Visualization-Using-Principal-Component-Analysis-From-Scratch

Visualization of various data using Principal Component Analysis and t-SNE Check source code which also includes explanation of the functions. Check report to learn more about PCA, Visualization and t-SNE methods.

• What you can find in the code and report

  PCA on MNİST DATA  
  

  1. 10 Sample Digit Images per Digit Class:
     • Figure 1. Sample Images 2. Generation of Eigenvectors

  • 2.1 Mean Digit Image

    • Figure 2: Mean digit image

  • 2.2 Eigenvectors

    • Figure 3: Largest 100 eigenvectors.

  • 2.3 Eigenvalues

    • Figure 4: Scree plot (Largest 50 eigenvalues)

  3. PCA Visualization

     • Figure 5: MNIST projection (Largest 50 eigenvalues)

  4. t-Distributed Stochastic Neighbor Embedding (t-SNE):

     • Figure 6: t-SNE of MNIST

  5. Fundamentals of t-SNE: How does t-SNE work?

     • Step 1: Find the pairwise similarities
     • Step 2: Based on the pairwise similarities in the high dimensional space, map the data to a low dimensional space.
     • Step 3: Use gradient descent based on Kullback–Leibler divergence (also called relative entropy) to minimize the
       difference between p_ij (similarity in high dimensional space) and q_ij (similarity in low dimensional space)
     • Parameters

  6. Reconstruction of Images Using PCA with Different Number of Eigenvectors

     • 6.1 MNIST DATA

     • Reconstruction with Different Dimensions

       • Figure 7: Reconstruction of MNIST 6.1.2 Explained Variance Ratio
       • Figure 8: MNIST - Explained Variance Ratio

     • Reconstruction of Image by Using Least Number of Eigenvectors

       • Figure 9: Reconstruction of 3

     • 6.2 FASHION DATA

     • Reconstruction with Different Dimensions

       • Figure 10: Fashion Data Reconstruction

     • Explained Variance Ratio

       • Figure 11: Fashion Variance Ratio

     • Reconstruction of Image by Using Least Number of Eigenvectors

       • Figure 12: Fashion Top Reconstruction

  PCA on HUMAN FACES  
  

  1. 10 Sample Digit Images per 10 Human Face Class: Figure 13: Human Face - Plot 2. Generation of Eigenvectors:

  • 2.1 Mean Human Face Image: Figure 14: Human Face - Mean

  • 2.2 Eigenvectors: Figure 15: Human Face - Top 100 Eigenvectors

  • 2.3 Eigenvalues: Figure 16: Human Face - Largest 50 Eigenvalues

  3. PCA Visualization: Figure 17: Human Face - Projection to two

  4. t-Distributed Stochastic Neighbor Embedding (t-SNE): Figure 18: Human Face - t-SNE

  5. Reconstruction of Images Using PCA with Different Number of Eigenvectors

  • 5.1. Reconstruction with Different Dimensions
    • Figure 19: Human Face - Reconstruction
  • 5.2 Explained Variance Ratio
    • Figure 10: Human Face - Explained Variance Ratio
  • 5.3 Reconstruction of Image by Using Least Number of Eigenvectors
    • Figure 10: Human Face Reconstruction with the elbow value