Body: <p>Are there references or links to examples about loss functions &quot;Distance Metrics&quot; which could be used to minimize the distance between two sets for a neural network. More precisely, this distance metric must depend on the whole set in calculation and not only a single point as the Euclidean distance.</p>
  <p>It is known that Hausdorff distance is used to find the distance between two sets and it is well used for images comparison but it depends additionally on a point in calculation. For my case, I can't depend on a single point for the distance metric but I must consider the whole set to compare it with the other set! Is there any recommendation?</p>
  
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-06-05T12:29:12.997Z
Comments.Text: Can you please provide more info about why you need to compute this distance based on all elements of the set? What are the sets in your case? So, what task are you exactly trying to solve with neural networks? What are the inputs and outputs of this neural network? How does your dataset look like?
Comments.UserDisplayName: nbro
Comments.ContentLicense: CC BY-SA 4.0
Comments.CreationDate: 2021-06-05T21:13:30.343Z
Comments.Text: @nbro In fact I don't have a data set in hand but I am thinking about transforming and modifying a numerical dataset to a new dataset then to use a distance metric to minimize the difference between them. Consequently, I am looking for a metric which calculates the distance based on all elements not only one!
Comments.UserDisplayName: Noah16
Tags: <neural-networks><machine-learning><objective-functions>
Title: Loss function to minimize the distance between sets
UserDisplayName: Noah16
ThreadText: # Loss function to minimize the distance between sets
  
  (Asked by: username_0 on 2021-06-04)
  
  Are there references or links to examples about loss functions "Distance Metrics" which could be used to minimize the distance between two sets for a neural network. More precisely, this distance metric must depend on the whole set in calculation and not only a single point as the Euclidean distance.
  
  It is known that Hausdorff distance is used to find the distance between two sets and it is well used for images comparison but it depends additionally on a point in calculation. For my case, I can't depend on a single point for the distance metric but I must consider the whole set to compare it with the other set! Is there any recommendation?
  
  **Tags:** neural-networks, machine-learning, objective-functions
  > **Comments:**
  > **username_1**: Can you please provide more info about why you need to compute this distance based on all elements of the set? What are the sets in your case? So, what task are you exactly trying to solve with neural networks? What are the inputs and outputs of this neural network? How does your dataset look like?  
  > **username_0**: @nbro In fact I don't have a data set in hand but I am thinking about transforming and modifying a numerical dataset to a new dataset then to use a distance metric to minimize the difference between them. Consequently, I am looking for a metric which calculates the distance based on all elements not only one!  
  
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  ## 0 answers
  
  