"perplexity $=40"$ is used in all T$-$SNE throughout this problem.

Compute the mean value of the data points in each cluster that you found using K$-$means. For this computation of mean, use the data in full original dimensions instead of the PCA projections $($so if the data matrix is and you found clusters, your cluster means should be vectors in dimensions.$)$

Visualize the cluster means in $2-$dimensional space using MDS and PCA. Which of the following best explains the difference between these two plots and the T$-$SNE plot? $($Choose all that apply.$)$

Grading note: This question will be regraded to accept answers that either include or not include the first option.

The MDS and PCA plots confirm there are $3$ groups of clusters, one group with $1$ cluster mean and two groups with $2$ cluster means each.

The T$-$SNE plots confirm there are $3$ groups of clusters, one group with $1$ cluster mean and two groups with $2$ cluster means each.

The PCA and MDS plots show relatively accurate representation of distances, with one cluster means far away from the others, indicating a different type of cell.