eng J 9(1):21–32CrossRef

13.

Al-Sahaf H, Zhang M, Johnston M (2016) Binary image classification: a genetic programming approach to the problem of limited training instances. Evol Comput 24(1):143–182CrossRef

14.

Zhou C, Xiao W, Tirpak TM, Nelson PC (2003) Evolving accurate and compact classification rules with gene expression programming. IEEE Trans Evol Comput 7(6):519–531CrossRef

15.

Trabelsi C, Bilaniuk O, Zhang Y, Serdyuk D, Subramanian S (2018) Deep complex networks. ICLR 2018:1–19

16.

Li S (2005) An modified error function for the complex-value backpropagation neural networks. Neural Inf Process Lett Rev 2005(1):1

17.

You C, Hong D (1998) Nonlinear blind equalization schemes using complex-valued multilayer feedforward neural networks. IEEE Trans Neural Netw 9(6):1442–1455CrossRef

18.

Chen S, Mclaughlin S, Mulgrew B (1994) Complex-valued radial basis function network, Part II: application to digital communications channel equalisation. Signal Process 36(2):175–188MATHCrossRef

19.

Popa CA (2018) Complex-valued deep belief networks. Lecture notes in computer science, pp 72–78CrossRef

20.

Xiong T, Bao Y, Hu Z, Chiong R (2015) Forecasting interval time series using a fully complex-valued RBF neural network with DPSO and PSO algorithms. Inf Sci 305(C):77–92CrossRef

21.

Saoud LS, Rahmoune F, Tourtchine V, Baddari K (2017) Fully complex valued wavelet network for forecasting the global solar irradiation. Neural Process Lett 45:475–505CrossRef

22.

Amin MF, Murase K (2009) Single-layered complex-valued neural network for real-valued classification problems. Neurocomputing 72(4):945–955CrossRef

23.

Amin MF, Islam MM, Murase K (2009) Ensemble of single-layered complex-valued neural networks for classification tasks. Neurocomputing 72(10):2227–2234CrossRef

24.

Savitha R, Suresh S, Sundararajan N (2012) Fast learning circular complex-valued extreme learning machine (CC-ELM) for real-valued classification problems. Inf Sci 187(1):277–290MathSciNetCrossRef

25.

Zhang Z, Wang H, Xu F, Jin YQ (2017) Complex-valued convolutional neural network and its application in polarimetric SAR image classification. IEEE Trans Geosci Remote Sens 55(12):1–12CrossRef

26.

Yang B (2015) Using additive expression programming for system identification. Lect Not Comput Sci 9225:671–681CrossRef

27.

Yang B (2015) A nonlinear system identification based on additive expression tree model with cuckoo search. Int J Hybrid Inf Technol 8(8):393–404CrossRef

28.

Cheng S, Qin Q, Chen J, Shi Y (2015) Brain storm optimization algorithm: a review. Artif Intell Rev 6728(CEC):1–14

29.

Chen YH, Abraham A (2006) Hybrid learning methods for stock index modeling. IdeaGroup Inc, Publishers, HersheyCrossRef

30.

Chen Y, Yang B, Dong J (2006) Time-series prediction using a local linear wavelet neural network. Neurocomputing 69(4):449–465CrossRef

31.

Chen Y, Yang B, Abraham A (2007) Flexible neural trees ensemble for stock index modeling. Neurocomputing 70(4–6):697–703CrossRef

32.

Chen YH, Yang B, Meng QF, Zhao YO, Abraham A (2011) Time-series forecasting using a system of ordinary differential equations. Inf Sci 181(1):106–114CrossRef

33.

Zhang W, Yang B (2017) Stock market forecasting using S-system model. In: Advances in intelligent systems and computing, pp 397–403

34.

Wang HF, Yang B, Lv JG (2017) Complex-valued neural network model and its application to stock prediction. Adv Intell Syst Comput 552:21–28

35.

Kamal P, Bhusry M (2016) Artificial bee colony optimization based negative selection algorithms to classify iris plant dataset. Int J Comput Appl 133(10):40–43

36.

Wandra KH, Gagnani LP (2017) Classification techniques in WEKA: a review. Int J Comput Sci Eng 5(8):49–52

37.

Mohan PM, Paul NK, Prakash M, Praveen KD, Chidambaram S (2018) Comparative evaluation of various techniques for Fisher’s iris classification. Int J Innov Res Sci Eng Technol 7(1):198–202

38.

Dutta D, Roy A, Choudhury K (2013) Trainning aritificial neural network using particle swarm optimization algorithms. IJARCSSE 3(3):430–434

39.

Halakatti ST (2017) Identification of iris flower species using machine learning. Int J Comput Sci 5(8):59–69

40.

Pietrzykowski M (2014) Use of the mini-model method in classification task on example of iris flower dataset. J Theor Appl Comput Sci 8(2):27–36

41.

Giacinto G, Roli F (2001) Dynamic classifier selection based on multiple classifier behaviour. Pattern Recognit 34:1879–1881MATHCrossRef

42.

Smits PC (2002) Multiple classifier systems for supervised remote sensing image classification based on dynamic classifier selection. IEEE Trans Geosci Remote Sens 40(4):801–813CrossRef

43.

Woods K, Kegelmeyer WP Jr, Bowyer K (1997) Combination of multiple classifiers using local accuracy estimates. IEEE Trans Pattern Anal Mach Intell 19:405–410CrossRef

44.

Ko AHR, Sabourin R, Britto AS Jr (2008) From dynamic classifier selection to dynamic ensemble selection. Pattern Recognit 41:1735–1748MATHCrossRef

45.

Cavalin PR, Sabourin R, Suen CY (2013) Dynamic selection approaches for multiple classifier systems. Neural Comput Appl 22(3–4):673–688CrossRef

46.

Chandrashekar G, Sahin F (2014) A survey on feature selection methods. Comput Electr Eng 40(1):16–28CrossRef

47.

Cruz RMO, Sabourin R, Cavalcanti GDC, Ren META-DESTI (2015) A dynamic ensemble selection framework using meta-learning. Pattern Recognit 48(5):1925–1935CrossRef

48.

Casasent D, Natarajan S (1995) A classifier neural network with complex-valued weights and square-law nonlinearities. Neural Netw 8(6):989–998CrossRef

49.

Li L, Zhou Y (2014) A novel complex-valued bat algorithm. Neural Comput Appl 25(6):1369–1381CrossRef

50.

Hirose A, Yoshida S (2012) Generalization characteristics of complex-valued feedforward neural networks in relation to signal coherence. IEEE Trans Neural Netw Learn Syst 23(4):541–551CrossRef

Title: A New Complex-Valued Polynomial Model
Authors: Bin Yang
Yuehui Chen
Publication date: 19-04-2019
Publisher: Springer US
Published in: Neural Processing Letters / Issue 3/2019
Print ISSN: 1370-4621
Electronic ISSN: 1573-773X
DOI: https://doi.org/10.1007/s11063-019-10042-8

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 3/2019

A Novel Genetically Optimized Convolutional Neural Network for Traffic Sign Recognition: A New Benchmark on Belgium and Chinese Traffic Sign Datasets

Dynamic Optimization of Neuron Systems with Leakage Delay and Distributed Delay via Hybrid Control

Double-Key Secure for N-1-N Sound Record Data (SRD) by the Drive-Response of BAM NNs

End-to-End Trained Sparse Coding Network with Spatial Pyramid Pooling for Image Classification

The Intermittent Control Synchronization of Complex-Valued Memristive Recurrent Neural Networks with Time-Delays

Learning Distance Metric for Support Vector Machine: A Multiple Kernel Learning Approach