By Constantin Cranganu, Henri Luchian, Mihaela Elena Breaban
This ebook offers numerous clever techniques for tackling and fixing difficult useful difficulties dealing with these within the petroleum geosciences and petroleum undefined. Written by way of skilled lecturers, this ebook bargains state of the art operating examples and offers the reader with publicity to the newest advancements within the box of clever tools utilized to grease and fuel study, exploration and creation. It additionally analyzes the strengths and weaknesses of every technique provided utilizing benchmarking, when additionally emphasizing crucial parameters equivalent to robustness, accuracy, velocity of convergence, computing device time, overlearning and the position of normalization. The clever ways offered comprise synthetic neural networks, fuzzy common sense, energetic studying approach, genetic algorithms and aid vector machines, among others.
Integration, dealing with info of titanic dimension and uncertainty, and working with danger administration are between an important concerns in petroleum geosciences. the issues we need to remedy during this area have gotten too advanced to depend on a unmarried self-discipline for powerful suggestions and the prices linked to terrible predictions (e.g. dry holes) elevate. consequently, there's a have to determine a brand new method geared toward right integration of disciplines (such as petroleum engineering, geology, geophysics and geochemistry), facts fusion, hazard aid and uncertainty administration. those clever concepts can be utilized for uncertainty research, chance overview, information fusion and mining, info research and interpretation, and data discovery, from varied facts reminiscent of 3D seismic, geological info, good logging, and creation information. This publication is meant for petroleum scientists, facts miners, information scientists and pros and post-graduate scholars fascinated with petroleum industry.
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In turn, each netk depends on oj , which depends on netj . This allows us to write: Intelligent Data Analysis Techniques … @E ðwÞ ¼ @netj ¼ 35 X Nk 2dsðNj Þ X Nk 2dsðNj Þ @EðwÞ @netk @netk @netj @EðwÞ @netk @oj : @netj @oj @netj Observe that @oj ¼ h0 ðnetj Þ ¼ hðnetj Þð1 À hðnetj ÞÞ @netj k because h is a sigmoid function, and @ net @oj ¼ wk j because Nk 2 dsðNj Þ. This yields @EðwÞ ¼ oj ð1 À oj Þ @netj X Nk 2dsðNj Þ @E ðwÞ wk j : @netk If di ¼ À @EðwÞ for every neuron Ni , then @ neti @EðwÞ ¼ @wji ( À Á À ÁÀ À ÁÁ netj 1 À h netj if Nj is an output neuron À tjÀÀ oj hÁ P Àoj 1 À oj w if Nj is a hidden neuron: d Nk 2dsðNj Þ k k j The changes in the weights can now be written as ( Dwji ¼ gðtj À oj Þhðnet P j Þð1 À hðnetj ÞÞ if Nj is an output neuron goj ð1 À oj Þ Nk 2dsðNj Þ dk wkj if Nj is a hidden neuron: The backpropagation algorithm consists of the following steps: for each training example (x, t), where x ∈ X do input x in the network and obtain ox,j for each unit Nj ; for each output unit Nj compute Δwji = η(tj − oj )h(netj )(1 − h(netj )) and update wji ; for each hidden unit Nj compute Δwji = ηoj (1 − oj ) Nk ∈ds(Nj ) δk wkj and update wji ; end for Observe that the weight updates proceed from the output layer toward the inner layers, which justiﬁes the name of the algorithm.
R>0 . In view of Equality (4), if the data are approximately linearly separable in the new space, the classiﬁcation decision is based on computing n X yi ui /ðxi Þ0 /ðxÞ À a i¼1 Let K : H 2 ! R be the function deﬁned by Kðu; vÞ ¼ ðUðuÞ; UðvÞÞ; this function is referred to as a kernelPfunction, and the decision in the new space is based on the sign of the expression ni¼1 ðyi ui K xi ; xÞ À a. Thus, we need to specify only the kernel function rather than the explicit transformation /. 1, / is the identical transformation and the corresponding kernel, Kðu; vÞ ¼ u0 v, is known as the vannila kernel.
Cm g. The partition p ^ r of S consists of all non-empty intersections of the form Bi \ Cj , where 1 6 i 6 n and 16 j 6 m. Clearly, we have p ^ r 6 p and p ^ r 6 r. Moreover, if s is a partition of S such that s 6 p and s 6 r, then s 6p ^ r. If T & S is a non-empty subset of S, then any partition p ¼ fB1 ; . ; Bn g of S determines a partition pT on T deﬁned by pT ¼ fT \ Bi jBi 2 p and T \ Bi 6¼ ;g: For example, if p ¼ ffx1 ; x2 g; fx6 g; fx3 ; x5 g; fx4 gg, the trace on p on the set fx1 ; x2 ; x5 ; x6 g is the partition pT ¼ ffx1 ; x2 g; fx6 g; fx5 gg.