Algorithmic Advances in Riemannian Geometry and Applications by Hà Quang Minh & Vittorio Murino

Author:Hà Quang Minh & Vittorio Murino
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(4.34)

Proof

Introduce the shorthand . Using (4.5) we have

The chain-rule of calculus then immediately yields the desired result

Writing and using Lemma 2 we obtain

(4.35)

Computing (4.35) for all is the dominant when running SPG. A a naïve implementation of (4.35) costs , but with slight care this cost can be reduced [14].

4.3 Applications of Sparse Coding

In this section, we describe an application of sparse coding for covariances, namely nearest neighbor (NN) retrieval. This is a fundamental task in several computer vision and machine learning applications in which the goal is to find a data point closest to a given query point within a large database.

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