Figure 5.

Classifying complex data. (A) Transforming data to enable linear separation of non-linearly separable raw data. Raw non-linear data are transformed by mapping functions that may include time, frequency, or other operations. This projects them into higher-dimensional parameters space in which they are now linearly separable. One example is classifying patients with heart failure with preserved ejection fraction whose response to beta-blockers may vary due to obesity, atrial fibrillation, left ventricular hypertrophy, diabetes, or other factors. Data transformation to a higher-dimensional space now enables a simple partitioning process. (B) Bias–variance tradeoff. Model with high bias (straight line), when a straight line could not classify appropriately (here, between atrial fibrillation and normal sinus rhythm) in both training dataset (5.B.a) and testing dataset (5.B.b). This leads to prediction errors on other datasets (low variance − frequent errors). In contrast, model with low bias (i.e. due to overtraining) when data is fitted well in training set (5.B.c), but not in testing set (5.B.d), leading to reduced generalization (high variability due to difference between training and validation sets).