# Properties by Category

Local Model Toolbox

## Contents

- Data Set Properties
- Termination Criterion Properties
- Lossfunction Properties
- Other Properties
- Global Model Properties
- Local Model Properties
- Data Set Information Properties
- History Properties
- Algorithm Specific Properties
- SYMBOLS AND ABBREVIATIONS

## Data Set Properties

- `input` - (N x p) Matrix of the inputs
- `scaleInput` - (class) Scale input object
- `output` - (N x q) Matrix of the outputs.
- `scaleOutput` - (class) Scale output object. Empty for no
- `dataWeighting` - Weighting of the inputs.
- `outputWeighting` - Weighting of the outputs.
- `validationInput` - (? x p) Matrix of the validation data inputs.
- `validationOutput` - (? x q) Matrix of the validation data outputs.
- `validationOutput` - (? x p) Matrix of the test data inputs.
- `testOutput` - (? x q) Matrix of the test data outputs.
- `unscaledInput` - (N x p) Matrix of the unscaled inputs
- `unscaledOutput` - (N x q) Matrix of the unscaled outputs

## Termination Criterion Properties

- `maxNumberOfLM` - (1 x 1) Maximum number of LLMs termination criterion
- `minError` - (1 x 1) Loss function threshold termination criterion
- `maxNumberOfParameters` - (1 x 1) Maximum number of Parameter termination criterion
- `maxTrainTime` - (1 x 1) Maximum allowed time for the calculation
- `maxIterations` - (1 x 1) Maximum number of iterations termination criterion
- `maxPenaltyDeterioration` - (1 x 1) Maximum number of deterioration of the penalty loss function

## Lossfunction Properties

- `lossFunctionGlobal` - Global lossfunction type ('MSE','RMSE','NMSE','NRMSE', 'MISCLASS' and 'R2' can be chosen).
- `lossFunctionLocal` - Local lossfunction type ('SE','RSE','DRSE' and 'MISCLASS' can be chosen).
- `noiseVariance` - This property allows the user to define a certain process noise variance, based on prior knowledge about the process noise.
- `complexityPenalty` - Complexity penalty.
- `estNoiseVariance` -
- `crossvalidationValues` - Crossvalidation values for different model complexities

## Other Properties

- `info` - Stores the data set informations
- `history` - (class) history class stores information concerning the training algorithmn

## Global Model Properties

- `estimationProcedure` - Precedure that is used for estimation
- `xRegressorDegree` - order of the polynomial within the regressor
- `xRegressorMaxPower` - highest power within the regressor for polynomials
- `xRegressorExponentMatrix` - exponent matrix for the regressors
- `xRegressorType` - Type of regressor; 'polynomial' (default) or 'sparsePolynomial'
- `xInputDelay` - Delays of the input regressors for rule consequents
- `xOutputDelay` - Delays of the output regressors for rule consequents
- `zInputDelay` - Delays of the input regressors for rule premises
- `zOutputDelay` - Delays of the input regressors for rule premises
- `smoothness` - Global smoothness value for all local model transitions
- `kStepPrediction` - (scalar) 0 or 1 for static model or one-step-predictor, inf for dynamic calculation
- `leafModels` - (1 x M) logical vector, true for active models, false for inactive models
- `localModels` - (1 x M) cell array of all local models objects
- `numberOfInputs` - (1 x 1) number of all physical inputs, set in training
- `numberOfOutputs` - (1 x 1) number of all physical outputs, set in training

## Local Model Properties

LOLIMOT

- `center` - (G x nz) center of the gaussian
- `lowerLeftCorner` - (G x nz) lower left corner of the rectangle surrounding the gaussian
- `localLossFunctionValue` - (1 x 1) local loss function value
- `standardDeviation` - (G x nz) standard deviations of all gaussians
- `upperRightCorner` - (G x nz) upper right corner of the rectangle surrounding the gaussian
- `parameter` - (nx x 1) parameter of the local model
- `zLowerBound` - (1 x nz) lower boundary of the training data
- `zUpperBound` - (1 x nz) upper boundary of the training data

HILOMOT

- `center` - (1 x nz) vector of the center coordinates
- `parameter` - (nx x q) vector/matrix of local model parameters
- `localLossFunctionValue` - (scalar) the local loss function value
- `parent` - (scalar) index of parent knot
- `children` - (1 x ?) indices of children knots
- `splittingParameter` - (nz+1 x 1) parameter of the sigmoid
- `localSmoothness` - (scalar) smoothness parameter
- `pseudoInv` -

## Data Set Information Properties

- `inputDescription` -
- `outputDescription` -
- `dataSetDescription` -
- `samplingTime` -

## History Properties

- `currentNumberOfParameters` - (1 x iter) Overall number of model parameters for each iteration
- `currentNumberOfEffParameters` - (1 x iter) Effective number of model parameters for each iteration
- `currentNumberOfLMs` - (1 x iter) Overall number of models for each iteration
- `globalLossFunction` - (1 x iter) Loss function values for the overall model
- `penaltyLossFunction` - (1 x iter) Complexity penalized loss function values
- `CVLossFunction` -
- `splitLM` - (iter-1 x 1) History of LMs which are split
- `splitDimension` - (iter-1 x 1) History of dimensions of the split
- `splitRatio` - (iter-1 x 1) History of ratio of the split
- `leafModelIter` - (1 x iter) History of the active models per iteration
- `trainingTime` - (1 x iter) Overall Training time up to this iteration
- `displayMode` - (logical) Flag to de-/activate printouts to the command window during training
- `iteration` - (1 x 1) Stores the number of the used iteration
- `validationDataLossFunction` - (1 x iter) Validation data loss function values for the overall model
- `testDataLossFunction` - (1 x iter) Test data loss function values for the overall model

## Algorithm Specific Properties

LOLIMOT

- `numberOfLMReliable` - (1 x 1) Number of LMs for a reliable model estimation
- `suggestedNet` - (1 x 1) Suggested net with best performance/complexity trade-off
- `idxAllowedLM` - (1 x M) Stores the allowed local models with respect to splitting
- `splits` - (1 x 1) Number of splits tested in each dimension
- `outputModel` - (N x q) Model outputs
- `xRegressor` - (N x nx) Regression matrix/Regressors for rule consequents
- `zRegressor` - (N x nz) Regression matrix/Regressors for rule premises
- `MSFValue` - (1 x M) Membership function values for each local model

HILOMOT

- `oblique` - logical 0: axes-orthogonal partitioning, 1: axis-oblique partitioning
- `numberOfPoints` - (1 x 1) Minimum number of points that have to be in a LM before it is allowed for splitting
- `optGrad` - logical 0: numerical gradient, 1: analytical gradient
- `optLOOCV` - logical If true, split opt. w.r.t. LOO cross val. error
- `suggestedNet` - (1 x 1) Suggested net with best performance/complexity trade-off
- `inputSensitivity` - (nz x 1) Sensitivity analysis of zRegressor-inputs. Value 1 has highest importance, value 0 seems to be a redundant input.
- `outputModel` - (N x q) Model outputs
- `xRegressor` - (N x nx) Regression matrix/Regressors for rule consequents
- `zRegressor` - (N x nz) Regression matrix/Regressors for rule premises
- `phi` - (N x M) Validity function matrix

## SYMBOLS AND ABBREVIATIONS

LM: Local model

p: Number of inputs (physical inputs)

q: Number of outputs

N: Number of data samples

M: Number of LMs

nx: Number of regressors (x)

nz: Number of regressors (z)

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