Test questions on SVD applications in data science.

📚 Quick Study Guide

• 🔢 Singular Value Decomposition (SVD): A matrix factorization technique that decomposes a matrix $A$ into three matrices: $U$, $\Sigma$, and $V^T$, where $A = U\Sigma V^T$.
• 📊 U (Left Singular Vectors): Columns of $U$ are orthonormal eigenvectors of $AA^T$.
• 📈 V (Right Singular Vectors): Columns of $V$ are orthonormal eigenvectors of $A^TA$.
• 📉 $\Sigma$ (Singular Values): A diagonal matrix containing singular values, which are the square roots of the eigenvalues of $A^TA$ or $AA^T$.
• 🖼️ Image Compression: SVD can be used to reduce the storage size of images by keeping only the largest singular values.
• 📝 Dimensionality Reduction: SVD is applied in techniques like Principal Component Analysis (PCA) for reducing the number of variables in a dataset while preserving important information.
• 🔍 Recommender Systems: SVD is used to predict user preferences and make recommendations based on user-item interaction data.

🤔 Practice Quiz

1. What is the primary purpose of Singular Value Decomposition (SVD) in data science?
   1. A. To create new features in a dataset.
   2. B. To decompose a matrix into constituent matrices.
   3. C. To increase the dimensionality of a dataset.
   4. D. To encrypt data for secure storage.
2. Which of the following matrices is NOT a result of SVD?
   1. A. U (Left Singular Vectors)
   2. B. $\Sigma$ (Singular Values)
   3. C. V (Right Singular Vectors)
   4. D. W (Weight Matrix)
3. In SVD, what do the columns of the matrix U represent?
   1. A. Eigenvectors of $A^TA$.
   2. B. Eigenvectors of $AA^T$.
   3. C. Original data points.
   4. D. Singular values of A.
4. What is the significance of the singular values in the $\Sigma$ matrix?
   1. A. They represent the correlation between features.
   2. B. They represent the amount of variance explained by each singular vector.
   3. C. They represent noise in the data.
   4. D. They are used for data encryption.
5. Which application of SVD involves reducing the storage size of an image?
   1. A. Natural Language Processing
   2. B. Image Compression
   3. C. Recommender Systems
   4. D. Anomaly Detection
6. In the context of recommender systems, how is SVD typically used?
   1. A. To predict stock market trends.
   2. B. To filter spam emails.
   3. C. To predict user preferences based on user-item interactions.
   4. D. To improve network security.
7. Which dimensionality reduction technique commonly utilizes SVD?
   1. A. Linear Regression
   2. B. Principal Component Analysis (PCA)
   3. C. K-Means Clustering
   4. D. Decision Trees