Is there a way to quantitatively calculate how similar one curve is to another curve?

Or at the very least say curve A is more or less similar to curve C than curve B is.

My friend needs help with some analysis for his research project, and he asked me for help and I told him that you guys could offer some help. Specifically, he has a reference curve and a bunch of experimental curves and would like to know a way to see which one is the most similar to the reference curve.

Thanks in advance for any help.

#Advice #Math

Note by Michael Tong
7 years, 8 months ago

No vote yet
3 votes

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list
  • bulleted
  • list

1. numbered
2. list
  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai−1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 ∑i=13 \sum_{i=1}^3
\sin \theta sin⁡θ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Yes, there are many depending on your need. Similarity of curve can mean different meanings depending upon the criteria. For example y=f(x) y = f(x) and y=f(x+2) y = f(x + 2) are very similar in contrast that they are just shifted by 2 units along x axis but can be very different if your consider their position along y axis in reference to the a particular x coordinate.

Anyway, calculating the area between two curves might be a good idea in most of the cases to determine their similarity.

Hope this helps.

Lokesh Sharma - 7 years, 8 months ago

Interesting problem. One could start by sampling several x-values, and the y-value at each of those points for each of those curves. Then you could calculate the mean difference between the y-values of the experimental curves with the reference curve. This could also be done in the s direction too. Or, one could sample several different points on the experimental curves and calculate their shortest distances to the reference curve. The average of these values would be a measure of similarity. You may want to use set distances along the actual curve to sample the points, and not along the x axis, saying oh we'll sample x = 0, 1, 2, 3, ... because there could be differing amount of variation in the curve between set x values. Also using this sampling method, one could calculate the slope of the tangent line at each of those points, and average them, comparing them to the reference curve. This one makes the most sense, since averaging the derivatives at certain points would get rid of the confounding variables of shifts. However, stretches and shrinks could affect this greatly.

All of these could be taken from a calculus approach, but if the curves have no defined formula, it makes just as much sense to calculate these values statistically.

Bob Krueger - 7 years, 8 months ago
×

Problem Loading...

Note Loading...

Set Loading...