Consider the following structured matrix factorization problem: given a D $$ N data matrix X

with zero mean column, we solve

min

U$$RD$$k

Z$$Rk$$N

$$X $!=$ UZ$2$

F

with the constraint that U is an orthogonal matrix. Solving the program above is best charac$-$

terized as

i$.$ Principal component analysis $($PCA$)$

ii$.$ Sparse PCA

iii. k$-$means clustering