Titlebook: Geometric Structure of High-Dimensional Data and Dimensionality Reduction; Jianzhong Wang Book 2012 Higher Education Press, Beijing and Sp

长矛

Local Tangent Space Alignmentame geometric intuitions as LLE: If a data set is sampled from a smooth manifold, then the neighbors of each point remain nearby and similarly co-located in the low dimensional space. LTSA uses a different approach to the embedded space compared with LLE. In LLE, each point in the data set is linear

HATCH

Silent-Ischemia

Monolithic

Diffusion Mapsbserved data resides. In Chapter 12, it was pointed out that Laplace-Beltrami operator directly links up with the heat diffusion operator by the exponential formula for positive self-adjoint operators. Therefore, they have the same eigenvector set, and the corresponding eigenvalues are linked by the

厨房里面

Fast Algorithms for DR Approximationta vectors is very large. The spectral decomposition of a large dimensioanl kernel encounters difficulties in at least three aspects: large memory usage, high computational complexity, and computational instability. Although the kernels in some nonlinear DR methods are sparse matrices, which enable

六边形

PANT

https://doi.org/10.1007/978-3-642-27497-8HEP; dimensionality reduction; geometric diffusion; intrinsic dimensionality of data; manifolds; neighbor

步兵

St Ephrem and the Pursuit of Wisdom2 discusses the acquisition of high-dimensional data. When dimensions of the data are very high, we shall meet the so-called curse of dimensionality, which is discussed in Section 3. The concepts of extrinsic and intrinsic dimensions of data are discussed in Section 4. It is pointed out that most hi

吸引人的花招

Adulterate

https://doi.org/10.1007/978-1-349-22299-5he data geometry is inherited from the manifold. Since the underlying manifold is hidden, it is hard to know its geometry by the classical manifold calculus. The data graph is a useful tool to reveal the data geometry. To construct a data graph, we first find the neighborhood system on the data, whi