Nonlinear Dimensionality Reduction of Brain MRI Data for Classification Applications

分类，或将图像分类成有意义的组，是脑图像分析中的重要应用。降维是许多分类算法的关键组成部分，对于降低处理脑图像的数学方法的复杂性至关重要。日常使用的降维的一个简单例子是将3D地理投影到2D地图上。不同的投影方法保留了不同的地理属性，就像不同的降维方法保留了脑图像的不同属性一样。最近，机器学习领域的突破性发现重新点燃了人们对一种名为深度信念网络(DBN)的神经网络的浓厚兴趣，它被证明在自动学习大量小图像组中的相似模式方面非常有效，方法是降低图像的维度，形成一个简化的虚拟景观，其中相似的图像占据相同的山谷，不同的图像被山丘隔开。事实证明，这种方法在识别人脸和手写数字方面比几乎所有其他方法都更准确。与之前用于DBN实验的数据相比，脑图像的维度要高得多，形状和强度变化也复杂得多。我们的长期研究目标是开发新的DBN方法，可以用来形成一组脑图像的简化景观，以便山谷代表可用于分类的有意义的相似之处。利用多发性硬化症患者的核磁共振图像(MRI)的非常大的数据库，我们将开发新的方法，使DBN能够处理大型、复杂的图像。我们将调查DBN能够从脑图像组中提取哪些类型的相似性，并确定这些相似性是否可能有助于将脑图像分类为各种类型的类别，这些类别的范围从视觉上明显的到不是图像派生的，例如临床结果。如果成功，这项工作将使神经成像的研究人员更有效地利用他们的数据，从而极大地受益于他们。

Classification, or the categorization of images into meaningful groups, is an important application in brain image analysis. Dimensionality reduction is a key component of many classification algorithms and is essential for reducing the complexity of mathematical methods for working with brain images. A simple example of dimensionality reduction in everyday use is the projection of 3D geography onto 2D maps. Different projection methods preserve different properties of the geography, just like different dimensionality reduction methods preserve different properties of brain images. Recently, groundbreaking discoveries in the field of machine learning have rekindled a strong interest in a type of neural network called the deep belief net (DBN), which has been shown to be very effective at automatically learning patterns of similarity in large groups of small images by reducing the dimensionality of the images to form a simplified virtual landscape in which similar images occupy the same valleys and dissimilar images are separated by hills. This approach has been shown to be more accurate for identifying faces and handwritten digits than practically all other methods. In comparison to the previous data used for DBN experiments, brain images are of much higher dimension and have much more complex shape and intensity variations. Our long-term research goal is to develop new DBN methods that can be used to form simplified landscapes of groups of brain images such that the valleys represent meaningful similarities that can be used for classification. Using a very large database of magnetic resonance images (MRIs) of patients with multiple sclerosis, we will develop new methods for making DBNs work with large, complex images. We will investigate what types of similarities DBNs are capable of extracting from groups of brain images, and determine whether those similarities are potentially useful for classifying brain images into various types of categories that will range from the visually obvious to ones that are not image-derived, such as clinical outcomes. If successful, this work will greatly benefit researchers in neuroimaging by allowing them to make much more effective use of their data.