úÎD>Aˆ(      !"#$%&'NoneB? Normalization strategies for " matrixTeacher matrix w0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 <- Desired class index is 2 0 0 0 0 0 <- Number of classes is 4 ^ 5 repetitionsLinear readout (matrix)ÌRegressor function that maps some feature matrix into a continuous multidimensional output. The feature matrix is expected to have columns corresponding to measurements (data points) and rows, features.Classifier function that maps some measurements as matrix columns and corresponding features as rows, into a categorical output. #Principal components analysis tools Compression matrix UCompression functionInverse to compression function0A dataset representation for supervised learning Create a 1 from list of samples (first) and labels (second)Compute the covariance matrix sigma and return its eigenvectors u' and eigenvalues s+Principal components analysis resulting in   tools_Perform PCA using the minimal number of principal components required to retain given varianceDPerform supervised learning (ridge regression) and create a linear I function. The regression is run with regularization parameter ¼ = 1e-4.DPerform supervised learning (ridge regression) and create a linear  function.Create a linear ) using the ridge regression. Similar to , but instead of a " function a (already transposed)  matrix may be returned.Create a binary ? matrix with ones row corresponding to the desired class index(FPerforms a supervised training that results in a linear readout. See 5https://en.wikipedia.org/wiki/Tikhonov_regularization&Winner-takes-all classification methodCEvaluate the network state (nonlinear response) according to some 4 matrix. Used by classification strategies such as .:Error rate in %, an error measure for classification taskserrorRate [1,2,3,4] [1,2,3,7]25.0 Accuracy of classification, 100% - accuracy [1,2,3,4] [1,2,3,7]75.0!AConfusion matrix for arbitrary number of classes (not normalized)";Normalized confusion matrix for arbitrary number of classes#9Confusion matrix normalized by row: ASCII representation.QNote: it is assumed that target (true) labels list contains all possible labels.  | Predicted ---+------------ | _ _ _ _ _ True | _ _ _ _ _ | _ _ _ _ _ label | _ _ _ _ _ | _ _ _ _ _ 0putStr $ showConfusion [1, 2, 3, 1] [1, 2, 3, 2] 1 2 31 50.0 50.0 0.02 0.0 100.0 0.03 0.0 0.0 100.0$)Pairs of misclassified and correct values(errors $ zip ['x','y','z'] ['x','b','a'][('y','b'),('z','a')]%fNormalized root mean square error (NRMSE), one of the most common error measures for regression tasks Data samples*Number of principal components to preserve ObservationsRetained variance, % Observations$All possible outcomes (classes) listŒNetwork state (nonlinear response) where each matrix column corresponds to a measurement (data point) and each row corresponds to a featureHorizontally concatenated 7 matrices where each row corresponds to a desired classMFeature matrix with data points (measurements) as colums and features as rows•Desired outputs matrix corresponding to data point columns. In case of scalar (one-dimensional) prediction output, it should be a single row matrix.Measurements (feature matrix)Horizontally concatenated  matricesNumber of classes (labels)(Desired class index (starting from zero),Number of repeated columns in teacher matrix(Regularization constant matrix#Vector of possible classes (labels) Input matrixLabel matrix Network state! Target labelsPredicted labels6Map keys: (target, predicted), values: confusion count" Normalize  or  Target labelsPredicted labels;Map keys: (target, predicted), values: normalized confusion# Target labelsPredicted labels% Target signalPredicted signalNRMSE&  !"#$%&   $#"!%  SafeAa)*+,-./01        !"#$%&'()*+,-./0%Learning-0.1.0-4yRERLp4WWv3GwFYN43E7xLearningPaths_Learning NormalizeByRowByColumnTeacherReadout Regressorpredict ClassifierclassifyPCA_u _compress _decompressDataset_samples_labelstoListfromListpca'pca pcaVariancelearnClassifierlearnRegressorlearn'teacherwinnerTakesAllscores errorRateaccuracy confusion' confusion showConfusionerrorsnrmse$fShowNormalize $fEqNormalizeridgeRegressionversion getBinDir getLibDir getDynLibDir getDataDir getLibexecDir getSysconfDirgetDataFileName