Answers.Body: <p>You can define different measures in this way:</p>
  <ol>
  <li>Maximum distance of the new point with all points of the configuration (<span class="math-container">$M$</span>)</li>
  <li>Minimum distance of the new point with all points of the configuration (<span class="math-container">$N$</span>)</li>
  <li><span class="math-container">$\frac{M}{\text{Maximum distance between two points of the configuration(}D)}$</span>: normalize (1) measure</li>
  <li><span class="math-container">$\frac{N}{D}$</span>:normalize (2) measure</li>
  </ol>
  <p>You can get more ideas from <a href="https://online.stat.psu.edu/stat555/node/85/#:%7E:text=For%20most%20common%20hierarchical%20clustering,when%20they%20are%20perfectly%20correlated." rel="nofollow noreferrer">distance measures in hierarchical clustering methods</a>. To select a proper one, you need to elaborate on the context of these points.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-10-15T16:50:00.393Z
Answers.Text: I think in the first or third one, Novelty will be directly proportional to the measure, but not so sure about the second and fourth one, because I think these two won't be very good in differentiating between novel and non novel configuration.
Answers.UserDisplayName: Vaibhav Thakkar
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2020-10-14T15:17:41.897Z
Answers.LastActivityDate: 2020-10-14T15:17:41.897Z
Answers.UserDisplayName: OmG
Body: <p>I am trying to implement Novelty search; I understand why it can work better than the standard Genetic Algorithm based solution which just rewards according to the objective.
  I am working on a problem which requires to generate a fixed number of points in a 2d box centered at the origin.
  In this problem, how can I identify which is a novel configuration of points?</p>
  <p><strong>Note:</strong> I have thought of one way of doing this: We call the mean of one configuration of points to be the mean of all points in that configuration (let's say this tuple is <span class="math-container">$(m_x, m_y)$</span>, we store the mean of all configurations generated till now, now for a new configuration it's novelty can be defined as the distance of the mean of this new configuration with <span class="math-container">$(m_x, m_y)$</span>.<br>
  But I think it will not work greatly as some very different configuration of points can also have the same mean.</p>
  
Tags: <genetic-algorithms><optimization><novelty-search>
Title: Measuring novel configuration of points
UserDisplayName: Vaibhav Thakkar
ThreadText: # Measuring novel configuration of points
  
  (Asked by: username_0 on 2020-10-10)
  
  I am trying to implement Novelty search; I understand why it can work better than the standard Genetic Algorithm based solution which just rewards according to the objective.
  I am working on a problem which requires to generate a fixed number of points in a 2d box centered at the origin.
  In this problem, how can I identify which is a novel configuration of points?
  
  **Note:** I have thought of one way of doing this: We call the mean of one configuration of points to be the mean of all points in that configuration (let's say this tuple is $(m\_x, m\_y)$, we store the mean of all configurations generated till now, now for a new configuration it's novelty can be defined as the distance of the mean of this new configuration with $(m\_x, m\_y)$.  
  But I think it will not work greatly as some very different configuration of points can also have the same mean.
  
  **Tags:** genetic-algorithms, optimization, novelty-search
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2020-10-14. Score: 1
  
  You can define different measures in this way:
  
  1. Maximum distance of the new point with all points of the configuration ($M$)
  2. Minimum distance of the new point with all points of the configuration ($N$)
  3. $\frac{M}{\text{Maximum distance between two points of the configuration(}D)}$: normalize (1) measure
  4. $\frac{N}{D}$:normalize (2) measure
  
  You can get more ideas from [distance measures in hierarchical clustering methods](https://online.stat.psu.edu/stat555/node/85/#:%7E:text=For%20most%20common%20hierarchical%20clustering,when%20they%20are%20perfectly%20correlated.). To select a proper one, you need to elaborate on the context of these points.
  
  > **Comments:**
  > **username_0**: I think in the first or third one, Novelty will be directly proportional to the measure, but not so sure about the second and fourth one, because I think these two won't be very good in differentiating between novel and non novel configuration.  
  
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