Discrete Graph Hashing
Hashing has emerged as a popular technique for fast nearest neighbor search in gigantic databases. In particular, learning based hashing has received considerable attention due to its appealing storage and search efficiency. However, the performance of most unsupervised learning based hashing methods deteriorates rapidly as the hash code length increases. We argue that the degraded performance is due to inferior optimization procedures used to achieve discrete binary codes. This paper presents a graph-based unsupervised hashing model to preserve the neighborhood structure of massive data in a discrete code space. We cast the graph hashing problem into a discrete optimization framework which directly learns the binary codes. A tractable alternating maximization algorithm is then proposed to explicitly deal with the discrete constraints, yielding high-quality codes to well capture the local neighborhoods. Extensive experiments performed on four large datasets with up to one million samples show that our discrete optimization based graph hashing method obtains superior search accuracy over state-of-the-art unsupervised hashing methods, especially for longer codes.
Summary:  This paper proposes an approach to learn r-bit binary hash codes for a given dataset, that are smooth with respect to an affinity graph. Unlike spectral hashing, the method does not relax the binary-value constraints on the hash codes upfront, and uses an approximate affinity graph based on a small subset of anchor points. After some transformations, the resulting optimization problem is solved using alternating updates, for which monotonic descent and convergence is established.Pros:- Detailed empirical comparisons on multiple datasets against a large set of alternative hashing techniques show that the proposed method consistently performs best. - Despite being a nasty-looking discrete optimization problem, the authors are able to derive relatively simple alternating update rules for which some notion of convergence can apparently be established.Cons:- The algorithm has a large number of hyper-parameters (excluding bit length): s,m in Anchor graph construction, rho, and number of iterations in the alternating updates. It is not really made clear how the performance varies with respect to choices for these hyper parameters for a given new problem.- The notion of convergence in Theorem 1 is not made clear. A proof should be sketched.- Ultimately, the method is based on non-convex optimization and the quality of the solution cannot be guaranteed.