Multivariate Pattern Classification

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SPM 2010 - 13. Kurs zur funktionellen BildgebungFeature SelectionSPM-Kurs Hamburg 2010Pereira et al. (2009)Peeking #1 (ANOVA and classification only) testing a trained classifier needs to be performed onindependent test datasets if entire dataset is used for feature selection,classification estimates become overly optimistic nested cross-validationvalidation!Feature ExtractionSPM-Kurs Hamburg 2010Solution 1: Feature selection select subset from all available features original features remain unchangedSolution 2: Feature extraction create new features as a function ofexisting features Linear functions (PCA, ICA,…) Nonlinear functions duringclassification (i.e. hidden units in aneural network)OutlineSPM-Kurs Hamburg 2010WHY PATTERN CLASSIFICATION?PROCESSING STREAMPREPROCESSING / FEATURE REDUCTIONCLASSIFICATIONEVALUATING RESULTSAPPLICATIONSPattern Classification8
SPM 2010 - 13. Kurs zur funktionellen BildgebungClassificationSPM-Kurs Hamburg 2010Linear classificationvoxel 2hyperplanevolume in t 1volume in t 2training data2volume in t 3volume in t 4independenttest datavolume in t 254voxel 1our task: : find a hyperplane that separates both conditionsClassificationSPM-Kurs Hamburg 2010Linear classificationvoxel 2hyperplanevolume in t 1volume in t 2training data2volume in t 3volume in t 4independenttest datadecision function:volume in t 254 voxel 1y = f ( x)= w1x1+w2x2+... + wn xn+b• if y < 0, predict red // if y > 0, predict blue• prediction = linear function of featuresClassificationSPM-Kurs Hamburg 2010Linear classificationhyperplaneProject data on a new axis that maximes the class separabilityHyperplane is orthogonal to the best projection axisPattern Classification9
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Multivariate Pattern Classification

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