Answers.Body: <p><span class="math-container">$D_{i}$</span> merely refers to the diagonal matrix that captures the variance for each principal component specific to class <span class="math-container">$i$</span>.</p>
  <p>We can pool data because the <span class="math-container">$C$</span> matrix is the same for every class, meaning principal components are derived from the collective data of all classes.</p>
  
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Answers.CreationDate: 2023-10-03T06:58:05.013Z
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Body: <p>The following is from Ethem Alpaydin, &quot;Introduction to Machine Learning&quot;, Fourth Edition, MIT Press, 2020, page 129.</p>
  <p><a href="https://i.sstatic.net/0oAlM.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/0oAlM.png" alt="enter image description here" /></a></p>
  <p>Here, <span class="math-container">$C$</span> is the orthogonal matrix found from the sample covariance of all matrices (S).
  But I did not understand what <span class="math-container">$D_i$</span> is and why we should have the above relation.</p>
  <p>Moreover, why does it allow pooling data?</p>
  
Tags: <machine-learning><statistics><principal-component-analysis>
Title: What is $D_i$ in "Common Principal Components Analysis"?
UserDisplayName: DSPinfinity
ThreadText: # What is $D_i$ in "Common Principal Components Analysis"?
  
  (Asked by: username_0 on 2023-10-02)
  
  The following is from Ethem Alpaydin, "Introduction to Machine Learning", Fourth Edition, MIT Press, 2020, page 129.
  
  [![enter image description here](https://i.sstatic.net/0oAlM.png)](https://i.sstatic.net/0oAlM.png)
  
  Here, $C$ is the orthogonal matrix found from the sample covariance of all matrices (S).
  But I did not understand what $D\_i$ is and why we should have the above relation.
  
  Moreover, why does it allow pooling data?
  
  **Tags:** machine-learning, statistics, principal-component-analysis
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2023-10-03. Score: 1 | Accepted answer
  
  $D\_{i}$ merely refers to the diagonal matrix that captures the variance for each principal component specific to class $i$.
  
  We can pool data because the $C$ matrix is the same for every class, meaning principal components are derived from the collective data of all classes.
  
  
  ---
  
  