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The big box electronics store, Good Buy, needs your help in applying Principal Components Analysis (PCA) to their appliance sales data. You are provided with records of monthly appliance sales (in thousands of units) for 100 different store locations worldwide. A few rows of the data are shown below:

| Location | Monitors | Televisions | Computers |
|--------------|----------|-------------|-----------|
| Bakersfield | 5 | 35 | 75 |
| Berkeley | 4 | 40 | 50 |
| Singapore | 11 | 22 | 40 |
| Paris | 15 | 8 | 20 |
| Capetown | 18 | 12 | 20 |
| SF 4th Street| 20 | 10 | 5 |

Suppose you perform PCA as follows:
1. First, you standardize the 3 numeric features above (i.e., transform to zero mean and unit variance).
2. Then, you store these standardized features into X and use singular value decomposition to compute [tex]X = U \Sigma V^T[/tex].

What is the dimension of [tex]U[/tex]?

A. [tex]3 \times 100[/tex]
B. [tex]100 \times 3[/tex]
C. [tex]3 \times 3[/tex]
D. [tex]6 \times 3[/tex]

Answer :

The dimension of U is 100 x 3.

:Principal Components Analysis (PCA) is a linear algebra-based statistical method for finding patterns in data.

It uses singular value decomposition to reduce a dataset's dimensionality while preserving its essential characteristics. The singular value decomposition of X produces three matrices: U, E, and V.

The dimension of each of these matrices is as follows:

The three matrices are used to reconstruct the original data matrix.

Learn more about dimension click here:

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