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The body produces DMG in the cells by breaking down choline (see reference 1 under Clinical Summary). In the body, it acts as an antioxidant and improves oxygenation of the cells (see reference 1 under Clinical Summary). The thought is that taking DMG as a supplement may further enhance oxygenation, which improves athletic performance (see reference 1 under Clinical Summary). It is also thought to act as a neurological stimulator, which is why it has gained popularity in the autism community (see reference 1 under Clinical Summary). According to an October 2009 review article on the use of complementary medicine in autism published in 'Child and Adolescent Psychiatric Clinics,' the two clinical trials testing the use of DMG on children with autism showed no positive effect or improvement in behavior (see reference 2 under DMG).
Safety Concerns
DMG is considered a safe and non-toxic substance, according to MSKCC (see reference 1 under Clinical Summary). If you're supplementing your diet with DMG, be sure to inform your doctor to monitor for any potential side effects or interactions. Additionally, while it's safe to take DMG, do not rely on it as a cure or treatment for any illness.
PMML 3.2 - Support Vector Machine
Support Vector Machine Models
The description of SupportVector Machine (SVM) models assumes some familiarity with the SVMtheory. Inthis specification, Support Vector Machine models for classificationandregression are considered. A Support Vector Machine is a function fwhich isdefined in the space spanned by the kernel basis functionsK(x,xi) ofthe support vectors xi:
f(x) = Sum_(i=1)nαi*K(x,xi) + b.
Here n is the number of allsupport vectors, αi are the basis coefficients and b is theabsolutecoefficient. In an equivalent interpretation, n could also beconsidered as thetotal number of all training vectors xi. Then the support vectors arethesubset of all those vectors xi whose coefficients αi are greaterthanzero. The term Support Vector (SV) has also a geometricalinterpretationbecause these vectors really support the discrimination functionf(x) = 0 in the mechanical interpretation.
Since a PMML document may contain some SVM models, for instance formulticlass problems or for trees with SVM nodes, which often share commonsupport vectors, it is useful to store the SVs only in one place of the PMMLdocument. The specification supports this by introducing a commonVectorDictionary.
The attribute modelNamespecifies the name of the SVM model.
The attribute functionNamecould be either classification or regression depending on the SVM type.
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The attribute svmRepresentation defines whether the SVM function is defined via support vectors orvia the coefficients of the hyperplane for the case of linear kernel functions.
The attribute alternateBinaryTargetCategory is required in case of binary classification models with onlyone SupportVectorMachine element. For binary classification, the numeric predictionmust be between 0 and 1. The corresponding class labels are determined by rounding the numeric prediction where 1 corresponds to the targetCategory attribute of the SupportVectorMachine element, and 0 to the alternateBinaryTargetCategory attribute of the SupportVectorMachineModel element.
Since SVMs require numeric attributes which also could be normalized,transformations are often applied which can be performed in theLocalTransformations element.
For each active MiningField,an element of type UnivariateStats (see ModelStats)holds information about the overall (background) population. Thisincludes(required) DiscrStatsor ContStats,which include possible field values and interval boundaries.Optionally, statistical information is included for the background data.
The KERNEL_TYPEdefines the function space of theSVM solution through the choice of the basis functions.
The VectorDictionaryelement holds all support vectors from all support vectormachines.
SVM Representation
Usually the SVM model usessupport vectors to define the model function. However, for the case ofa linearfunction (linear kernel type) the function is a linear hyperplane thatcan bemore efficiently expressed using the coefficients of all mining fields.In this case, no support vectors are required at all, and henceSupportVectors will be absent and only the Coefficients element isnecessary.
The SVM representation specifies which of both representations is used:
KernelTypes
The kernel defines the typeof the basis functions of the SVM model. There exists a huge number ofkerneltypes. The most popular ones are:
LinearKernelType: linear basis functions which lead to a hyperplane as classifier
PolynomialKernelType: polynomial basis functions which lead to a polynome classifier
RadialBasisKernelType: radial basis functions, the most common kernel type
SigmoidKernelType: sigmoid kernel functions for some models of Neural Network type
Support Vectors
As already mentioned, a vector dictionary was introduced to store allsupport vectors. The VectorDictionary is a general container of vectorsand could, in principle, also be used for models other than Support VectorMachine.
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The VectorDictionarycontains the set of support vectors which are of the typeVectorInstance.If present, the attribute numberOfVectors must be equal to the number ofvectorscontained in the dictionary.
VectorFields defines which entries in the vectors correspond to which fields. The sequence of the fields as given in VectorFields corresponds to the entries in the vectors. Fields referenced can be from the MiningSchema, TransformationDictionary or LocalTransformations. numberOfFields gives the number of entries in VectorFields, which corresponds to the dimension of the vectors in the VectorDictionary.
The elements VectorInstancerepresent support vectors and are referenced by the id-attribute.They do not contain the value of the predicted mining field.
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The VectorInstance isa data vector given in sparse array format. The order of the values corresponds to that of the VectorFields. The sizes of the sparse arrays must match the number of fields included in the VectorFields element.
Notice that the sparserepresentation is an important issue because SVMs are usually able tohandle very high-dimensional data whereas the number of support vectors tendsto be small.
SupportVectorsholds the support vectors as references towards VectorDictionary used by therespective SVM instance.For storing the SVM coefficients, the elementCoefficients is used.Both are combined in the element SupportVectorMachine, whichholds a single instance of an SVM.
targetCategory is required for classification models and gives the corresponding class label.
The element SupportVectorscontains all support vectors required for the respective SVM instance.
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The support vectors are represented by the element SupportVectorwhich only has the attribute vectorId - the reference to the supportvector in VectorDictionary.If numberOfSupportVectors is specified, then it mustmatch the number of SupportVector elements. If numberOfAttributes isspecified, then it must match the number of attributes in the support vectors(which all must have the same length). If one of these requirements is not fulfilled,then the PMML is not valid.
Support Vector Coefficients
The element Coefficientsis used to store the support vector coefficients αi and b.
Each coefficientαi is described by the element Coefficient and the numberofcoefficients corresponds to that of the support vectors. Hence theattribute numberOfCoefficientsis equal to the number of support vectors. The attribute absoluteValuecontains the value of the absolute coefficient b.
Example Model
Scoring procedure, example
Consider the same example as above in order to illustrate the scoringprocedure of the Support Vector Machine. Given the first support vectoras input vector
x = mv0 = (x1=0.0, x2=0.0)
we calculate as follows:
f(x) = Sum_(i=1)n αi*K(x,xi) + bDmg File Download
= -1.0*K(x,mv0) + 1.0*K(x,mv1) + 1.0*K(x,mv2) -1.0*K(x,mv3) + 0.5
= -1.0*exp(-1.0* x - mv02) + 1.0*exp(-1.0* x - mv12) +1.0*exp(-1.0* x - mv22) -1.0*exp(-1.0* x - mv32) + 0.5
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= -1.0*exp(-1.0* (0,0)T - (0,0)T2) +1.0*exp(-1.0* (0,0)T - (0,1)T2) +1.0*exp(-1.0* (0,0)T - (1,0)T2) -1.0*exp(-1.0* (0,0)T - (1,1)T2) + 0.5
= -1.0*exp(-1.0* (0,0)T2) + 1.0*exp(-1.0* (0,-1)T2) +1.0*exp(-1.0* (-1,0)T2) -1.0*exp(-1.0* (-1,-1)T2) + 0.5
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= -1.0*exp(0.0) + 1.0*exp(-1.0) + 1.0*exp(-1.0) -1.0*exp(-2.0) + 0.5
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f(x) = 0.100424 .
In the same way, the scoring of the other support vectors delivers
f(x = mv1) = 0.899576thus reasonably approximating the training data.
f(x = mv2) = 0.899576
f(x = mv3) = 0.100424
A classification with a threshold of 0.5 would assign the vectors mv0 and mv3 toclass no and the vectors mv1 and mv2 to class yes delivering an exactclassification of the training data.