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Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some specific sense defined by the analyst) to each other than to those in other groups (clusters).
A multivariate Gaussian mixture model is used to cluster the feature data into k number of groups where k represents each state of the machine. The machine state can be a normal state, power off state, or faulty state. [6] Each formed cluster can be diagnosed using techniques such as spectral analysis.
Sometimes one or more clusters deviate strongly from the Gaussian assumption. If a Gaussian mixture is fitted to such data, a strongly non-Gaussian cluster will often be represented by several mixture components rather than a single one. In that case, cluster merging can be used to find a better clustering. [20]
Animation of the clustering process for one-dimensional data using Gaussian distributions drawn from a Dirichlet process. The histograms of the clusters are shown in different colours. During the parameter estimation process, new clusters are created and grow on the data.
It can be seen that asymptotically, the distortion of a clustering to the power (/) is proportional to , which by definition is approximately the number of clusters K. In other words, for a single Gaussian distribution, increasing K beyond the true number of clusters, which should be one, causes a linear growth in distortion.
Clustering or Cluster analysis is a data mining technique that is used to discover patterns in data by grouping similar objects together. It involves partitioning a set of data points into groups or clusters based on their similarities. One of the fundamental aspects of clustering is how to measure similarity between data points.
Mean shift is a non-parametric feature-space mathematical analysis technique for locating the maxima of a density function, a so-called mode-seeking algorithm. [1] Application domains include cluster analysis in computer vision and image processing .
k-means clustering is a method of vector quantization, originally from signal processing, that aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean (cluster centers or cluster centroid), serving as a prototype of the cluster.