🧪 Feature Engineering and Data Preprocessing

About this simulation

The dataset shown is two concentric rings of points — an inner class and an outer class — arranged in the classic "circles" pattern that trips up any model relying on a straight decision boundary. No flat line through the raw x/y plane can separate them. This lab lets you apply real preprocessing steps and watch the data reshape in 3D until a single flat plane can separate the classes.

How it works

• Polynomial feature — engineers a new axis z = x² + y², lifting the outer ring upward relative to the inner cluster. This is the same trick behind polynomial features and kernel methods: a non-linear transform can make non-linearly-separable data linearly separable.
• Scaling method — Min-Max squeezes every feature into a fixed range; Standardization centers each feature on zero mean and unit variance. Watch how the point cloud's spread and center shift.
• Injected outliers — adds extreme far-away points, the way real sensor glitches or data-entry errors do. Notice how they stretch the min/max range and pull the whole scaled cloud toward the middle, squashing the "real" data into a tiny corner.
• Clip outliers — caps every value to a robust bounding box before scaling, exactly like clipping or winsorizing in a real preprocessing pipeline, restoring a sensible scale for the bulk of the data.

Controls

• Polynomial feature slider — blends the engineered z-axis in from 0% (flat, raw 2D data) to 100% (fully lifted).
• Scaling method — choose none, min-max, or z-score standardization.
• Injected outliers — number of extreme points added to the dataset.
• Clip outliers — toggle robust clipping before scaling statistics are computed.
• Show separating plane — toggle the translucent decision plane at z = 0.
• ↺ New dataset — resample fresh random data. Drag to rotate, scroll to zoom.

Did you know?

A large share of the performance gain in many real machine-learning projects comes not from a fancier model but from better features: scaling numeric inputs to comparable ranges, removing or capping outliers, and engineering interaction or polynomial terms that expose structure a linear model could never find on its own.