GAMs and Smoothing Splines (Part-2) — Tensor Product Splines

Author(s): Sai Pradeep Peri

Originally published on Towards AI.

Tensor Product Splines Introduction:

In this article, I will extend the concepts of 1D-spline smooths to higher-order dimensional function approximations called Tensor Product smooths. If you haven’t read part-1, please give it a read.

The article is structured mainly into two parts:

Tensor Product Splines2D-Tensor interpolation using GAMs on an artificial dataset

Tensors:

Tensors are the generalizations of 1D arrays to higher dimensions, and that’s why they are called multi-dimensional arrays.

Tensor Product:

Suppose we have V, an n-dimensional vector, and W, an m dimensional vector. In that case, the tensor product V⊗W defines the vector space of m*n dimension with a basis spanning the product of V_basis and W_basis… Read the full blog for free on Medium.

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Published via Towards AI