Identify the clustering method which takes care of variance in data(1 Point)Decision treeGaussian mixture modelK meansAll of the above

Break Down the Problem

1. Identify the clustering methods listed: Decision Tree, Gaussian Mixture Model, K Means, All of the Above.
2. Analyze how each method handles variance in data.

Relevant Concepts

3. Clustering Methods:
   • K Means: Partitions data into K clusters, aiming to minimize variance within each cluster by computing the mean of data points.
   • Gaussian Mixture Model (GMM): Models data as a mixture of multiple Gaussian distributions, effectively capturing variance through its probabilistic approach.
   • Decision Tree: Primarily a classification/reduction method that does not focus on variance in the same clustering context.

Analysis and Detail

4. K Means aims for compact clusters by minimizing intra-cluster variance, which directly considers variance during clustering.
5. GMM, by utilizing multi-variate Gaussian distributions, incorporates variance in its model, allowing for flexible cluster shapes to fit the data.
6. Decision Trees do not inherently manage cluster variance as they focus on splitting data based on the most informative attributes.

Verify and Summarize

7. Both K Means and Gaussian Mixture Models directly handle variance in the data, while Decision Trees are not classified as clustering methods concerning variance.

Final Answer

The clustering methods that take care of variance in data are Gaussian Mixture Model and K Means; hence the correct answer is All of the above.