Fuzzy clustering
These similarity measures include distance, connectivity, and intensity.
Different similarity measures may be chosen based on the data or the application.
Membership grades are assigned to each of the data points (tags).
These membership grades indicate the degree to which data points belong to each cluster.
Fuzzy c-means (FCM) clustering was developed by J.C. Dunn in 1973,[2] and improved by J.C. Bezdek in 1981.
[3] The fuzzy c-means algorithm is very similar to the k-means algorithm: Any point x has a set of coefficients giving the degree of being in the kth cluster wk(x).
The FCM algorithm attempts to partition a finite collection of
Given a finite set of data, the algorithm returns a list of
, converge to 0 or 1, and the Fuzzy C-means objective coincides with that of K-means.
The algorithm minimizes intra-cluster variance as well, but has the same problems as 'k'-means; the minimum is a local minimum, and the results depend on the initial choice of weights.
[4][5] Fuzzy C-means (FCM) with automatically determined for the number of clusters could enhance the detection accuracy.
[6] Using a mixture of Gaussians along with the expectation-maximization algorithm is a more statistically formalized method which includes some of these ideas: partial membership in classes.
To better understand this principle, a classic example of mono-dimensional data is given below on an x axis.
By selecting a threshold on the x-axis, the data is separated into two clusters.
Each point belonging to the data set would therefore have a membership coefficient of 1 or 0.
This membership coefficient of each corresponding data point is represented by the inclusion of the y-axis.
[7] Clustering problems have applications in surface science, biology, medicine, psychology, economics, and many other disciplines.
[9] In this case, genes with similar expression patterns are grouped into the same cluster, and different clusters display distinct, well-separated patterns of expression.
Use of clustering can provide insight into gene function and regulation.
In the 1970s, mathematicians introduced the spatial term into the FCM algorithm to improve the accuracy of clustering under noise.
[11] Furthermore, FCM algorithms have been used to distinguish between different activities using image-based features such as the Hu and the Zernike Moments.
[12] Alternatively, A fuzzy logic model can be described on fuzzy sets that are defined on three components of the HSL color space HSL and HSV; The membership functions aim to describe colors follow the human intuition of color identification.
[13] In marketing, customers can be grouped into fuzzy clusters based on their needs, brand choices, psycho-graphic profiles, or other marketing related partitions.
[citation needed] Image segmentation using k-means clustering algorithms has long been used for pattern recognition, object detection, and medical imaging.
However, due to real world limitations such as noise, shadowing, and variations in cameras, traditional hard clustering is often unable to reliably perform image processing tasks as stated above.
[citation needed] Fuzzy clustering has been proposed as a more applicable algorithm in the performance to these tasks.
Given is gray scale image that has undergone fuzzy clustering in Matlab.
Colors are used to give a visual representation of the three distinct clusters used to identify the membership of each pixel.
Below, a chart is given that defines the fuzzy membership coefficients of their corresponding intensity values.
Depending on the application for which the fuzzy clustering coefficients are to be used, different pre-processing techniques can be applied to RGB images.
