CNRS, LTCI Lab, Telecom ParisTech, 46 rue Barrault, 75013 Paris, France.
IEEE Trans Pattern Anal Mach Intell. 2011 Apr;33(4):699-708. doi: 10.1109/TPAMI.2010.198.
Kernels are functions designed in order to capture resemblance between data and they are used in a wide range of machine learning techniques, including support vector machines (SVMs). In their standard version, commonly used kernels such as the Gaussian one show reasonably good performance in many classification and recognition tasks in computer vision, bioinformatics, and text processing. In the particular task of object recognition, the main deficiency of standard kernels such as the convolution one resides in the lack in capturing the right geometric structure of objects while also being invariant. We focus in this paper on object recognition using a new type of kernel referred to as "context dependent.” Objects, seen as constellations of interest points, are matched by minimizing an energy function mixing 1) a fidelity term which measures the quality of feature matching, 2) a neighborhood criterion which captures the object geometry, and 3) a regularization term. We will show that the fixed point of this energy is a context-dependent kernel which is also positive definite. Experiments conducted on object recognition show that when plugging our kernel into SVMs, we clearly outperform SVMs with context-free kernels.
核函数是为了捕捉数据之间的相似性而设计的函数，它们被广泛应用于机器学习技术中，包括支持向量机 (SVM)。在其标准版本中，常用的核函数，如高斯核，在计算机视觉、生物信息学和文本处理等领域的许多分类和识别任务中表现出相当好的性能。在对象识别的特定任务中，标准核函数（如卷积核）的主要缺陷在于缺乏对物体正确几何结构的捕捉，同时也缺乏不变性。我们专注于使用一种新的核函数来进行对象识别，这种核函数被称为“上下文相关”。对象被视为兴趣点的组合，可以通过最小化一个混合能量函数来匹配，该函数混合了 1）测量特征匹配质量的保真度项，2）捕捉物体几何形状的邻域准则，以及 3）正则化项。我们将证明，这个能量的不动点是一个上下文相关的核函数，它也是正定的。在对象识别实验中，当我们将我们的核函数插入 SVM 中时，我们明显优于使用无上下文核函数的 SVM。
