OPTICS algorithm

OPTICS

OPTICS algorithm (Ordering Points To Identify the Clustering Structure) is an algorithm designed for cluster analysis in data mining. Unlike many clustering algorithms, OPTICS does not produce a single set of clusters. Instead, it creates an augmented ordering of the database representing its density-based clustering structure. This ordering contains information which is equivalent to the density-based clusterings corresponding to a broad range of parameter settings.

Overview

OPTICS is similar to the DBSCAN algorithm in that it grows regions with sufficiently high density into clusters and can discover clusters of arbitrary shape in spatial databases with noise. However, OPTICS does not require the user to specify a global value for the density threshold parameter, ε (epsilon), beforehand. Instead, it generates an ordering of points based on their core-distance and reachability-distance, which can be visualized as a reachability plot. This plot helps in determining the clustering structure of the dataset.

Algorithm

The OPTICS algorithm processes data points in a manner that is sensitive to local density variations within the dataset. It requires two parameters:

• minPts: The minimum number of points to form a dense region (a cluster).
• ε: The maximum distance between two points for one to be considered as in the neighborhood of the other.

However, unlike DBSCAN, ε in OPTICS is considered as the maximum value for the purposes of ordering points, and not for cluster formation.

The key concepts in OPTICS are:

• Core-distance: For a point p, the core-distance is the smallest distance such that p is the center of a circle with radius ε containing at least minPts points.
• Reachability-distance: For a point p and another point o within its ε-neighborhood, the reachability-distance of p with respect to o is the maximum of the core-distance of o and the Euclidean distance between p and o. If o is not in the ε-neighborhood of p, then the reachability-distance is undefined.

The OPTICS algorithm sorts the database such that spatially closest points become neighbors in the ordering, with the aim that points belonging to the same cluster are positioned close to each other in the ordering, facilitating the extraction of clusters based on the reachability plot.

Applications

OPTICS is used in various fields such as bioinformatics, geographic information systems (GIS), marketing, and astronomy for identifying clusters of different shapes and sizes in large datasets. Its ability to handle noise and discover clusters of varying densities makes it suitable for complex data analysis tasks.

Advantages and Limitations

Advantages:

• Does not require the user to specify an ε value for cluster formation.
• Can identify clusters of arbitrary shape and varying densities.
• Handles noise effectively.

Limitations:

• The quality of the clustering result is sensitive to the minPts parameter.
• The reachability-plot interpretation can be subjective and requires experience.
• Higher computational complexity compared to simpler clustering algorithms like k-means clustering.

See Also

• Cluster analysis
• DBSCAN
• k-means clustering
• Data mining

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