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

用于处理视觉信息的计算机技术的快速发展产生了对新的图像表示和分类技术的持续需求。在越来越多的应用中，数据挖掘和分类扮演着关键角色。生物识别是使用面部图像、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身份的一个例子。病理细胞的自动分类和癌症恶性分级是另一个需要可靠的分类系统的应用。在过去的十年中，机器学习的广泛研究表明，具有较强区分能力的好特征和对分类器的仔细调整可以显著提高分类器的性能。这一建议建立在我早先研究各种非参数分类算法的渐近性质的基础上。我提出的研究的目的是自动提取“强”特征，提供良好的不同类别分离，并通过仔细选择依赖于数据的参数和考察它们的收敛速度来设计更好的分类器。收敛速度的知识将允许设计者在给定的应用领域选择最好的分类器，并且对于评估分类系统的计算复杂性是重要的。我将研究在高维空间中使用主曲面进行降维的新技术，并将通过卷积神经网络改进自动特征选择。这项研究的结果将应用于自动人脸和手写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.