▷ Exercise 20.3. [3, p. 291] Explore the properties of the soft K-means algorithm, version 1, assuming that the datapoints {x} come from a single separable two-dimensional Gaussian distribution with mean zero and variances (var(x₁), var(x2)) = (0,02), with o> o. Set K = 2, assume N is large, and investigate the fixed points of the algorithm as 3 is varied. [Hint: assume that m(¹) = (m, 0) and m (2) = (-m, 0).] =

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▷ Exercise 20.3.[³, p.291] Explore the properties of the soft K-means algorithm,
version 1, assuming that the datapoints {x} come from a single separable
two-dimensional Gaussian distribution with mean zero and variances
(var(x₁), var(x2)) = (0²,0²), with o² > 02. Set K = 2, assume N is
large, and investigate the fixed points of the algorithm as 3 is varied.
[Hint: assume that m(¹) = (m, 0) and m(²) = (−m, 0).]
Transcribed Image Text:▷ Exercise 20.3.[³, p.291] Explore the properties of the soft K-means algorithm, version 1, assuming that the datapoints {x} come from a single separable two-dimensional Gaussian distribution with mean zero and variances (var(x₁), var(x2)) = (0²,0²), with o² > 02. Set K = 2, assume N is large, and investigate the fixed points of the algorithm as 3 is varied. [Hint: assume that m(¹) = (m, 0) and m(²) = (−m, 0).]
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