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	Sigmoid function - Wikipedia, the free encyclopedia
		A sigmoid function is a mathematical function that produces a sigmoid curve — a curve having an "S" shape.
		In general, a sigmoid function is real-valued and differentiable, having a non-negative or non-positive first derivative, one local minimum, and one local maximum.
		Sigmoid functions are often used in neural networks to introduce nonlinearity in the model and/or to make sure that certain signals remain within a specified range.
	en.wikipedia.org /wiki/Sigmoid_function (238 words)

	Encyclopedia: Sigmoid function
		In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena.
		In mathematics, the hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.
		This function is also called the standard logistic function and is often encountered in many technical domains, especially in artificial neural networks as a transfer function, probability, statistics, biomathematics, and economics.
	www.nationmaster.com /encyclopedia/Sigmoid-function (1051 words)

	United States Patent Application: 0040150602
		Further, since the inverse function of the sigmoid function which is an S-shaped function is used, it is possible to provide a display device which corrects the input/output characteristic of the display panel by performing the approximation in accordance with not plural functions but a single function (without dividing the characteristic into sections).
		In the sigmoid inverse function generator 10, an inverse function of a sigmoid function defined by an expression 1 described later is used to convert an input signal into an output signal.
		Thus, the sigmoid function is approximated to the applied voltage-transmittance characteristic curve (V-T curve) of the liquid crystal in which the voltage is applied from the driving circuit to the liquid crystal element.
	appft1.uspto.gov /netacgi/nph-Parser?Sect1=PTO1&Sect2=HITOFF&d=PG01&p=1&u=/netahtml/PTO/srchnum.html&r=1&f=G&l=50&s1="20040150602".PGNR.&OS=DN/20040150602&RS=DN/20040150602 (15224 words)

	Sigmoid function
		The terms sigmoid function or sigmoid curve are also used in the general sense of any real function of a real variable with a sigmoid ("S"-shaped) graph: i.e.
		Besides the standard function above and its examples of sigmoid functions (in this general sense) are the ordinary arc-tangent, the hyperbolic tangent, and the error function.
		In a neural network, a sigmoid function is often used to introduce nonlinearity in the model and/or to make sure that certain signals remains within a specified range.
	www.brainyencyclopedia.com /encyclopedia/s/si/sigmoid_function.html (302 words)

	Logistic function - Wikipedia, the free encyclopedia
		In addition, an important logistic function is the Rasch model, which is a general stochastic measurement model.
		The logistic function is the inverse of the natural logit function and so can be used to convert the logarithm of odds into a probability; the conversion from the log-likelihood ratio of two alternatives also takes the form of a sigmoid curve.
		Cohen explains that Verhulst attempted to fit a logistic curve based on the logistic function to 3 separate censuses of the population of the United States of America in order to predict future growth.
	en.wikipedia.org /wiki/Logistic_curve (957 words)

	Tutorial 4
		Note that all the functions are differentiable - this is because the backpropagation algorithm requires that activation functions have to be differentiable.
		A linear activation function is equivalent to having no activation function at all (ie the sum of the "signals" is the result sent to a node's children).
		The linear activation function does not suffer from this problem, but since it is not a "squashing" function (the sigmoid and hyperbolic tangent has finite ranges), it also has numerical problems with large training sets as all the sum of squares errors add up to large numbers.
	www.cs.ubc.ca /labs/lci/CIspace/Version4/neural/help/tutorial4.html (617 words)

	Training Setup - Network Design
		The sigmoid function is represented by the mathematical relationship 1/(1+e-x).
		Where the sigmoid function acts as a gate (opened, closed or somewhere in-between) for a node’s output response, the gaussian function acts as a probabilistic output controller.
		Like the sigmoid function, the output response is normalized between 0 and 1, but the gaussian transfer function is more likely to produce the “in-between state”.
	www.qnetv2k.com /Qnet2000Manual/html/qnet8awe.htm (1147 words)

	Transfer Functions (Site not responding. Last check: 2007-10-06)
		A node’s transfer functions serves the purpose of controlling the output signal strength for the node (except for the input layer which uses the inputs themselves).
		This sigmoid function is Qnet’s default transfer function and it is the most widely used function for backpropagation neural networks.
		The hyperbolic function counterparts to the sigmoid and gaussian functions are the hyperbolic tangent and hyperbolic secant functions.
	www.qnetv2k.com /Qnet2000Manual/html/qnet0n3n.htm (483 words)

	Artificial neuron - Wikipedia, the free encyclopedia
		The canonical form of transfer functions is the sigmoid, but they may also take the form of other non-linear functions, piecewise linear functions, or step functions.
		The transfer function of a neuron is chosen to have a number of properties which either enhance or simplify the network containing the neuron.
		A fairly simple non-linear function, the sigmoid also has an easily calculated derivative, which is used when calculating the weight updates in the network.
	en.wikipedia.org /wiki/Artificial_neuron (365 words)

	[No title]
		ERROR FUNCTION: The task of supervised learning is generally to minimize some function of the difference between the observed and the desired outputs, taken over all the outputs and over some set of input/output pairs.
		The most common error function is "mean squared error": the square of the difference between desired and observed outputs is averaged over all outputs and over the entire set of trials.
		This is the limiting case of the sigmoid activation function as T goes to 0.
	www.ics.uci.edu /~mlearn/databases/undocumented/connectionist-bench/GLOSSARY (1726 words)

	SIGMOID (Site not responding. Last check: 2007-10-06)
		Sigmoid generally means resembling the letter "S" or the lower-case Greek letter sigma.
		In mathematics, either a specific function - the logistic curve - or any real function whose graph has a sigmoid shape: see sigmoid function.
		In anatomy, the sigmoid colon is a part of the large intestine.
	www.yotor.org /wiki/en/si/Sigmoid.htm (67 words)

	[No title]
		For the sigmoid11 function the three sets of output values investigated are {-1, 1), {-0.9, 0.9} and {-0.99, 0.99} and for the standard sigmoid function the three sets are {-1.71, 1.71}, {-1.70, 1.70} and {-1.60, 1.60}.
		The sigmoid01 function achieves error values of less than 0.02452 for the training data which is not as good as the sigmoid11 function but it is better than the results obtained with the standard sigmoid function.
		For the sigmoid01 function it is the set {0.1, 0.9}, for the sigmoid11 function it is the set {-0.9, 0.9} and for the standard sigmoid function it is the set {-1.61, 1.61}.
	www.moonstar.com /~morticia/thesis/chapter5.html (4017 words)

	The activation function (Site not responding. Last check: 2007-10-06)
		The sigmoid function is global in the sense that it divides the feature space into two halves, one where the response is approaching 1 and another where it is approaching 0 (-1).
		Other choices are the Gaussian bar [41], which replaces the sigmoid function with a Gaussian, and the radial basis function [42].
		These are examples of local activation functions that can be useful if the effective dimension of the problem is lower than the actual number of variables, or if the problem is local.
	www.thep.lu.se /public_html/jetnet_30_manual/node16.html (245 words)

	Backpropogation and tanh - GameDev.Net Discussion Forums (Site not responding. Last check: 2007-10-06)
		Only the output is preprocess to be scaled to 0-1 as that is the output of the sigmoid function.
		A sigmoid is usually preferred in a classification task, because this makes it possible to interpret results in terms of likelihoods.
		In function approximation usually a tanh is preferred for the hidden units and a linear activation for the output neurons.
	www.gamedev.net /community/forums/topic.asp?topic_id=277726&whichpage=1� (875 words)

	2.3.3 Artificial Neuron with Continuous Characteristics
		The sum-of-product value is then passed into the second stage to perform the activation function which generates the output from the neuron.
		One convenient form of such ``semi-linear" function is the logistic sigmoid function, or in short, sigmoid function as shown in figure 2.6.
		Additionally, the sigmoid function describes the ``closeness" to the threshold point by the slope.
	www.ece.utep.edu /research/webfuzzy/docs/kk-thesis/kk-thesis-html/node14.html (291 words)

	OhioLINK ETD: BHARKHADA, BHARAT
		In the digital implementation of an ANN, the activation function is most widely implemented as a lookup table, and the accuracy of the output of the processing element depends partially on the number of words stored in the lookup table.
		As a case study, we compute the widely used activation function, the sigmoid function, by using a generic third order polynomial evaluator which is based on prior work addressing the problem of efficient function approximation for a system on a chip.
		The sigmoid function is approximated with a set of polynomials with integer coefficients.
	www.ohiolink.edu /etd/view.cgi?ucin1060978658 (350 words)

	Neural Networks: The Sigmoid Function
		The sigmoid function is so-called because it is shaped like one form of the Greek letter Sigma.
		Note that the speed advantage in BASIC between the exp function and the look-up table is nowhere near as much as it is in 'C'.
		An exerciser for the 'C' version of Sigmoid() was therefore written and exercised within the Microsoft Programmer's Workbench development environment using Microsoft C 6.00 as follows.
	users.computerweekly.net /robmorton/projects/neural/sigmoid.htm (2006 words)

	ipedia.com: Logistic function Article (Site not responding. Last check: 2007-10-06)
		The terms logistic function and logistic curve mean either the standard sigmoid function, or any function obtained from it by linear scaling and tr...
		These functions are found in a range of fields, from biology to economics.
		The logistic function is the inverse of the logit function and so can be used to convert the logarithm of odds into a probability; the conversion from the log-likelihood ratio of two alternatives also takes the form of a sigmoid curve.
	www.ipedia.com /logistic_function.html (324 words)

	Wikinfo \| Logistic curve
		The sigmoid curve is the curve whose formula is the sigmoid function.
		Members of the family of curves obtained by linear scaling and translation of the sigmoid curve are called logistic curves, and are found in a range of fields, from biology to economics.
		The sigmoid curve shows early exponential growth which slows to linear growth then decelerates until it reaches a saturation level at y = 1.
	www.wikinfo.org /wiki.php?title=Logistic_curve (329 words)

	Sigmoid Function Applet (Site not responding. Last check: 2007-10-06)
		The applet is provided to demonstrate the behaviour of the sigmoid output function.
		Also by changing the value of constant K, observe how the sigmoid function approaches to the sign; that is a threshold function taking valus of -1 and +1.
		You can observe the behaviour of the function in a larger range by changing "a" range.
	www.ii.metu.edu.tr /~ion526/demo/java/NNOC/Sigmoid.html (71 words)

	The Neuron Function in an Feedforward Network
		The sigmoid function is also recommended as the output of an FF network when you work on classification problems.
		The hyperbolic tangent and sigmoid functions are equivalent when used in the hidden neurons because there is a similarity transformation for the parameters that takes an FF network with one of the activation functions to the other.
		This activation function gives a local linear model that might be of interest in many situations.
	documents.wolfram.com /applications/neuralnetworks/ChangingTheNeuralNetworkStructure/13.3.2.html (222 words)

	Contents (Site not responding. Last check: 2007-10-06)
		A sigmoid unit is a type of threshold unit that has a smooth threshold function, rather than a step function.
		The output of a sigmoid unit is in the interval (0,1).
		The advantage of the sigmoid transfer function is that it is differentiable.
	www.cs.bham.ac.uk /~jlw/sem2a2/Web/LearningSigmoid.htm (309 words)

	Sigmoid function - Encyclopedia, History, Geography and Biography
		Sigmoid function - Encyclopedia, History, Geography and Biography
		This encyclopedia, history, geography and biography article about Sigmoid function contains research on
		Sigmoid function, Members of the sigmoid family, Sigmoid functions in neural networks, See also, Neural networks and Special functions.
	www.arikah.com /encyclopedia/Sigmoid_function (271 words)

	Imaging On-Line Store
		Sigmoid functions are usually utilized to overcome the nature loss in perceived lightness contrast that results when an image from a full dynamic range device is scaled into the limited dynamic range of a destination device.
		The adaptive quartile sigmoid function operator (QSFO) is selected based on cumulative distribution function that was developed from the results of a psychophysical experiment.
		The results of this study revealed that adaptive quartile sigmoid function operator was possible to enhance contrast of source images into preferred destination images.
	www.imaging.org /store/epub.cfm?abstrid=6900 (343 words)

	Programming a Neural Network
		An artificial neuron is, at it’s simplest, a set of numerical weights to be applied to the related incoming connections and a sigmoid function to adjust the output of the neuron.
		A sigmoid function is used to set the output value of any given neuron by processing the sum of the weighted input values and any bias applied.
		The sigmoid function outputs a value that is close to zero for a low total input value and close to one for a high input value.
	www.adit.co.uk /html/programming_a_neural_network.html (2013 words)

	2.13 The Sigmoid Function (Site not responding. Last check: 2007-10-06)
		Previously in section 2.5 it was said that any continuous function can be used as the transfer function.
		Notice that unlike the step function figure 3 there is not a straight jump up at the threshold value A. The function goes up smoothly and gently.
		The function is useful in multi layer networks since The function will give an 'on' or 'off' response for activations well above or below the threshold value The function will still give useful information if the activation is close to the threshold value.
	www.dalterio.demon.co.uk /projects/nnn/html/sigmoid.html (227 words)

	Holistic Health Encyclopedia - S (Site not responding. Last check: 2007-10-06)
		Although the main function of the stomach is to continue the breakdown of food that is started in the mouth and completed in the small intestine, it also acts as a storage organ, enabling food to be eaten only two or three times a day.
		Epidermis varies in thickness throughout the body depending mainly on frictional forces and is thickest on the palms of the hands and soles of the feet.
		This interferes with the function of a part of the body and is the beginning of degenerative disease.
	www.findhealer.com /glossary/S.php3 (8360 words)

	PopEcol Lect 23
		The sigmoid harvest function is shown in Fig.
		The sigmoid harvest function may be more a fact of life than something one can easily manipulate.
		Although it is not mathematically similar, a somewhat analogous alternation of effects occurs in some trophic interactions (look back at the sigmoid functional response curve and the coyote, scrubland bird examples of Lecture 21 and forward to the examples in Lecture 29 on regulation and trophic interactions).
	www.uwyo.edu /dbmcd/popecol/marlects/lect23.html (2059 words)

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