基于视觉系统的聚类算法

人类对于结构的感知方式和产生数据的物理系统原理对于聚类分析而言具有同等的重要性。因此，在聚类算法的设计和分析中，模拟人类的主要器官－视觉系统将帮助我们解决这一领域的一些基本问题。从这一观点出发，文中提出一类基于初级视觉系统尺度空间理论的聚类算法，并通过引入显著性假设，将生物物理学中的Weber定律与聚类结构的有效性联系起来。由此产生的聚类算法简洁有效，并可部分地回答那些与人类感知数据结构相关联的聚类有效性问题。我们的数值试验表明这一方法具有广泛的应用前景。

Clustering Methods by Simulating Visual Systems

In pattern recognition and image processing, the major application areas of cluster analysis, human eyes seem to possess a singular aptitude to group objects and find the important structures in an efficient and effective way. The process of data clustering in general is very similar to form perception of the human eyes. Thus an efficient clustering algorithm should depend not only on the principle of physical system by which the data are generated but also on the manner in which human perceives structures. A clustering algorithm mimicking our visual system can thus solve some basic problems in cluster analysis. From this point of view, we propose a new approach to data clustering based on scale space theory which models the blurring effect of lateral retinal interconnections. In the proposed approach, a data set is considered as an image with each light point located at the datum position. As we blur this image, smaller light blobs (clusters) merge into larger ones until the whole image becomes one light blob at a low enough level of resolution. Identifying each blob with a cluster, the blurring process generates a family of clusterings along the hierarchy. By introducing a significance hypothesis on the neural networks, we can relate Weber's Law in psychophysics to the validity of clusters, and this allows us to select an effective clustering from many alternatives. The advantages of the proposed approach are: (1) It identifies natural clusters and enhances accuracy of classification in practice. (2) The derived algorithms are computationally stable and insensitive to initialization, and they are totally free from solving the difficult global optimization problems. (3) It facilitates the construction of novel checks on cluster validity and provides the final clustering a significant degree of robustness to noise in data and change in scale. (4) It can detect outliers which are not normal clusters in a data set. (5) The clustering is highly consistent with the perception of human eyes. (6) The new approach provides an example of unifying the different level of models and theories to solve practical problems. The proposed algorithms can be applied to a large variety of clustering problems ranging from the classification of remotely sensed images to pattern detection in very large spatial and aspatial data sets.