Contents
What is spherical data?
Spherical data takes the form of a set of directions in space (or equivalently, positions on the surface of a sphere) and is used in areas of science including earth sciences, biological sciences and astrophysics. Brownian motions on a circle and a sphere led to the appropriate wrapped Normal distributions.
What is a spherical cluster?
In galaxy: Spherical clusters. Spherical clusters are dense and consist almost exclusively of elliptical and S0 galaxies. They are enormous, having a linear diameter of up to 50,000,000 light-years. Spherical clusters may contain as many as 10,000 galaxies, which are concentrated toward the cluster centre.
What is directional data?
Directional data arise naturally in many scientific fields where observations are recorded as directions or angles relative to a system with a fixed orientation. Examples of circular data include wind directions, wave directions or directions of animal movement.
How is clustering used in exploratory data analysis?
Clustering is one of the most common exploratory data analysis technique used to get an intuition about the structure of the data. It can be defined as the task of identifying subgroups in the data such that data points in the same subgroup (cluster) are very similar while data points in different clusters are very different.
Which is the best algorithm for clustering data?
Kmeans algorithm is good in capturing structure of the data if clusters have a spherical-like shape. It always try to construct a nice spherical shape around the centroid. That means, the minute the clusters have a complicated geometric shapes, kmeans does a poor job in clustering the data.
How to determine the degree of separation between clusters?
Silhouette analysis can be used to determine the degree of separation between clusters. For each sample: Compute the average distance from all data points in the same cluster (ai). Compute the average distance from all data points in the closest cluster (bi). Compute the coefficient:
How to find homogeneous subgroups in a cluster?
In other words, we try to find homogeneous subgroups within the data such that data points in each cluster are as similar as possible according to a similarity measure such as euclidean-based distance or correlation-based distance. The decision of which similarity measure to use is application-specific.