When does it make sense to try to learn a Mixture model from a data set? $($Multiple answers with negative points$)$

A$.$ When the data set is multimodal, so it is unlikely that a simple distribution will fit the data well.

B$.$ When we want to describe a complex distribution by combining simpler component distributions.

C$.$ When there are no clear indications or theoretical justifications for the presence of multiple subpopulations.

D$.$ When we have ovrelaping clusters.

E$.$ When your data can be adequately represented by a simple, well$-$understood distribution.

F$.$ When there is a clear linear relationship between input data variables.In machine learning, the k$-$means algorithm is often used for clustering. Consider a dataset that consists of observations from a multi$-$

dimensional feature space. When applying the k$-$means clustering algorithm to this dataset, which of the following statements are

correct? $($Multiple answers with negative points$)$

The number of clusters, $k,$ must be specified in advance.

k$-$means clustering algorithm can guarantee finding the global optimum solution.

The algorithm assigns each observation to the nearest cluster center based on Euclidean distance.

k$-$means can be used for hierarchical clustering.

The algorithm iteratively updates the positions of the centroids until the positions do not change significantly.

k$-$means clustering is sensitive to the initial placement of the centroids.

The algorithm can handle non$-$numeric data without any pre$-$processing.

The algorithm assigns each observation to the nearest cluster center based on Manhattan distance.