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AnArtificialNeuralNetwork(ANN)modelstherelationshipbetweenaset of input signals and an output signal using a model derived from our understandingofhowabiologicalbrainrespondstostimulifromsensory inputs. Just as a brain uses a network of interconnected cells called neurons to create a massive parallel processor, ANN uses a network of artificialneuronsornodestosolvelearningproblems The human brain is made up of about 85 billion neurons, resulting ina network capable of representing a tremendous amount of knowledge Understanding neuralnetworks For instance, a cat has roughly a billion neurons, amouse has about 75 million neurons, and a cockroach has only about a million neurons. In contrast, many ANNs contain far fewer neurons, typically only several hundred,sowe'reinnodangerofcreatinganartificialbrainanytimein the nearfuture
Biological toartificial neurons Incomingsignalsarereceivedbythecell'sdendritesthroughabiochemicalprocess. Theprocessallowstheimpulsetobeweightedaccordingtoits relativeimportanceor frequency.Asthecellbodybeginsaccumulatingtheincomingsignals,athresholdis reached at which the cell fires and the output signal is transmitted via an electrochemicalprocessdowntheaxon.Attheaxon'sterminals,theelectricsignalis againprocessedasachemicalsignaltobepassedtotheneighbouringneurons.
This directed network diagram defines a relationship between the input signals received by the dendrites (x variables), andtheoutputsignal (yvariable).Justas with the biological neuron, each dendrite's signal is weighted (w values) according to its importance. The input signalsaresummedbythecellbodyand the signal is passed on according to an activationfunctiondenotedbyf A typical artificial neuron with n input dendrites can be represented by the formula that follows. Thewweightsalloweachoftheninputs(denoted by xi) to contribute a greater or lesser amount to thesumofinputsignals.Thenettotalis usedbythe activation function f(x), and the resulting signal, y(x), is the outputaxon
In biological sense, the activation function could be imagined as a process thatinvolvessummingthetotalinputsignalanddeterminingwhetheritmeets the firing threshold. If so, the neuron passes on the signal; otherwise, it does nothing. In ANN terms, this is known as a threshold activation function, as it results in an output signal only once a specified input threshold has been attained The following figure depicts a typical threshold function; in this case, the neuron fires when the sum of input signals is at least zero.Becauseitsshaperesemblesastair,itissometimescalleda unit step activationfunction
Theabilityofaneuralnetworktolearnisrootedinitstopology,or • the patterns andstructures of interconnected neurons • keycharacteristics • The number oflayers • Whetherinformationinthenetworkisallowedtotravelbackward • Thenumberofnodeswithineachlayerofthenetwork Networktopology
Number oflayers Theinputandoutputnodesarearrangedingroupsknownaslayers Inputnodesprocesstheincomingdataexactlyasitisreceived, thenetworkhas onlyonesetofconnectionweights(labeledhere as w1, w2, and w3). It is therefore termed asingle-layer network
A Support Vector Machine (SVM) can be imagined as a surface that creates aboundarybetweenpointsofdataplottedinmultidimensional thatrepresentexamplesandtheirfeaturevalues ThegoalofaSVMistocreateaflatboundarycalledahyperplane,which dividesthespacetocreatefairlyhomogeneous partitions on eitherside SVMscanbeadaptedforusewithnearlyanytypeoflearningtask, includingbothclassificationandnumericprediction
For example, the following figure depicts hyperplanes that separate groups of circles and squares in two and three dimensions. Because thecirclesandsquarescanbeseparatedperfectlybythestraightline orflatsurface,theyaresaidtobelinearlyseparable Classification with hyperplanes
Intwodimensions,thetaskoftheSVMalgorithmistoidentifyalinethat separatesthetwoclasses.Asshown inthefollowingfigure,thereismore than one choice of dividing line between the groups of circles and squares. How doesthe algorithm choose Which is the “best”Fit!
AkeyfeatureofSVMsistheirabilitytomaptheproblemintoahigher dimensionspaceusingaprocessknownasthekerneltrick.Indoingso, anonlinearrelationshipmaysuddenlyappeartobequitelinear. Using kernels for non-linearspaces Afterthekerneltrickhasbeenapplied,welookatthedata through the lens of a new dimension: altitude. With the addition of this feature, the classes are now perfectly linearlyseparable