NumPy: Numerical Python

If Python is the skeleton of Machine Learning, NumPy is the muscle. It is a library for scientific computing that introduces the ndarray (N-dimensional array), which is significantly faster and more memory-efficient than standard Python lists.

1. Why NumPy? (Speed & Efficiency)

Python lists are flexible but slow because they store pointers to objects scattered in memory. NumPy arrays store data in contiguous memory blocks, allowing the CPU to process them using SIMD (Single Instruction, Multiple Data).

2. Array Anatomy and Shapes

In ML, we describe data by its Rank (number of dimensions) and Shape.

• Scalar (Rank 0): A single number.
• Vector (Rank 1): A line of numbers (e.g., a single sample's features).
• Matrix (Rank 2): A table of numbers (e.g., a whole dataset).
• Tensor (Rank 3+): Higher dimensional arrays (e.g., a batch of color images).

import numpy as np

# Creating a 2D Matrix
data = np.array([[1, 2, 3], [4, 5, 6]])
print(data.shape)  # Output: (2, 3) -> 2 rows, 3 columns

3. Vectorization

Vectorization is the practice of replacing explicit for loops with array expressions. This is how we achieve high performance in Python.

Instead of this:

# Slow: Element-wise addition with a loop
result = []
for i in range(len(a)):
    result.append(a[i] + b[i])

Do this:

# Fast: NumPy handles the loop in C
result = a + b

4. Broadcasting: The Magic of NumPy

Broadcasting allows NumPy to perform arithmetic operations on arrays with different shapes, provided they meet certain compatibility rules.

Example: Adding a constant bias to every row in a dataset.

features = np.array([[10, 20], [30, 40]]) # Shape (2, 2)
bias = np.array([5, 5])                  # Shape (2,)
result = features + bias                 # [[15, 25], [35, 45]]

5. Critical ML Operations in NumPy

Operation	NumPy Function	ML Use Case
Dot Product	np.dot(a, b)	Calculating weighted sums in a neuron.
Reshaping	arr.reshape(1, -1)	Changing an image from 2D to a 1D feature vector.
Transposing	arr.T	Aligning dimensions for matrix multiplication.
Aggregations	np.mean(), np.std()	Normalizing data (Standard Scaling).
Slicing	arr[:, 0]	Extracting a single column (feature) from a dataset.

6. Slicing and Masking

NumPy allows for "Boolean Indexing," which is incredibly powerful for filtering data.

# Select all values in the array greater than 0.5
weights = np.array([0.1, 0.8, -0.2, 0.9])
positive_weights = weights[weights > 0] 
# Result: [0.1, 0.8, 0.9]

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While NumPy handles the raw numbers, we need a way to manage data with column names, different data types, and missing values. For that, we turn to the most popular data manipulation library.