4,810 research outputs found
Any-k: Anytime Top-k Tree Pattern Retrieval in Labeled Graphs
Many problems in areas as diverse as recommendation systems, social network
analysis, semantic search, and distributed root cause analysis can be modeled
as pattern search on labeled graphs (also called "heterogeneous information
networks" or HINs). Given a large graph and a query pattern with node and edge
label constraints, a fundamental challenge is to nd the top-k matches ac-
cording to a ranking function over edge and node weights. For users, it is di
cult to select value k . We therefore propose the novel notion of an any-k
ranking algorithm: for a given time budget, re- turn as many of the top-ranked
results as possible. Then, given additional time, produce the next lower-ranked
results quickly as well. It can be stopped anytime, but may have to continues
until all results are returned. This paper focuses on acyclic patterns over
arbitrary labeled graphs. We are interested in practical algorithms that
effectively exploit (1) properties of heterogeneous networks, in particular
selective constraints on labels, and (2) that the users often explore only a
fraction of the top-ranked results. Our solution, KARPET, carefully integrates
aggressive pruning that leverages the acyclic nature of the query, and
incremental guided search. It enables us to prove strong non-trivial time and
space guarantees, which is generally considered very hard for this type of
graph search problem. Through experimental studies we show that KARPET achieves
running times in the order of milliseconds for tree patterns on large networks
with millions of nodes and edges.Comment: To appear in WWW 201
On Correcting Inputs: Inverse Optimization for Online Structured Prediction
Algorithm designers typically assume that the input data is correct, and then
proceed to find "optimal" or "sub-optimal" solutions using this input data.
However this assumption of correct data does not always hold in practice,
especially in the context of online learning systems where the objective is to
learn appropriate feature weights given some training samples. Such scenarios
necessitate the study of inverse optimization problems where one is given an
input instance as well as a desired output and the task is to adjust the input
data so that the given output is indeed optimal. Motivated by learning
structured prediction models, in this paper we consider inverse optimization
with a margin, i.e., we require the given output to be better than all other
feasible outputs by a desired margin. We consider such inverse optimization
problems for maximum weight matroid basis, matroid intersection, perfect
matchings, minimum cost maximum flows, and shortest paths and derive the first
known results for such problems with a non-zero margin. The effectiveness of
these algorithmic approaches to online learning for structured prediction is
also discussed.Comment: Conference version to appear in FSTTCS, 201
A New Computational Framework for Efficient Parallelization and Optimization of Large Scale Graph Matching
There are so many applications in data fusion, comparison, and recognition that require a robust and efficient algorithm to match features of multiple images. To improve accuracy and get a more stable result is important to take into consideration both local appearance and the pairwise relationship of features. Graphs are a powerful and flexible data structure, allowing for the description of complex relationships between data elements, whose nodes correspond to salient features and edges correspond to relational aspects between features. Therefore, the problem of graph matching is to find a mapping between the two sets of nodes that preserves the relationships between them as much as possible. This graph-matching problem is mathematically formulated as an IQP problem which solving it is NP-hard, and obtaining exact Optima only plausible for very small data. Therefore, handling large-scale scientific visual data is quite limited, necessitating both efficient serial algorithms, as well as scalable parallel formulations. In this thesis, we first focused on exploring techniques to reduce the computation cost as well as memory usage of Pairwise graph matching by adopting a heuristic pruning strategy together with a redundancy pattern suppression scheme. We also modified the structure of the affinity matrix for minimizing memory requirement and parallelizing our algorithm by employing CPU’s and GPU’s accelerated libraries. Any pair of features with similar distance from first image results in same sub-matrices, therefore instead of constructing the whole affinity matrix, we only built the sub-blocked affinity for those distinct feature distances. By employing this scheme not only saved large memory and reduced computation time tremendously but also, the matrix-vector multiplication of gradient computation performed in parallel, where each block-vector calculation computed independently without synchronization. The accelerated libraries such as MKL, cuSparse, cuBlas and thrust applied to solving the GM problem, following the scheme of the spectral matching algorithm. We also extended our work for Multi-graph imaging, since many tasks require finding correspondences across multiple images. Also, considering more graph improves the matching accuracy. Most algorithms obtain approximate solutions for solving the GM NP-hard problem, result in a weak optimal solution. Therefore, we proposed a new solver, which iteratively modified the affinity matrix and binarized the solution by optimizing the original problem with its integer constraints
Robust Non-Rigid Registration with Reweighted Position and Transformation Sparsity
Non-rigid registration is challenging because it is ill-posed with high
degrees of freedom and is thus sensitive to noise and outliers. We propose a
robust non-rigid registration method using reweighted sparsities on position
and transformation to estimate the deformations between 3-D shapes. We
formulate the energy function with position and transformation sparsity on both
the data term and the smoothness term, and define the smoothness constraint
using local rigidity. The double sparsity based non-rigid registration model is
enhanced with a reweighting scheme, and solved by transferring the model into
four alternately-optimized subproblems which have exact solutions and
guaranteed convergence. Experimental results on both public datasets and real
scanned datasets show that our method outperforms the state-of-the-art methods
and is more robust to noise and outliers than conventional non-rigid
registration methods.Comment: IEEE Transactions on Visualization and Computer Graphic
- …