基于極端學習機算法的學習

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摘要 人工智能是一門邊沿學科，屬于自然科學、社會科學、技術(shù)科學三向的交叉學科。半個世紀以來，作為一門新興學科，人工智能一直在不停地發(fā)展，其涉及的學科越來越多，研究的范疇也越來越大，應(yīng)用的領(lǐng)域也越來越廣。在其眾多學科中，機器學習的前饋神經(jīng)網(wǎng)絡(luò)以及極端學習機算法便是本文要研究的內(nèi)容。
通常，前饋神經(jīng)網(wǎng)絡(luò)的學習速度遠遠慢于需求。這已經(jīng)成為了在過去的幾十年里其應(yīng)用的一個主要瓶頸?？赡艿膬蓚€關(guān)鍵原因是：1）較為緩慢的基于梯度的學習算法被廣泛用來訓練神經(jīng)網(wǎng)絡(luò)，以及2）網(wǎng)絡(luò)中的所有參數(shù)都使用這種學習算法反復調(diào)整。因此，有學者提出了極端學習機（ELM）算法。ELM是一種簡單易用、有效的單隱層前饋神經(jīng)網(wǎng)絡(luò)（SLFNs）學習算法，其本質(zhì)在于隱層是不需要調(diào)整。理論上講，這種算法易于以極快的學習速度提供更好的泛化性能。
盡管ELM性能優(yōu)于前饋神經(jīng)網(wǎng)絡(luò)，但依舊有著一些缺陷。為此，研究人員又提出了改進的ELM算法以彌補ELM的一些不足，例如增量極端學習機（I-ELM）、加強I-ELM（EI-ELM）、自適應(yīng)增長極端學習機（AG-ELM）、基于微粒群算法改進的極端學習機（PSO-ELM）等等。實驗結(jié)果表明，PSO-ELM比ELM擁有更好的泛化性能，I-ELM、EI-ELM可以處理廣泛的神經(jīng)元，AG-ELM有優(yōu)于ELM的逼近能力。本文對極端學習機及各種改進的極端學習機進行研究學習，并將其應(yīng)用到sinc函數(shù)的回歸和UCI數(shù)據(jù)集中。

關(guān)鍵詞：人工智能；前饋神經(jīng)網(wǎng)絡(luò)；極端學習機。

Learning based on ELM algorithms
Abstract Artificial intelligence is an edge discipline, which is an interdisciplinary course combining natural science, social science and technology science. As a new discipline, artificial intelligence has been developing for half a century. Meanwhile, more and more disciplines have been involved, larger and larger areas has been researched and wider and wider field has been applied. Among its large number of disciplines, feedforward neural networks of machine learning and the algorithms of extreme learning machine(ELM) are to be studied in this paper.
As usual, the learning speed of feedforward neural networks is in general far lower than required and it has been a major bottleneck in their applications for past decades. Two key reasons behind may be: 1) the slow gradient-based learning algorithms are extensively used to train neural networks, and 2) all the parameters of the networks are tuned iteratively by using such learning algorithms. Therefore, some scholars have proposed extreme learning machine algorithm. ELM is an easy-to-use and effective algorithm of single hidden-layer feedforward neural networks (SLFNs) and its essence is that the hidden-layers don’t need to be tuned.
Although ELM performs better than feedforward neural networks, it still has some drawbacks. To make up the drawbacks, the researchers also proposed some improved algorithms of ELM such as: incremental ELM(I-ELM), enhanced incremental ELM(EI-ELM), Extreme Learning Machine with Adaptive Growth of Hidden Nodes(AG-ELM), and Extreme Learning Machine with Particle Swarm Optimization(PSO-ELM) etc. Experimental results show that PSO-ELM has better generalization performance than ELM; I-ELM, EI-ELM can handle a wide range of neurons; AG-ELM has a better approximation ability than ELM. In this paper, we will learn ELM and various improved ELM, and apply them to the regression of the function sinc and the data sets of UCI.
Key words Artificial intelligence; feedforward neural networks; ELM; drawbacks.

目 錄
第一章 緒論 1
1.1 神經(jīng)網(wǎng)絡(luò)的發(fā)展史 1
1.2 前饋神經(jīng)網(wǎng)絡(luò)和BP算法 2
1.2.1 前饋神經(jīng)網(wǎng)絡(luò)概述 2
1.2.2 BP算法 3
1.3 極端學習機ELM的提出 5
1.4 論文的結(jié)構(gòu)安排 5
第二章 極端學習機（ELM）相關(guān)概念及其算法 6
2.1 極端學習機的學習理論 6
2.2 極端學習機 7
2.2.1 摩爾彭德羅斯廣義逆 7
2.2.2 極端學習機算法 8
2.2.3 極端學習機的優(yōu)缺點 10
第三章 ELM的改進算法 11
3.1 I-ELM 11
3.2 AG-ELM 12
3.3 PSO-ELM 14
3.3.1 微粒群算法（PSO） 14
3.3.2 PSO-ELM 15
第四章 極端學習機及其改進算法的應(yīng)用 18
4.1 PSO-ELM的應(yīng)用和UCI數(shù)據(jù)集的分類 18
4.1.1. PSO-ELM應(yīng)用于SINC函數(shù)逼近 18
4.1.2 PSO的UCI數(shù)據(jù)集分類 19
4.2 ELM及其改進算法在UCI數(shù)據(jù)集上的應(yīng)用 20
結(jié)論 24
致謝 25
參考文獻 26