Activity 15: Expectation Maximization

🕑07:14, 21 Nov 2019

For this activity [1], I used the separated banana, apple, and orange feature data from a previous activity. The fruits form clear clusters in feature space and is suitable for this activity. Figure 1 shows the clustering of the fruit data.

ab space

Figure 1: feature space of fruit data.

Since we are working only with two dimensions (two features), we assume a 2D Gaussian distribution, given by

In the interest of computational efficiency, we define an intermediate matrix whose elements are given by

which are used throughout one entire iteration, in order to avoid redundant calculation of exponentials and matrix inversions. We then iterate with the update rules

until the log-likelihood goes above some pre-set value. The log-likelihood is given by
EM feature space

Figure 1: Estimated PDF in the - feature space of bananas, apples, and oranges.

References

  1. M. N. Soriano, A15 - Expectation maximization (2019).
  2. C. Chan, and J. McCarthy, Expectation maximization (EM) algorithm (2017).

Keywords

image processing
computer vision
expectation maximization
feature extraction
probability density function