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	<pub:Article rdf:about="http://ebiquity.umbc.edu/paper/html/id/933/The-Normalized-Risk-Averting-Error-Criterion-for-Avoiding-Nonglobal-Local-Minima-in-Training-Neural-Networks">
		<rdfs:label><![CDATA[The Normalized Risk-Averting Error Criterion for Avoiding Nonglobal Local Minima in Training Neural Networks]]></rdfs:label>
		<pub:title><![CDATA[The Normalized Risk-Averting Error Criterion for Avoiding Nonglobal Local Minima in Training Neural Networks]]></pub:title>
		<pub:publishedOn rdf:datatype="&xsd;dateTime">2015-02-01T00:00:00-05:00</pub:publishedOn>
		<pub:abstract><![CDATA[The convexification method for data fitting is capable of avoiding nonglobal local minima, but suffers from two shortcomings:
The risk-averting error (RAE) criterion grows exponentially as its risk-sensitivity index λ increases, and the existing method of
determining λ is often not effective. To eliminate these shortcomings, the normalized RAE (NRAE) is herein proposed. As NRAE
is a monotone increasing function of RAE, the region without a nonglobal local minimum of NRAE expands as does that of RAE.
However, NRAE does not grow unboundedly as does RAE.
The performances of training with NRAE at a fixed λ are reported. Over a large range of the risk-sensitivity index, such training
has a high rate of achieving a global or near global minimum starting with different initial weight vectors of the neural network
under training. It is observed that at a large λ, the landscape of the NRAE is rather flat, which slows down the training to a halt. This
observation motivates the development of the NRAE-MSE method that exploits the large region of an NRAE without a nonglobal
local minimum and takes excursions from time to time for training with the standard mean squared error (MSE) to zero into a
global or near global minimum. A number of examples of approximating functions that involve fine features or unevenly-sampled
segments are used to test the method. Numerical experiments show that the NRAE-MSE training method has a success rate of
100% in all the testing trials for each example, all starting with randomly selected initial weights. The method is also applied
to classifying numerals in the well-known MNIST dataset. The new training method outperforms other methods reported in the
literature under the same operating conditions.]]></pub:abstract>
		<pub:number><![CDATA[3]]></pub:number>
		<pub:volume><![CDATA[149]]></pub:volume>
		<pub:counter>598</pub:counter>
		<pub:tag><![CDATA[convexification]]></pub:tag>
		<pub:tag><![CDATA[global optimization]]></pub:tag>
		<pub:tag><![CDATA[local minimum]]></pub:tag>
		<pub:tag><![CDATA[neural network]]></pub:tag>
		<pub:tag><![CDATA[risk-averting error]]></pub:tag>
		<pub:tag><![CDATA[training]]></pub:tag>
		<pub:booktitle><![CDATA[Neurocomputing]]></pub:booktitle>
		<pub:author>
			<rdf:List>
				<rdf:first>
					<person:Person rdf:about="http://ebiquity.umbc.edu/person/html/Yun/Peng"><person:name><![CDATA[Yun Peng]]></person:name><rdfs:label><![CDATA[Yun Peng]]></rdfs:label></person:Person>
				</rdf:first>
				<rdf:rest>					<rdf:List>
						<rdf:first>
							<person:Person rdf:about="http://ebiquity.umbc.edu/person/html/James/Lo"><person:name><![CDATA[James Lo]]></person:name><rdfs:label><![CDATA[James Lo]]></rdfs:label></person:Person>
						</rdf:first>
						<rdf:rest>							<rdf:List>
								<rdf:first>
									<person:Person rdf:about="http://ebiquity.umbc.edu/person/html/Yichuan/Gui"><person:name><![CDATA[Yichuan Gui]]></person:name><rdfs:label><![CDATA[Yichuan Gui]]></rdfs:label></person:Person>
								</rdf:first>
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		</pub:author>
		<pub:firstAuthor>
<person:Person rdf:about="http://ebiquity.umbc.edu/person/html/Yun/Peng"><person:name><![CDATA[Yun Peng]]></person:name><rdfs:label><![CDATA[Yun Peng]]></rdfs:label></person:Person>
		</pub:firstAuthor>
		<pub:softCopy><pub:SoftCopy>
			<pub:softCopyFormat><![CDATA[PDF Document]]></pub:softCopyFormat>
			<pub:softCopyURI><![CDATA[http://ebiquity.umbc.edu/get/a/publication/1018.pdf]]></pub:softCopyURI>
			<pub:softCopySize>2203309</pub:softCopySize>
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	</pub:Article>

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