### Principal Component Analysis (PCA) Visualization**Question:**The following is a 3D scatter plot of some data. The colored vectors correspond to the three principal components of this data, obtained by performing PCA. Which of these vectors is most likely to be the first principal component?**Explanation:**#### 3D Scatter Plot Description:The image shows a 3D scatter plot with three axes labeled X, Y, and Z. The scatter plot contains blue points scattered throughout the 3D space, representing the dataset. There are three colored vectors in the plot:- **Red Vector:** Extends along the plane in the direction which seems to capture most of the variation in the data.- **Yellow Vector:** Shorter and appears at a smaller angle relative to the plane of the scatter plot.- **Blue/Cyan Vector:** Extends perpendicularly to the plane formed by X and Y axes, capturing the least variation in that direction.#### Principal Components Explanation:In PCA, the first principal component represents the direction in which the data varies the most. Therefore, the principal component with the maximum spread is most likely to capture the most critical features of the dataset.- **First Principal Component:** - The **Red Vector** is most likely to be the first principal component because it extends in the direction with the largest spread of data points, indicating the highest variance.#### Answer:- **Red** vector is most likely to be the first principal component.

The first principal component (PC1) is the line that best accounts for the shape of the point swarm.…

The following is a 3D scatter plot of some data. The colored vectors correspond to the three principal components of this data, obtained by performing PCA. Which of these vectors is most likely to be the first principal component? 2. -1 -1.00 0.75 15-0.50 -2 -0.25 200 025 0.50 0.75 100 yellow

The following is a 3D scatter plot of some data. The colored vectors correspond to the three principal components of this data, obtained by performing PCA. Which of these vectors is most likely to be the first principal component? 2. -1 -1.00 0.75 15-0.50 -2 -0.25 200 025 0.50 0.75 100 yellow

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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