2. (15 points) Create a spectral clustering algorithm spectral clustering(L, t, k) that uses the eigenvectors and eigenvalues of e- to embed the nodes into a 3-dimensional Euclidean space and then uses the k-means algorithm with the given k to identify k clusters (i.e., communities). I suggest using the kmeans function in the Python package Scikit Learn. Your algorithm should output the coordinates {[e-tA2u(2),e-tAau(3),e-a4ui4)]T} E R3 for i E V, where u(j)-HPng) , tlW1T denotes the right eigenvector of LT associated with the j-th smallest eigenvalue, . (I recommend using the eigenvectors and eigenvalues of L rather than L.) For each t E 2,4,8, 16), make a 3-dimensional scatter plot, which represents a 3-dimensional embedding of the graph. Make sure to set the x, y, and z-ranges (i.e., limits) to all be the same. Comment on how varying t affects the clusters/communities you find. 2. (15 points) Create a spectral clustering algorithm spectral clustering(L, t, k) that uses the eigenvectors and eigenvalues of e- to embed the nodes into a 3-dimensional Euclidean space and then uses the k-means algorithm with the given k to identify k clusters (i.e., communities). I suggest using the kmeans function in the Python package Scikit Learn. Your algorithm should output the coordinates {[e-tA2u(2),e-tAau(3),e-a4ui4)]T} E R3 for i E V, where u(j)-HPng) , tlW1T denotes the right eigenvector of LT associated with the j-th smallest eigenvalue, . (I recommend using the eigenvectors and eigenvalues of L rather than L.) For each t E 2,4,8, 16), make a 3-dimensional scatter plot, which represents a 3-dimensional embedding of the graph. Make sure to set the x, y, and z-ranges (i.e., limits) to all be the same. Comment on how varying t affects the clusters/communities you find