Talk:Minkowski distance

Merging into Lp space
I think that the Lp space article is too complex and intimidating to be the only reference on the useful topic of Minkowski distances. This article was exactly what I was looking for. A cross-reference to the more general topic would be good. However, merging would destroy a clear and to-the-point article. BrotherE (talk) 07:09, 11 August 2010 (UTC)

I agree for the same reasons. Also, I clicked on the link in the merge header and I didn't see any discussion of a merger. I'm going to be bold and remove the merge tag. Amead (talk) 23:09, 1 November 2011 (UTC)

huh?

 * The Minkowski distance is a metric on Euclidean space

1. What does Euclidean space mean here? Doesn't it usually mean ordinary flat space, requiring that the only metric on it is the Euclidean/Pythagorean/L2 metric? 2. Shouldn't there be a clarification in the lead, explaining if the Minkowski distance metric has absolutely nothing to do with the very commonly used Minkowski space metric? Cesiumfrog (talk) 00:15, 26 August 2011 (UTC)

I agree with your comment #2. I found this article after someone mistakenly linked an article to Minkowski space metric (instead of Minkowski distance); they don't seem to have any connection and the confusion is exacerbated by the technical nature of these two concepts. But for the same reason, I don't feel I could make a credible edit. Amead (talk) 23:12, 1 November 2011 (UTC)

Unit circle diagram is confusing
I don't think the unit circle diagram is useful or helps explain the concept. Without the functional definition of how the circle is plotted with respect to p, then how is the reader to know how the shape relates to p? The diagram was probably a good idea, but was not fully executed in explanation. — Preceding unsigned comment added by 169.234.41.8 (talk) 21:22, 17 October 2011 (UTC)

By all means, make the example better but I found this illustration extremely helpful in conceptualizing this issue. Amead (talk) 23:14, 1 November 2011 (UTC)

It would be nice if more diagrams were shown such as the important special cases p = 0, p = -1/2, p = -1, p = -2, p = -infinity. Especially since p = 0 and p = -infinity were mentioned within the article. — Preceding unsigned comment added by 71.201.95.139 (talk) 21:48, 22 May 2013 (UTC)

@Amead, could you add to the article by explaining what you found extremely helpful? I am also at a loss because I don't know how those plots were generated, what they mean, etc. — Preceding unsigned comment added by 165.225.38.75 (talk) 15:27, 28 March 2018 (UTC)

More on the captions
The captions underneath the various circles are misleading. May be helpful to say something like $$p=.5 \implies (x_1-y_1)^{1/2} + (x_2-y_2)^{1/2} = 1 \implies \text{these are the points which satisfy this condition, etc., now for all values of p, here are the various unit circles traced out.$$.

The current captions seem to be computing the distance between $(0,1)$ and $(1,0)$ for various values of $p$ where $p$ is called out in the exponent of 2. While both facts are 'interesting' in their own right, the image seems to be conflating these concepts.24.6.1.233 (talk) 22:14, 25 October 2015 (UTC)Steven24.6.1.233 (talk) 22:14, 25 October 2015 (UTC)

Modified Lp for 0 < p < 1
Since Lp norm is only a metric for $$p \geq 1$$, I've seen the following variation for $$0 < p < 1$$
 * $$\sum_{i=1}^n |x_i-y_i|^p.$$

i.e. without the term $$^{\frac{1}{p}}$$ around it. It was claimed that this is then a metric for $$0 < p < 1$$. You can find this for example discussed in Lp_space. Do you know if this has any name? It might be worth discussing this in this article, too. --138.246.2.177 (talk) 12:26, 16 August 2013 (UTC)