We use this function to pre$-$calculate a W for X$.$ The code cell below loads this W:

with open$(\text{'}$resource$/$asnlib$/$publicdata$/$W$.$dill', $\text{'}$rb$\text{'})$ as fp:

W $=$ dill.load$($fp$)$

print $($W$.$shape$)$

Output: $(72282,10)$

Your task: Define get$\_$nmf$\_$clusters as follows:

Determine cluster assignments from an NMF computation.

Return:

labels: Cluster assignments: for each row i of W$,$ labels$[$i$]$ is the cluster $($column$)$ assignment.

ids: Cluster IDs: a Numpy array containing the values from $0$ to m$-1$

sizes: Cluster sizes: sizes$[$c$]$ is the number of rows of W that are assigned to cluster c

STEPS:

$*)$ let m be the number of clusters, which is equal to the number of columnsof W

$*)$For each row i of W$,$ assign it to the cluster c having largest value of W$[$i$,$ c$]$

$*)$ the ids array is simply a Numpy array of length m whose values go from $0$ to m$-1$

$*)$For each cluster c$,$ count how many rows were assigned to it and store that as sizes$[$c$].$

Example: For the demo code, a correct implementation should return:

$($array$([1,0,2,0,2,1,3,0,0]),$ array$([0,1,2,3]),$ array$([4,2,2,1\}))$

Solution:

def get$\_$nmf$\_$clusters$($W: np$.$ndarray$)->($np$.$ndarray, np$.$ndarray, np$.$ndarray$)$:

##code here##

with open$(\text{'}$resource$/$asnlib$/$publicdata$/$demo$\_$get$\_$nmf$\_$clusters$\_$W$.$dill', $\text{'}$rb$\text{'})$ as fp:

demo$\_$W$=$ dill.load$($fp$)$

print$("$demo input W:$")$

pprint$($demo$\_$W$)$

print$("$

Your output:"$)$

print$($get$\_$nmf$\_$clusters$($demo$\_$W$))$