k-NN is a method used to predict the value of a new data point based on the values of its 'k' nearest neighbors. It is a simple and effective way to make predictions without needing to learn a complex model. For example, if you have a list of fruits and you want to predict if a new fruit is a banana or an apple, you would look at the fruits that are closest to the new fruit and see if the majority are bananas or apples.

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How it Works:

1. When you label a point, it acts as a reference point.

2. Every unlabeled (grey) point looks at its "5 nearest labeled neighbors" (k=5).

3. It takes the "majority vote" (e.g., 3 Blue, 2 Red = Predict Blue).

4. Your goal: Achieve 100% accuracy with minimum number of clicks.

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Goal: Select the best heuristic to find the shortest path from Start (Green) to Goal (Red). Then, analyze the trade-off between path length and the number of cells explored.

What This Game Teaches:

• A* Algorithm: It is a smart way to find the shortest path between two points in a graph. It uses two parts: one part tells us how far we are from the starting point, and the other part tells us how far we are from the goal.
• Cost Function (f(n)): The balance between Actual Cost (g(n)) and Heuristic Cost (h(n)).
• g(n) (Actual Cost): The distance traveled from the start point to the current cell.
• h(n) (Heuristic): The estimated distance from the current cell to the goal. A good heuristic guides the search efficiently.
• Heuristic Comparison:
  • Manhattan: Only counts horizontal/vertical steps. Faster exploration, guaranteed shortest path on a grid without diagonal movement.
  • Euclidean: Straight-line distance. Often less efficient on a grid but common in robotics.
  • Zero (Dijkstra's): Ignores h(n). Guaranteed shortest path, but explores the largest number of cells (slowest).

Clustering is a fundamental task in Unsupervised Machine Learning, where the goal is to group similar data points together without prior knowledge of the groups.

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The Goal: Find K and Place Centroids

1. Guess the right K value: Look at the scatter plot on the right and determine the likely number of distinct clusters (the true K value is hidden).
2. Set the initial Centroids: Click on the map to place K centroids close to the visual center of the clusters you see.
3. Run K-Means: Press the "Run K-Means" button. K-Means will iteratively refine the centroid positions to minimize the total squared distance (Inertia).

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Understanding K-Means

1. Assignment (E-Step): Each data point is assigned to the nearest centroid.
2. Update (M-Step): Each centroid is moved to the mean (average) location of all the points assigned to it.

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