Want Answers?A Reddit Inspired Study on How to Pose Questions
TABLE IV: Effect of extension using Wordnet synsets on the co-occurence matrix. See Section IV-F
['Tags', '#Questions', '#co-occurrence entries', '#co-occurrence after', 'Factor increase']
To overcome this limitation, we explore other latent factorization methods. Recently, Non-Negative Sparse Embedding (NNSE) In order to apply NNSE to our question dataset, we first represent the data as a co-occurrence matrix X where rows correspond to questions and columns correspond to words. Each question is additionally augmented with word sense-restricted synsets from Wordnet. This extended co-occurrence matrix X is usually of very high dimension (e.g., 100k x 1m). We first reduce dimensionality of the matrix using sparse SVD. The number of dimensions in the SVD space is selected based on knee-plot analysis of eigenvalues obtained during SVD decomposition. The rank r approximation Xn×r obtained from SVD is then factorized into two matrices using NNSE, which minimize the following objective. argminA,D12n∑i=1∥Xi,:−Ai,:×D∥2 st :Di,:DTi,:≤1,∀1≤i≤k Ai,j≥0,1≤i≤n,1≤k ∥Ai:∥1≤λ1,1≤i≤n where n is the number of questions, and k is the resulting number of latent factors induced by NNSE. We note that NNSE imposes non-negativity and sparsity penalty on the rows of matrix A. Though the objective represents a non-convex system, but when we solve for A with a fixed D (and vice versa) the loss function is convex. At the end of this process, Ai,j represents the membership weight of question i belonging to latent factor j.