New coordinates, not selected original columns

Understand the idea

PCA rotates numeric measurements into component axes and can retain fewer axes. Components combine original features; they are not selected original columns or cluster assignments.

Illustrative data

Illustrative data
Column	Values
`x`	1, 2, 3, 4, 5, 6
`y`	1, 3, 2, 5, 4, 6

Click the highlighted code to change the result.

scaled = StandardScaler().fit_transform(example[["x", "y"]])
example_pca = PCA(n_components=)
scores = example_pca.fit_transform(scaled)

2 components retain 100% of variance. Output: 6 rows × 2 columns.

What the syntax does

PCA(n_components=2): Creates a PCA model that finds directions of greatest input variation.
n_components: 2, None, 0.9
An integer n_components requests that many axes; no argument retains all available axes.
Fit scale and axes on the declared discovery population.
Explained variance describes retained variation, not prediction accuracy.
pca.fit_transform(scaled): Learns these axes and returns two coordinates per input row; it does not select two original columns.

Outputs you create

answer: The requested result, with the values, labels and row order described by this task.

PCA48 · first 8 rows
`a`	`b`	`c`	`d`	`e`
103.047	50.8622	22.7157	44.6184	0.906993
89.6002	44.3015	20.2703	40.1253	-0.680116
107.505	53.9521	21.1565	41.7009	0.818161
109.406	54.2501	22.5252	44.9095	1.39291
80.4896	40.0557	14.1714	29.4087	-3.27953
86.9782	44.1387	18.7213	37.5997	-1.70077
101.278	50.4611	18.1185	36.0784	-0.343557
96.8376	48.7875	17.4445	33.8533	-0.987809

Your task

Standardise the supplied measurements
Create two PCA coordinates for every row, and store the coordinates in answer.

answer

Hints

Think: Call fit_transform() to learn a representation and return coordinates in the new feature space.

Tools: Use StandardScaler().fit_transform(X), PCA(n_components=2), pca.fit_transform(scaled). Read the visible syntax meanings before editing.

Approach: Standardise the supplied measurements, create two PCA coordinates for every row, and store the coordinates in answer. Keep the supplied row order and inspect the named output after running.

Explained solution

from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
X = df.select_dtypes(include='number')
scaled = StandardScaler().fit_transform(X)
pca = PCA(n_components=2)
answer = pca.fit_transform(scaled)

The output has one row per observation and two new coordinate columns. Each coordinate combines original measurements. This first two-axis picture introduces the API; later lessons use explained variance to decide how many components to retain.