A New Paradigm for Classification Based on Dissimilarity Information via Regularized Kernel Estimation

基于正则化核估计的不相似信息分类新范式Grace Wahba， pii本研究的目的是开发改进的分类和聚类方法，当感兴趣对象的属性向量未知或维度过高时，但当对对象之间的不相似信息可用时。在提出的工作中，这种不相似信息可能是主观的、粗糙的、嘈杂的、不完整的、局限于非线性流形的、来自多个来源的和/或不一致的。该方法是建立在PI和合作者的一些初步工作的基础上，他们已经提出了两种新的鲁棒非参数方法，用于在各种情况下从嘈杂的不相似数据中获得正定核（又名“复制核”）。这些核生成“伪属性”向量，可用于聚类、离群值检测，或用于具有大量标记数据或稀疏标记数据（“半监督学习”）的支持向量机，用于分类。针对不同的科学重要场景，结合鲁棒估计核和支持向量机实现基于不相似信息的分类，提出了构建一系列优化分类系统的任务。建议为这些系统开发理论有效和实际有用的优化程序和高效算法，在精心设计的已知答案的试验台上测试结果，将其应用于各种不同的分类任务，将结果与相关系统进行比较，并公布结果。随着大量数据和高速计算的可用性，现代分类工具在语音识别、文本分类、图像分析、蛋白质和微阵列数据分类等方面发挥了令人印象深刻的作用。然而，在某些领域仍有很大的改进空间。当可用的数据可能是主观的，粗糙的，嘈杂的，不完整的，满足复杂的约束，来自多个来源并且可能不一致时，这项工作将为分类的理论和实践提供独特和新颖的贡献。预计拟议的工作将提供改进的统计分析方法，这些方法有可能严重影响收集待分类数据的任何工程或科学努力。

ABSTRACTA New Paradigm for Classification Based on Dissimilarity Information Via Regularized Kernel Estimation Grace Wahba, PIThe objective of this research is to develop improved methods for classification and clustering when attribute vectors for the objects of interest are either not known or or are of a much higher dimension than is useful, but when dissimilarity information between pairs of objects is available. In the work being proposed, this dissimilarity information may be subjective, crude, noisy, incomplete, confined within a nonlinear manifold, come from multiple sources and/or be inconsistent.The approach is to build on some preliminary work by the PI and collaborators, who have initiated two new robust nonparametric methods for obtaining positive definite kernels (a.k.a "reproducing kernels")from noisy dissimilarity data under various circumstances. These kernels generate "pseudo-attribute" vectors which may be used for clustering, for outlier detection, or in a support vector machine with copiously labeled data, or with sparsely labeled data ("semi-supervised learning") for classification. Tasks are proposed to build a series of optimized classification systems under a variety of scientifically important scenarios regarding the nature of the data available, which combine robustly estimated kernels with support vector machines to effect classification based on dissimilarity information. It is proposed to develop theoretically valid and practically useful optimization procedures and efficient algorithmsfor these systems, test the results in carefully designed test beds where the answer is known, apply them to a variety of different classification tasks, compare the results with related systems, and publicize the results.With the availability of extremely large amounts of data and high speed computing, modern classification tools are doing impressive things in speech recognition, text classification, image analysis, and classification of proteins and microarray data, among other things. However there is still much room for improvementin certain areas. This work will provide a unique and novel contribution to the theory and practice of classification when the data available may be subjective, crude, noisy, incomplete, satisfy complex constraints, come from multiple sources and may be inconsistent. It is anticipated that the proposed work will provide improved methods of statistical analysis that have the potential to seriously impact essentially any engineering or scientific endeavor that collects data to be classified.