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This example demonstrates a Gaussian Mixture Model (GMM) visualization. We'll create three normal distributions with different means, combine them with weights, and plot the resulting mixture distribution.

Initial setup

First, let's set up the canvas with appropriate scale and colors:

• Set scale: unit = \scalar 150
• Hide origin point: \hide p0
• Define gray color: gray = \text 666
• Define white color: white = \text fff

Define the Gaussian mixture components

We'll create three normal distributions with different means, all having the same variance, and different weights:

• Define x: x = \scalar 0
• Define means mus: mus = \array 0 -2 1
• Define variances sigmas: sigmas = \array 0.6 0.6 0.6
• Define weights weights: weights = \array 0.7 0.2 0.1

The means are at positions 0, -2, and 1. The weights indicate that the first distribution (at 0) contributes 70% to the mixture, the second (at -2) contributes 20%, and the third (at 1) contributes 10%.

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Plot individual PDF curves

Let's calculate and plot each normal distribution's probability density function (PDF) at the current x value:

• Calculate densities at x for these points: densities = \prob-normal-pdf x mus sigmas
• Plot PDF curves: \plot x densities

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Setting their color to gray

This creates three plots (plot1, plot2, plot3) showing the individual Gaussian curves. Let's color them gray:

• Define array of plots: plots = \array plot1 plot2 plot3
• Set their color to gray: \set-stroke plots gray

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Calculate and plot the weighted mixture

Now we'll combine the three distributions using their weights to get the mixture density:

• Take weighted sum: weighted-densities = \mul densities weights
• Calculate weighted density y: y = \reduce-sum weighted-densities

The weighted sum gives us the contribution of each distribution at point x, and reducing the sum gives us the final mixture density value y.

• Plot x vs y: \plot x y

This creates plot3, which shows the combined Gaussian mixture distribution.

Visualize the mapping

Draw a line joining the input and output points

• Draw input point: \point x 0
• Draw output points: \point x y
• Join input and output points: \line p1 p2
• Change its color to white: \set-stroke line0 white

This creates a vertical line from the x-axis to the mixture curve, showing the density value at the current x.

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Draw the tangent line

We can also draw the tangent line to the mixture curve at the current point:

• Draw tangent at current point: \tangent plot3 x 1
• Hide tangent points: \hide p3 p4
• Change color of tangent: \set-stroke line1 white

The tangent line shows the slope of the mixture distribution at the current x value.

Change the x value

Try changing x to see how the mapping and tangent update:

• Change x to -1: x = \scalar -1