Title: Clustering for Different Scales of Measurement - the Gap-Ratio Weighted K-means Algorithm,
Abstract: This paper describes a method for clustering data that are spread out over
large regions and which dimensions are on different scales of measurement. Such
an algorithm was developed to implement a robotics application consisting in
sorting and storing objects in an unsupervised way. The toy dataset used to
validate such application consists of Lego bricks of different shapes and
colors. The uncontrolled lighting conditions together with the use of RGB color
features, respectively involve data with a large spread and different levels of
measurement between data dimensions. To overcome the combination of these two
characteristics in the data, we have developed a new weighted K-means
algorithm, called gap-ratio K-means, which consists in weighting each dimension
of the feature space before running the K-means algorithm. The weight
associated with a feature is proportional to the ratio of the biggest gap
between two consecutive data points, and the average of all the other gaps.
This method is compared with two other variants of K-means on the Lego bricks
clustering problem as well as two other common classification datasets.