So one can study the signal in some much lower-dimensional subspaces, specifically, some planes.

事实上，经过坐标变换，我们可以在维数更低的子空间（甚至是在平面上）来研究信号。

youdao

However, when the underlying lower-dimensional manifold is self-intersecting at some points, it's difficult to obtain local lower-dimensional structure from the Euclidean neighborhoods.

然而，当高维数据所逼近或近似的一个低维流形自相交时，欧氏距离意义上的邻域不能完全反映低维点的相邻关系，往往难以体现真实的局部线性结构。

youdao

I will be more light centered and less lower dimensional.

我将会是以光为中心的，较少低次元的。

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So Stojkovic and Mureika have reasoned that the Laser Interferometer Space Antenna (LISA), a planned international gravitational observatory, should not detect any gravitational waves emanating from the lower-dimensional epochs of the early universe.

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