Question

Assume that we have a set of 3 one-dimensional data points D = {2,4,7} belonging to a class. We wish to represent this data as a Gaussian Mixture Model with 2 Gaussian components. We initialize the component parameters as μ1 = 3, μ2 = 6, σ1 = σ2 = 1/√2, π1 = π2 = 0.5. Perform one iteration of the Expectation Maximization algorithm and obtain the updated means and mixing coefficients. Explain the solution to this question with the complete steps in detail.
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Answer 1

Step-by-step explanation:

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Answer 2

Three normal distributions are combined into a Gaussian mixture.

Gaussian mixture models are a quantitative representation of normally distributed subpopulations within a larger population. In general, mixture frameworks don't require knowing which subpopulation a data item belongs to, allowing the algorithm to detect and classify the clusters. This is a form of unsupervised learning because the demographic classification is unknown.

For example, height is often modelled as a normal distribution for each gender, with a mean of roughly 5'10" for males and 5'5" for females when modelling biological height data. The distribution of all heights would follow the sum of two given only the height data and not the sexual identity designations for each data point.