Body: <p>I have a dataset with four features:</p>
  <ul>
  <li>the x coordinate</li>
  <li>the y coordinate</li>
  <li>the velocity magnitude</li>
  <li>angle</li>
  </ul>
  <p>Now, I want to measure the distance between two points in the dataset, taking into account the facts that the angle dimension is toroidal, and taking into account the difference in nature of the dimensions (2 of them are distances, one of them is velocity magnitude, and the other an angle).</p>
  <p>What kind of distance function would suit this need?</p>
  <p>If I have to go for an <span class="math-container">$L^p$</span> norm, can I determine which value of <span class="math-container">$p$</span> would be apt by some means?</p>
  <p>Also, if you are aware, please, let me know how such problems have been solved in various applications.</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-10-04T21:39:02.057Z
Comments.Text: Can you explain more about the nature of your data? Although I can imagine that the x and y coordinates and the angle could constitute a pose (e.g. of a robot) and the other feature would represent the magnitude of the velocity when that pose was recorded. I think that computing the distance between points will depend on what you want to achieve. Why do you want to compute the distance between observations in the dataset?
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-10-05T10:26:41.220Z
Comments.Text: The purpose is for clustering the data points. I want the metric to be robust enough such that if two points have their X and Y coordinates close and their velocity magnitude are almost same, yet their orientation is in the opposite direction, they should be treated to belong to different clusters
Comments.UserDisplayName: Manish Kausik Hari Baskar
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-10-05T10:28:55.100Z
Comments.Text: So, you want to take into account all 4 properties.
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2020-10-05T10:29:39.510Z
Comments.Text: Yes, all four properties should be considered. Even if the opposite is true, that is the data points are far apart in space but have similar orientation, they must be clustered into different clusters
Comments.UserDisplayName: Manish Kausik Hari Baskar
Tags: <datasets><objective-functions><linear-algebra>
Title: How to find distance between 2 points when dimensions are all of different nature?
UserDisplayName: Manish Kausik Hari Baskar
ThreadText: # How to find distance between 2 points when dimensions are all of different nature?
  
  (Asked by: username_0 on 2020-10-03)
  
  I have a dataset with four features:
  
  * the x coordinate
  * the y coordinate
  * the velocity magnitude
  * angle
  
  Now, I want to measure the distance between two points in the dataset, taking into account the facts that the angle dimension is toroidal, and taking into account the difference in nature of the dimensions (2 of them are distances, one of them is velocity magnitude, and the other an angle).
  
  What kind of distance function would suit this need?
  
  If I have to go for an $L^p$ norm, can I determine which value of $p$ would be apt by some means?
  
  Also, if you are aware, please, let me know how such problems have been solved in various applications.
  
  **Tags:** datasets, objective-functions, linear-algebra
  
  > **Comments:**
  > **username_1**: Can you explain more about the nature of your data? Although I can imagine that the x and y coordinates and the angle could constitute a pose (e.g. of a robot) and the other feature would represent the magnitude of the velocity when that pose was recorded. I think that computing the distance between points will depend on what you want to achieve. Why do you want to compute the distance between observations in the dataset?  
  > **username_0**: The purpose is for clustering the data points. I want the metric to be robust enough such that if two points have their X and Y coordinates close and their velocity magnitude are almost same, yet their orientation is in the opposite direction, they should be treated to belong to different clusters  
  > **username_1**: So, you want to take into account all 4 properties.  
  > **username_0**: Yes, all four properties should be considered. Even if the opposite is true, that is the data points are far apart in space but have similar orientation, they must be clustered into different clusters  
  
  ---
  
  ## 0 answers
  
  