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The many-light formulation provides a general framework for rendering various illumination effects using hundreds of thousands of virtual point lights (VPLs). To efficiently gather the contributions of the VPLs, lightcuts and its extensions cluster the VPLs, which implicitly approximates the lighting matrix with some representative blocks similar to vector quantization. In this paper, we propose a new approximation method based on the previous lightcut method and a low-rank matrix factorization model. As many researchers pointed out, the lighting matrix is low rank, which implies that it can be completed from a small set of known entries. We first generate a conservative global light cut with bounded error and partition the lighting matrix into slices by the coordinate and normal of the surface points using the method of lightslice. Then we perform two passes of randomly sampling on each matrix slice. In the first pass, uniformly distributed random entries are sampled to coarsen the global light cut, further clustering the similar light for the spatially localized surface points of the slices. In the second pass, more entries are sampled according to the possibility distribution function estimated from the first sampling result. Then each matrix slice is factorized into a product of two smaller low-rank matrices constrained by the sampled entries, which delivers a completion of the lighting matrix. The factorized form provides an additional speedup for adding up the matrix columns which is more GPU friendly. Compared with the previous lightcut based methods, we approximate the lighting matrix with some signal specialized bases via factorization. The experimental results shows that we can achieve significant acceleration than the state of the art many-light methods.