Feature and label notation

In ML, features are typically represented as matrix X and labels as vector y.

Feature matrix X

By convention inputs are written as capital X and labels as lowercase y. X is two-dimensional (examples × features), y is one-dimensional (one label per example).

import numpy as np
X = np.array([[170, 65], [160, 55], [180, 80]])  # height, weight
y = np.array([1, 0, 1])
print(X.ndim, y.ndim)   # 2 1

The capital letter for a matrix and the lowercase for a vector come from mathematical notation.

reshape(-1, 1)

The way to turn single-feature data into a column is reshape(-1, 1). -1 means "work out this dimension yourself":

x = np.array([10, 20, 30])
X = x.reshape(-1, 1)
print(X.shape)   # (3, 1)

The labels should stay one-dimensional; turning y into a column causes a warning in some models.

Exercise Turn into a column

Turn the array x into X with reshape(-1, 1); print X.shape and X.ndim separated by a space.

Show example solution

import numpy as np

x = np.array([4, 8, 15, 16, 23, 42])

X = x.reshape(-1, 1)
print(X.shape, X.ndim)

Test yourself

Why can't <code>X = np.array([10, 20, 30])</code> be given to scikit-learn directly?
- Three examples are too few
- NumPy arrays aren't accepted
- It is one-dimensional; X must be two-dimensional
- The numbers are integers
Show answer

It is one-dimensional; X must be two-dimensional — It must be converted to a single-column two-dimensional array with reshape(-1, 1).
Turn the one-dimensional array into a single-column matrix.
```
X = x.reshape(____)
```
Show answer
```
X = x.reshape(-1, 1)
```
Match the notations.

X

Feature matrix
y

Label vector
ndim

Number of dimensions
reshape(-1, 1)

Turning into one column

Next lesson: Summary - ML fundamentals

We Are Enhancing Your Experience

Cookie Preferences

Strictly Necessary Cookies

Analytical Cookies