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arXiv 1502.00946cs.CV
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镶嵌型格拉斯曼动物的高光谱图像分类

Classification of Hyperspectral Imagery on Embedded Grassmannians

Colorado State University(科罗拉多州立大学)

Sofya Chepushtanova, Michael Kirby

摘要:

我们提出了一种方法来捕捉信号的变化,在高光谱图像的格拉斯曼流形的框架。从每个类的标记点进行采样,并用于形成格拉斯曼上的抽象点。格拉斯曼上的结果点具有作为标准正交矩阵的表示,因此在通常意义上不存在于欧几里得空间中。有各种度量,使我们能够确定距离矩阵,可以用来实现格拉斯曼作为嵌入在欧几里得空间。我们说明,我们可以实现一个近似等距嵌入的格拉斯曼流形使用弦度量,而这是不是与测地距离的情况下。然而,通过使用格拉斯曼伪度量产生的非等距嵌入导致最好的分类结果。我们观察到,随着格拉斯曼维数的增加,分类的准确性在两个示例中增长到100%。我们还观察到分类率下降,如果格拉斯曼上的点的尺寸是太大的维度的欧几里得空间。我们使用稀疏支持向量机来执行额外的模型简化。所得到的分类器选择嵌入的维度的子集,而不损失分类性能。

英文摘要:

We propose an approach for capturing the signal variability in hyperspectral imagery using the framework of the Grassmann manifold. Labeled points from each class are sampled and used to form abstract points on the Grassmannian. The resulting points on the Grassmannian have representations as orthonormal matrices and as such do not reside in Euclidean space in the usual sense. There are a variety of metrics which allow us to determine a distance matrices that can be used to realize the Grassmannian as an embedding in Euclidean space. We illustrate that we can achieve an approximately isometric embedding of the Grassmann manifold using the chordal metric while this is not the case with geodesic distances. However, non-isometric embeddings generated by using a pseudometric on the Grassmannian lead to the best classification results. We observe that as the dimension of the Grassmannian grows, the accuracy of the classification grows to 100% on two illustrative examples. We also observe a decrease in classification rates if the dimension of the points on the Grassmannian is too large for the dimension of the Euclidean space. We use sparse support vector machines to perform additional model reduction. The resulting classifier selects a subset of dimensions of the embedding without loss in classification performance.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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