Feature Engineering and PCA for Binary Classification in R

Feature engineering is a technique that encodes predictive factors in a way that makes it easier for models to achieve good performance; for example, encoding a date variable to capture weekend versus weekday effects can improve results.

The effectiveness of feature engineering depends on many factors, including the model used and domain‑specific knowledge about the data patterns.

Model dependency matters: if the decision boundary is diagonal, tree‑based models may struggle because they rely on orthogonal splits.

Domain knowledge is crucial; understanding the underlying data patterns helps transform predictors appropriately, and the approach varies across domains such as image processing, information retrieval, or RNA expression profiling.

A simple training set with two predictors is introduced to build a binary classification model, followed by visualizations of the data.

The data show high correlation (0.85), both predictors are right‑skewed, and a diagonal line could roughly separate the classes.

These variables are highly correlated.

Each predictor appears right‑skewed.

They contain enough information that a diagonal decision boundary might work.

Because of the correlation, the choice of model can affect performance; we evaluate each predictor using the area under the ROC curve (AUC).

Box plots of each predictor on a log scale reveal overlapping distributions, and the AUCs for models A and B are 0.61 and 0.59, respectively, indicating poor discrimination.

Principal Component Analysis (PCA) is introduced as an unsupervised preprocessing step that creates new composite predictors (principal components) by rotating the data; the first component captures most variance, and the second captures the remaining variance.

R code examples demonstrate the process:

> library(caret)
> head(example_train)
   PredictorA PredictorB Class
2    3278.726  154.89876   One
3    1727.410   84.56460   Two
4    1194.932  101.09107   One
12   1027.222   68.71062   Two
15   1035.608   73.40559   One
16   1433.918   79.47569   One

Applying preProcess with centering, scaling, and PCA yields two components that capture 95% of the variance:

> pca_pp <- preProcess(example_train[, 1:2], method = c("center", "scale", "pca"))
> pca_pp
Call:
preProcess.default(x = example_train[, 1:2], method = c("center",
 "scale", "pca"))

Created from 1009 samples and 2 variables
Pre-processing: centered, scaled, principal component signal extraction 

PCA needed 2 components to capture 95 percent of the variance

Predictions on the training and test sets are obtained with predict :

> train_pc <- predict(pca_pp, example_train[, 1:2])
> test_pc <- predict(pca_pp, example_test[, 1:2])
> head(test_pc, 4)
        PC1         PC2
1 0.8420447  0.07284802
5 0.2189168  0.04568417
6 1.2074404 -0.21040558
7 1.1794578 -0.20980371

The test set shows a simple rotation of the original predictors.

PCA, being unsupervised, does not consider class labels during computation; however, the AUC for the first component is 0.5 (random) while the second component achieves 0.81, indicating that the second component separates the classes well, as also reflected in its box plot.

The discussion highlights that PCA can discover useful new predictors even without supervision, though it does not guarantee predictive power for all components.

When many predictors are present, retaining only the top X components can capture most information while discarding less useful features; in this example, the first component accounts for 92.4% of variance.

The article concludes that feature engineering benefits from domain insight, but automated methods like PCA can alleviate the burden of designing numerous correlated features, and a balance between bias‑driven and unbiased model discovery is valuable in R&D.