1,829 research outputs found
Top-N Recommendation on Graphs
Recommender systems play an increasingly important role in online
applications to help users find what they need or prefer. Collaborative
filtering algorithms that generate predictions by analyzing the user-item
rating matrix perform poorly when the matrix is sparse. To alleviate this
problem, this paper proposes a simple recommendation algorithm that fully
exploits the similarity information among users and items and intrinsic
structural information of the user-item matrix. The proposed method constructs
a new representation which preserves affinity and structure information in the
user-item rating matrix and then performs recommendation task. To capture
proximity information about users and items, two graphs are constructed.
Manifold learning idea is used to constrain the new representation to be smooth
on these graphs, so as to enforce users and item proximities. Our model is
formulated as a convex optimization problem, for which we need to solve the
well-known Sylvester equation only. We carry out extensive empirical
evaluations on six benchmark datasets to show the effectiveness of this
approach.Comment: CIKM 201
Low-Rank Matrices on Graphs: Generalized Recovery & Applications
Many real world datasets subsume a linear or non-linear low-rank structure in
a very low-dimensional space. Unfortunately, one often has very little or no
information about the geometry of the space, resulting in a highly
under-determined recovery problem. Under certain circumstances,
state-of-the-art algorithms provide an exact recovery for linear low-rank
structures but at the expense of highly inscalable algorithms which use nuclear
norm. However, the case of non-linear structures remains unresolved. We revisit
the problem of low-rank recovery from a totally different perspective,
involving graphs which encode pairwise similarity between the data samples and
features. Surprisingly, our analysis confirms that it is possible to recover
many approximate linear and non-linear low-rank structures with recovery
guarantees with a set of highly scalable and efficient algorithms. We call such
data matrices as \textit{Low-Rank matrices on graphs} and show that many real
world datasets satisfy this assumption approximately due to underlying
stationarity. Our detailed theoretical and experimental analysis unveils the
power of the simple, yet very novel recovery framework \textit{Fast Robust PCA
on Graphs
- …