Difference between revisions of "Fuzzy C-Means (FCM)"
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* [[Capabilities]] | * [[Capabilities]] | ||
* [[K-Means]] | * [[K-Means]] | ||
| + | * [http://www.sciencedirect.com/science/article/pii/0098300484900207 FCM: The fuzzy c-means clustering algorithm | J. Bezdek, R. Ehrlich, and W. Full - ScienceDirect] | ||
| − | <youtube> | + | One of the most widely used fuzzy clustering algorithms is the Fuzzy C-means clustering (FCM) Algorithm. Fuzzy logic principles can be used to cluster multidimensional data, assigning each point a membership in each cluster center from 0 to 100 percent. This can be very powerful compared to traditional hard-thresholded clustering where every point is assigned a crisp, exact label. |
| − | <youtube> | + | |
| − | <youtube> | + | The fuzzy c-means algorithm is very similar to the k-means algorithm: |
| − | <youtube> | + | |
| + | # Choose a number of clusters. | ||
| + | # Assign coefficients randomly to each data point for being in the clusters. | ||
| + | # Repeat until the algorithm has converged (that is, the coefficients' change between two iterations is no more than {\displaystyle \varepsilon } \varepsilon , the given sensitivity threshold) : | ||
| + | * Compute the centroid for each cluster (shown below). | ||
| + | * For each data point, compute its coefficients of being in the clusters. | ||
| + | |||
| + | |||
| + | http://pythonhosted.org/scikit-fuzzy/_images/plot_cmeans_1.png | ||
| + | [http://pythonhosted.org/scikit-fuzzy/auto_examples/plot_cmeans.html Fuzzy c-means clustering] | ||
| + | |||
| + | <youtube>SdyukrDWTe0</youtube> | ||
| + | <youtube>xtDMHPVDDKk</youtube> | ||
| + | <youtube>MLlk6h692BQ</youtube> | ||
| + | <youtube>nGWmgHxIoPk</youtube> | ||
Revision as of 18:24, 22 April 2019
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- AI Solver
- Capabilities
- K-Means
- FCM: The fuzzy c-means clustering algorithm | J. Bezdek, R. Ehrlich, and W. Full - ScienceDirect
One of the most widely used fuzzy clustering algorithms is the Fuzzy C-means clustering (FCM) Algorithm. Fuzzy logic principles can be used to cluster multidimensional data, assigning each point a membership in each cluster center from 0 to 100 percent. This can be very powerful compared to traditional hard-thresholded clustering where every point is assigned a crisp, exact label.
The fuzzy c-means algorithm is very similar to the k-means algorithm:
- Choose a number of clusters.
- Assign coefficients randomly to each data point for being in the clusters.
- Repeat until the algorithm has converged (that is, the coefficients' change between two iterations is no more than {\displaystyle \varepsilon } \varepsilon , the given sensitivity threshold) :
- Compute the centroid for each cluster (shown below).
- For each data point, compute its coefficients of being in the clusters.
