DBSCAN Core Points
Identify core points in the DBSCAN algorithm.
A point is a core point if it has at least min_pts neighbors (including itself) within distance epsilon.
Given data points, epsilon, and min_pts, return the indices of all core points (sorted).
Use Euclidean distance for proximity.
Example:
X = [[0, 0], [1, 0], [0, 1], [10, 10]] epsilon = 1.5 min_pts = 3
[0, 1, 2]
- The algorithm starts by calculating the Euclidean distance between each point and every other point in the dataset, using the formula d=(x2​−x1​)2+(y2​−y1​)2​.
- For each point, it counts the number of neighbors (including itself) within the given distance
epsilonof 1.5. - The points [0, 0], [1, 0], and [0, 1] all have at least
min_pts(3) neighbors within the distanceepsilon, since they are close to each other and themselves, thus qualifying as core points. - The point [10, 10] does not have at least
min_pts(3) neighbors within the distanceepsilon, so it is not a core point, resulting in the output [0, 1, 2] which are the indices of the core points.
Constraints:
- X: 2D list of data points
- epsilon: maximum distance for neighborhood
- min_pts: minimum number of points in neighborhood (including self)
- Return sorted list of core point indices
Background Knowledge
The DBSCAN (Density-Based Spatial Clustering of Applications with Noise) algorithm is a popular clustering technique used in unsupervised machine learning. It groups data points into clusters based on their density and proximity to each other. The algorithm identifies three types of points: core points, border points, and noise points. Core points are points with a high density of neighbors, border points are points that are part of a cluster but don't have enough neighbors to be considered core points, and noise points are points that don't belong to any cluster.
In the context of DBSCAN, a core point is a point that has at least min_pts neighbors (including itself) within a distance of epsilon. The epsilon value represents the maximum distance between two points in a cluster, and min_pts is the minimum number of points required to form a dense region. The DBSCAN algorithm relies on these two parameters to determine the density of the data points and group them into clusters.
The Euclidean distance is a common distance metric used to measure the proximity between two points in a multi-dimensional space. It is calculated as the square root of the sum of the squared differences between corresponding coordinates. In this problem, we will use the Euclidean distance to determine if a point is within the epsilon distance of another point.
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