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Clustering is the grouping of similar objects into a class. Local clustering feature refers to the phenomenon whereby one group of data is separated from another, and the data from these different groups are clustered locally. A compact class is defined as one cluster in which all similar elements cluster tightly within the cluster. Herein, the essence of the local clustering feature, revealed by mathematical manipulation, results in a novel clustering algorithm termed as the special local clustering (SLC) algorithm that was used to process gene microarray data related to Alzheimer's disease (AD). SLC algorithm was able to group together genes with similar expression patterns and identify significantly varied gene expression values as isolated points. If a gene belongs to a compact class in control data and appears as an isolated point in incipient, moderate and/or severe AD gene microarray data, this gene is possibly associated with AD. Application of a clustering algorithm in disease-associated gene identification such as in AD is rarely reported.