Lecture 2: Geometric Embeddings (continued) 2 Lowerbound for Embedding into 2
نویسندگان
چکیده
In the last lecture we defined metric spaces, normed spaces, and considered the distortion resulting from certain embeddings. In particular, we proved that l1 norms cannot always be embedded isometrically into l2 by considering a specific four-point l1 norm and showing that it requires at least √ 2 distortion. Today’s lecture further explores the 1 norm. We see a couple of interesting examples of 1 spaces. We try to understand the distortion required to embed 1 into 2. We also see that this apparently simple norm (“Manhattan distance”) is computationally very interesting. We will explore this further in future lectures.
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