Nonparametric estimation and learning with applications to object recognition and image analysis

计算机处理视觉信息技术的快速发展对新的图像表示和分类技术产生了不断的需求。数据挖掘和分类发挥关键作用的应用正在迅速增加。生物识别技术就是一个例子，它使用面部图像、指纹或视网膜扫描来提供对受保护信息的安全访问或识别个人。病理细胞的自动分类和恶性肿瘤分级是另一个需要可靠分类系统的应用。在过去十年中，机器学习领域的大量研究表明，具有强大判别能力的良好特征和对分类器的仔细调优可以显著提高分类器的性能。这个建议建立在我早期研究各种非参数分类算法的渐近性质的工作之上。我提出的研究旨在自动提取“强”特征，提供不同类别的良好分离，并通过以数据依赖的方式仔细选择其参数并通过调查其收敛速度来设计更好的分类器。对收敛率的了解将允许设计者在给定的应用领域中选择最好的分类器，并且对于评估分类系统的计算复杂性非常重要。我将研究在高维空间中使用主曲面进行降维的新技术，并通过卷积神经网络改进自动特征选择。该研究成果将应用于人脸和手写自动识别以及癌细胞的恶性分级。

Rapid advances in computer technologies for processing visual information create constant demand for new image representation and classification techniques. There is rapidly growing number of applications where data mining and classification play key role. Biometrics is one example where face images, fingerprints or retina scans are used to provide secure access to protected information or to identify an individual. Automatic categorization of pathological cells and cancer malignancy grading is another application where reliable classification systems are needed. Extensive research in machine learning in the last decade demonstrated that good features with strong discriminative power and careful tuning of classifiers lead to significant improvements in classifiers performance. This proposal builds on my earlier work investigating asymptotic properties of various nonparametric classification algorithms. The research that I propose is aimed at automatic extraction of "strong" features providing good separation of different categories and at designing better classifiers by carefully choosing their parameters in data-dependent way and by investigating their rates of convergence. Knowledge of the rates of convergence will allow the designer to choose the best classifiers in a given application domain and is important for assessing computational complexity of the classification systems. I will investigate new techniques for dimensionality reduction using principal surfaces in high dimensional spaces and I will refine automatic feature selection by means of convolutional neural networks. The results of this research will be applied to automatic face and handwriting recognition and malignancy grading of cancer cells.