FLAME clustering: Difference between revisions

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{{Short description|Type of algorithm for data clustering}}

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'''Fuzzy clustering by Local Approximation of MEmberships (FLAME)''' is a novel [[data clustering]] algorithm that defines clusters in the dense parts of a dataset and performs cluster assignment solely based on the '''neighborhood relationships''' among objects. The key feature of this algorithm is that, the neighborhood relationships among neighboring objects in the [[feature space]] are used to constrain the memberships of neighboring objects in the fuzzy membership space.

==Description of the FLAME algorithm==

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### Cluster Outliers: object with density lower than all its neighbors, and lower than a predefined threshold;

### the rest.

# Local/Neighborhood approximation of [[fuzzy membershipsmembership]]s:

## Initialization of fuzzy membership:

### Each CSO is assigned with fixed and full membership to itself to represent one cluster;

### All outliers are assigned with fixed and full membership to the outlier group;

### The rest are assigned with equal memberships to all clusters and the outlier group;

## Then the fuzzy memberships of all type 3 objects are updated by a converging iterative procedure called '''Local/Neighborhood Approximation of Fuzzy Memberships''', in which the fuzzy membership of each object is updated by a linear combination of the fuzzy memberships of its nearest neighbors.

# Cluster construction from fuzzy memberships in two possible ways:

## One-to-one object-cluster assignment, to assign each object to the cluster in which it has the highest membership;

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==The optimization problem in FLAME==

The '''Local/Neighborhood Approximation of Fuzzy Memberships''' is a procedure to minimize the '''Local/Neighborhood Approximation Error (LAE/NAE)''' defined as the following:

::<math>

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==A simple illustration on a 2-Dimension testing dataset==

[[Image:FLAME_DemoFLAME Demo.png|800px]]

==See also==

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==External links==

* [http://www.biomedcentral.com/1471-2105/8/3 BMC Bioinformatics (2007): FLAME, a novel fuzzy clustering method for the analysis of DNA microarray data]

* [https://web.archive.org/web/20080622172700/http://flame-clustering.googlecode.com/svn/trunk/ FLAME source codes in C released under FreeBSD-like license on GoogleCode]

{{DEFAULTSORT:Flame Clustering}}

[[Category:Data clustering algorithms]]

[[Category:StatisticalCluster analysis algorithms]]

[[Category:Data mining]]

[[Category:Machine learning]]