You have some data, which is shown in the graphic below. The two dimensions are X and Y, and the shade of each dot represents what class it is. You want to classify this data accurately using a…

Question

Exhibit

Options

• AX^2+Y^2
• BX^2
• CY^2
• Dcos(X)

• A
  79% (34)
• B
  5% (2)
• C
  14% (6)
• D
  2% (1)

Explanation

Adding X²+Y² as a synthetic feature computes the squared Euclidean distance from the origin, which transforms circularly-distributed data (one class forming a ring around another) into data that is linearly separable - a simple threshold on this new feature cleanly divides the classes. Options B (X²) and C (Y²) each capture only one axis of radial distance, so they fail for points that are symmetric across the Y-axis or X-axis respectively, leaving the classes still mixed along the ignored dimension. Option D (cos(X)) applies a periodic transformation that has no relationship to the circular boundary separating the classes and does not reduce the distance-from-origin structure the data exhibits. Memory tip: When you see dots arranged in concentric rings or circles in 2D, think "radius squared" - X²+Y² is the squared distance formula, and adding it "unfolds" the circle into a straight line a linear classifier can draw.

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