Gleason patterns of prostate cancer histopathology, characterized primarily by morphological and architectural attributes of histological structures (glands and nuclei), have been found to be highly correlated with disease aggressiveness and patient outcome. Gleason patterns 4 and 5 are highly correlated with more aggressive disease and poorer patient outcome, while Gleason patterns 1-3 tend to reflect more favorable patient outcome. Because Gleason grading is done manually by a pathologist visually examining glass (or digital) slides subtle morphologic and architectural differences of histological attributes, in addition to other factors, may result in grading errors and hence cause high inter-observer variability. Recently some researchers have proposed computerized decision support systems to automatically grade Gleason patterns by using features pertaining to nuclear architecture, gland morphology, as well as tissue texture. Automated characterization of gland morphology has been shown to distinguish between intermediate Gleason patterns 3 and 4 with high accuracy. Manifold learning (ML) schemes attempt to generate a low dimensional manifold representation of a higher dimensional feature space while simultaneously preserving nonlinear relationships between object instances. Classification can then be performed in the low dimensional space with high accuracy. However ML is sensitive to the samples contained in the dataset; changes in the dataset may alter the manifold structure. In this paper we present a manifold regularization technique to constrain the low dimensional manifold to a specific range of possible manifold shapes, the range being determined via a statistical shape model of manifolds (SSMM). In this work we demonstrate applications of the SSMM in (1) identifying samples on the manifold which contain noise, defined as those samples which deviate from the SSMM, and (2) accurate out-of-sample extrapolation (OSE) of newly acquired samples onto a manifold constrained by the SSMM. We demonstrate these applications of the SSMM in the context of distinguish between Gleason patterns 3 and 4 using glandular morphologic features in a prostate histopathology dataset of 58 patient studies. Identifying and eliminating noisy samples from the manifold via the SSMM results in a statistically significant improvement in area under the receiver operator characteristic curve (AUC), 0.832 ± 0.048 with removal of noisy samples compared to a AUC of 0.779 ± 0.075 without removal of samples. The use of the SSMM for OSE of newly acquired glands also shows statistically significant improvement in AUC, 0.834 ± 0.051 with the SSMM compared to 0.779 ± 0.054 without the SSMM. Similar results were observed for the synthetic Swiss Roll and Helix datasets.

中文翻译：

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流形正则化的统计形状模型：前列腺组织学的格里森分级。


前列腺癌组织病理学的格里森模式主要以组织学结构（腺体和细胞核）的形态和结构属性为特征，已发现与疾病侵袭性和患者结果高度相关。格里森模式 4 和 5 与更具侵袭性的疾病和较差的患者预后高度相关，而格里森模式 1-3 往往反映更有利的患者预后。由于格里森分级是由病理学家通过目视检查玻璃（或数字）载玻片手动完成的，因此除了其他因素外，组织学属性的细微形态和结构差异可能会导致分级错误，从而导致观察者之间的高度变异性。最近，一些研究人员提出了计算机决策支持系统，通过使用与核结构、腺体形态以及组织纹理有关的特征来自动对格里森模式进行分级。腺体形态的自动表征已被证明可以高精度区分中间格里森模式 3 和 4。流形学习（ML）方案尝试生成高维特征空间的低维流形表示，同时保留对象实例之间的非线性关系。然后可以在低维空间中高精度地进行分类。然而，机器学习对数据集中包含的样本很敏感；数据集的变化可能会改变流形结构。在本文中，我们提出了一种流形正则化技术，将低维流形限制在可能的流形形状的特定范围内，该范围通过流形统计形状模型（SSMM）确定。 在这项工作中，我们演示了 SSMM 在以下方面的应用：(1) 识别流形上包含噪声的样本（定义为偏离 SSMM 的样本），以及 (2) 对新采集的样本进行准确的样本外外推 (OSE)到受 SSMM 约束的流形上。我们使用 58 名患者研究的前列腺组织病理学数据集中的腺体形态特征，在区分格里森模式 3 和 4 的背景下展示了 SSMM 的这些应用。通过 SSMM 识别并消除流形中的噪声样本，接收器算子特征曲线 (AUC) 下的面积在统计学上显着改善，去除噪声样本后的面积为 0.832 ± 0.048，而未去除样本的 AUC 为 0.779 ± 0.075。使用 SSMM 对新获得的腺体进行 OSE 还显示出统计上显着的 AUC 改善，使用 SSMM 时为 0.834 ± 0.051，而未使用 SSMM 时为 0.779 ± 0.054。在合成 Swiss Roll 和 Helix 数据集上也观察到了类似的结果。