Curve Types

Understanding the curve and direction parameters is essential for correct knee/elbow detection. This guide shows all four combinations with visual examples.

The Four Combinations

KneeLocator supports four combinations of curve and direction:

Curve	Direction	Use Case	Example
concave	increasing	Diminishing returns curve	K-means inertia vs. k
concave	decreasing	Accelerating decline	Model accuracy vs. pruning
convex	increasing	Accelerating growth	Exponential-like curves
convex	decreasing	Diminishing decline (elbow)	Sorted eigenvalues

Concave Increasing

The most common case. The curve rises steeply at first, then levels off. The knee is where the curve transitions from steep to flat.

from kneed import KneeLocator, DataGenerator as dg

x, y = dg.concave_increasing()
kl = KneeLocator(x, y, curve="concave", direction="increasing")
kl.plot_knee()
print(f"Knee at x={kl.knee}")

Concave Decreasing

The curve starts flat and then drops steeply. The knee is where the decline accelerates.

x, y = dg.concave_decreasing()
kl = KneeLocator(x, y, curve="concave", direction="decreasing")
kl.plot_knee()
print(f"Knee at x={kl.knee}")

Convex Increasing

The curve starts flat and then rises steeply. The elbow is where the growth accelerates.

x, y = dg.convex_increasing()
kl = KneeLocator(x, y, curve="convex", direction="increasing")
kl.plot_knee()
print(f"Elbow at x={kl.elbow}")

Convex Decreasing

The curve drops steeply at first, then levels off. The elbow is where the decline slows. This is the classic "elbow method" shape (e.g., sorted eigenvalues, decreasing loss).

x, y = dg.convex_decreasing()
kl = KneeLocator(x, y, curve="convex", direction="decreasing")
kl.plot_knee()
print(f"Elbow at x={kl.elbow}")

How to Choose

Not sure which to use?

Use find_shape() to auto-detect:

from kneed import find_shape

direction, curve = find_shape(x, y)
print(f"Detected: direction={direction}, curve={curve}")

Rules of Thumb

• Concave vs. Convex: If your curve bends like a bowl opening upward, it's concave. If it bends like a bowl opening downward, it's convex.
• Increasing vs. Decreasing: Look at the overall trend from left to right. If values go up, it's increasing. If they go down, it's decreasing.
• Knee vs. Elbow: The terms "knee" and "elbow" are interchangeable in kneed. Both kl.knee and kl.elbow return the same value.