In this question, you will apply K$-$means and Hierarchical Clustering for data clustering tasks. In this question, you will run K$-$means and Hierarchical Clustering on the USPS database. To evaluate the clustering performance, you will use metrics: $(1)$ Adjusted Rand Index $($ARI$)$ and $(2)$ Normalized Mutual Information $($NMI$).$ More details can be found in the attached Python Notebook file $$Clustering$.$ipynb$$ a$.(40$ pts$)$ For K$-$means, please run five trials and report the average and standard deviation of ARI and NMI. Please also visualize your five clustering results through TSNE. You can reuse your Assignment$-4$myEmbedding$.$ipynb$$ for this purpose. Note that predicted labels rather than the ground truth labels would be used for visualization. In this way, you can visually perceive the quality of the clustering. b$.(40$ pts$)$ For Hierarchical Clustering, please evaluate the USPS dataset and report ARI and NMI for four settings: $(1)$ single $($Min$),(2)$ complete $($Max$),(3)$ average, and $(4)$ ward. Hint: you can set $$linkage$$ to different values to change the clustering criteria. Please also visualize your four clustering results through TSNE.