Fourier analysis is a mathematical technique that represents complex signals as the sum of simple waves (sine and cosine waves) with different frequencies. Why is it important? Basic Concept Let’s take a complex waveform as an example and compare it to the timbre of a piano sound. A piano’s timbre is created by multiple strings vibrating at different… Read More »
Merge sort is an efficient sorting algorithm based on the divide-and-conquer paradigm. It recursively divides a large array into smaller sub-arrays, sorts those sub-arrays, and then merges them back together to create the final sorted array. Features: Algorithm Steps Example Let’s look at the process of sorting the array [8, 3, 1, 7, 0, 10, 2] using merge sort. Python… Read More »
What is the Fibonacci Sequence? The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. It’s defined as follows: The sequence looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34,… Implementing with Recursion Recursion is a technique where a function calls itself to solve a… Read More »
The Levenshtein distance (also known as edit distance) is a metric for measuring the similarity between two strings. It’s defined as the minimum number of operations required to transform one string into the other using insertion, deletion, and substitution operations. We can efficiently calculate the Levenshtein distance using dynamic programming. Example: Levenshtein Distance between “kitten” and “sitting” Let’s… Read More »
Quicksort is an efficient sorting algorithm based on the divide-and-conquer paradigm. It works as follows: Example of Quicksort: Let’s consider sorting the following array [5, 2, 8, 1, 9, 4, 7]. Python Code Example Quicksort Characteristics: Pivot Selection Strategies: The choice of pivot significantly impacts Quicksort’s performance. Quicksort is widely used due to its relatively simple implementation and speed.… Read More »
Bubble sort is one of the simplest sorting algorithms. It works by repeatedly stepping through the list, comparing adjacent elements and swapping them if they are in the wrong order. Larger elements “bubble” to the end of the list with each pass. This process continues until the entire list is sorted in ascending (or descending) order. Example: Let’s… Read More »
k-means clustering is an unsupervised learning algorithm used to partition a given dataset into several groups (clusters). It works by iteratively updating the “centroids” – the center points of each cluster – and assigning data points to the closest centroid. Features: Steps of k-Means Clustering Let’s consider the following 2D dataset as an example: We want to cluster… Read More »
Basic Concept Example: Classifying Flower Types with KNN Data: Flower Color Petal Length Type Red 5.0 Morning Glory Red 4.8 Morning Glory White 6.2 Lily White 6.0 Lily Yellow 7.1 Rose Yellow 6.9 Rose Unknown Data: Predict the type of a flower with Red color and Petal Length of 5.2. Steps: Python Code Example (using scikit-learn) Advantages and Disadvantages… Read More »
Cosine similarity is a metric used to measure the similarity between two vectors. It’s commonly employed for comparing high-dimensional data, such as text data. Features: Example: Let’s say we have two users, A and B, who rate movies using vectors. In this case, users A and B have similar ratings for Action and Comedy, so the cosine similarity… Read More »
The Monte Carlo method is a technique that uses random numbers to solve complex problems. For example, consider the following types of problems: These problems can be difficult to solve analytically. The Monte Carlo method involves performing experiments using a large number of randomly generated numbers and making statistical estimations based on the results. Origin of the name: It’s named… Read More »