FLAME clustering: Difference between revisions

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

'''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 perform 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.

{{COI|date=August 2010}}

'''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 performperforms 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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The FLAME algorithm is mainly divided into three steps:

# ExtrationExtraction of the structure information from the dataset:

## Construct a neighborhood graph to connect each object to its K-Nearest Neighbors (KNN);

## Estimate a density for each object based on its proximities to its KNN;

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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;

## One-to-multiple object-clusters assignment, to assign each object to the cluster in which it has a membership higher than a threshold.

==The Optimizationoptimization Problemproblem 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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</math>

==A Simplesimple Illustrationillustration on a 2D2-Dimension Testingtesting Datasetdataset==

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

==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]

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

==See also==

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* [[Fuzzy clustering]]

==External links==

[[Category:Data clustering algorithms]]

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

[[Category:Statistical algorithms]]

* [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]

[[Category:Data mining]]

[[Category:Machine learning]]

{{DEFAULTSORT:Flame Clustering}}

[[Category:DataCluster clusteringanalysis algorithms]]