二元二次问题的快速半定解法
A Fast Semidefinite Approach to Solving Binary Quadratic Problems
摘要：
许多计算机视觉问题都可以用二元二次规划（binary quadratic programmes，BQP）表示。两种经典的松弛方法，即谱方法和半定规划（SDP）被广泛用于求解BQP问题，每一种方法都有自己的优点和缺点。谱松弛方法简单易行，但其边界较松。半定松弛法有一个更紧的界，但它的计算复杂性是高的大规模问题。我们提出了一个新的SDP制定BQP，具有两个理想的属性。首先，它具有与常规SDP公式类似的松弛约束。其次，与传统的SDP方法相比，新的SDP制定导致一个显着更有效的和可扩展的双重优化方法，它具有相同程度的复杂度的谱方法。广泛的实验上的各种应用，包括聚类，图像分割，共分割和注册证明了我们的SDP制定解决大规模BQP的有用性。
英文摘要：
Many computer vision problems can be formulated as binary quadratic programs (BQPs). Two classic relaxation methods are widely used for solving BQPs, namely, spectral methods and semidefinite programming (SDP), each with their own advantages and disadvantages. Spectral relaxation is simple and easy to implement, but its bound is loose. Semidefinite relaxation has a tighter bound, but its computational complexity is high for large scale problems. We present a new SDP formulation for BQPs, with two desirable properties. First, it has a similar relaxation bound to conventional SDP formulations. Second, compared with conventional SDP methods, the new SDP formulation leads to a significantly more efficient and scalable dual optimization approach, which has the same degree of complexity as spectral methods. Extensive experiments on various applications including clustering, image segmentation, co-segmentation and registration demonstrate the usefulness of our SDP formulation for solving large-scale BQPs.
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