Answers.Body: <p>I think the following is the way to look at your question.</p>
  <ul>
  <li>RP reduces dimensionality based on distance.</li>
  <li>LSH clusters data based on a similar distance method used in RP.</li>
  </ul>
  <p>The primary function of any dimensionality reduction algorithm is to project data into a space that maximizes signal and reduces noise. So when you perform RP now you have data that is representative of the actual signal with less garbage. In such cases, if you plug this data into another algorithm that clusters data, in practice the result should be better. This is because now you have applied a transform to maximize the distance between the data points and when you feed this data to another algorithm whose job is to put them into different buckets, it is much easier. You already have increased the variance among data points and any clustering method will work well and easily with that data.</p>
  <p>Therefore it makes sense to cluster points via LSH after performing RP (even though they are related) and there is no theoretical redundancy in such a method.</p>
  
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2022-10-07T15:34:53.313Z
Answers.LastActivityDate: 2022-10-07T15:34:53.313Z
Answers.UserDisplayName: Arun Aniyan
Body: <p>It is well known that Random Projection (RP) is tightly linked to Locality Sensitive Hashing (LSH). My goal is to cluster a large number of points lying in a <span class="math-container">$d$</span>-dimensional Euclidean space, where <span class="math-container">$d$</span> is very large.</p>
  <hr />
  <p><strong>Questions:</strong> Does it make sense to cluster the points via LSH <em>after</em> having reduced the dimensionality of their input space by using first RP? Why yes/no? Is there any redundancy in the combined use of RP as dimensionality reduction method before LSH as clustering method?</p>
  
Tags: <machine-learning><clustering><dimensionality-reduction><randomness><k-nearest-neighbors>
Title: Clustering by using Locality sensitive hashing *after* Random projection
UserDisplayName: Penelope Benenati
ThreadText: # Clustering by using Locality sensitive hashing *after* Random projection
  
  (Asked by: username_0 on 2022-09-26)
  
  It is well known that Random Projection (RP) is tightly linked to Locality Sensitive Hashing (LSH). My goal is to cluster a large number of points lying in a $d$-dimensional Euclidean space, where $d$ is very large.
  
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  **Questions:** Does it make sense to cluster the points via LSH *after* having reduced the dimensionality of their input space by using first RP? Why yes/no? Is there any redundancy in the combined use of RP as dimensionality reduction method before LSH as clustering method?
  
  **Tags:** machine-learning, clustering, dimensionality-reduction, randomness, k-nearest-neighbors
  
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  ## 1 answers
  
  ### Answer by username_1 on 2022-10-07. Score: 1 | Accepted answer
  
  I think the following is the way to look at your question.
  
  * RP reduces dimensionality based on distance.
  * LSH clusters data based on a similar distance method used in RP.
  
  The primary function of any dimensionality reduction algorithm is to project data into a space that maximizes signal and reduces noise. So when you perform RP now you have data that is representative of the actual signal with less garbage. In such cases, if you plug this data into another algorithm that clusters data, in practice the result should be better. This is because now you have applied a transform to maximize the distance between the data points and when you feed this data to another algorithm whose job is to put them into different buckets, it is much easier. You already have increased the variance among data points and any clustering method will work well and easily with that data.
  
  Therefore it makes sense to cluster points via LSH after performing RP (even though they are related) and there is no theoretical redundancy in such a method.
  
  
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