FLAME clustering: Difference between revisions

Revision as of 07:21, 5 June 2010

Revision as of 09:19, 5 June 2010

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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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### 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>