In this paper, we study latent factor models with the dependency structure in the latent space. We propose a general learning framework which induces sparsity on the undirected graphical model imposed on the vector of latent factors. A novel latent factor model SLFA is then proposed as a matrix factorization problem with a special regularization term that encourages collaborative reconstruction. The main benefit (novelty) of the model is that we can simultaneously learn the lower-dimensional representation for data and model the pairwise relationships between latent factors explicitly. An on-line learning algorithm is devised to make the model feasible for large-scale learning problems. Experimental results on two synthetic data and two real-world data sets demonstrate that pairwise relationships and latent factors learned by our model provide a more structured way of exploring high-dimensional data, and the learned representations achieve the state-of-the-art classification performance.