Discovering clusters in subspaces, or subspace clustering and related clustering paradigms, is a research field where we find many frequent pattern mining related influences. In fact, as the first algorithms for subspace clustering were based on frequent pattern mining algorithms, it is fair to say that frequent pattern mining was at the cradle of subspace clustering—yet, it quickly developed i...

Low rank representation (LRR) has recently attracted great interest due to its pleasing efficacy in exploring low-dimensional subspace structures embedded in data. One of its successful applications is subspace clustering, by which data are clustered according to the subspaces they belong to. In this paper, at a higher level, we intend to cluster subspaces into classes of subspaces. This is nat...

Speech recognition systems typically contain many Gaussian distributions, and hence a large number of parameters. This makes them both slow to decode speech, and large to store. Techniques have been proposed to decrease the number of parameters. One approach is to share parameters between multiple Gaussians, thus reducing the total number of parameters and allowing for shared likelihood calcula...

Subspace clustering (SC) is a promising technology involving clusters that are identified based on their association with subspaces in high-dimensional spaces. SC can be classified into hard subspace clustering (HSC) and soft subspace clustering (SSC). While HSC algorithms have been studied extensively and are well accepted by the scientific community, SSC algorithms are relatively new. However...

Many clustering problems in computer vision and other contexts are also classification problems, where each cluster shares a meaningful label. Subspace clustering algorithms in particular are often applied to problems that fit this description, for example with face images or handwritten digits. While it is straightforward to request human input on these datasets, our goal is to reduce this inp...

In clustering we often face the situation that only a subset of the available attributes is relevant for forming clusters, even though this may not be known beforehand. In such cases it is desirable to have a clustering algorithm that automatically weights attributes or even selects a proper subset. In this paper I study such an approach for fuzzy clustering, which is based on the idea to trans...

Most available static data are becoming more and more highdimensional. Therefore, subspace clustering, which aims at finding clusters not only within the full dimension but also within subgroups of dimensions, has gained a significant importance. Recently, OpenSubspace framework was proposed to evaluate and explorate subspace clustering algorithms in WEKA with a rich body of most state of the a...

In fuzzy clustering algorithms each object has a fuzzy membership associated with each cluster indicating the degree of association of the object to the cluster. Here we present a fuzzy subspace clustering algorithm, FSC, in which each dimension has a weight associated with each cluster indicating the degree of importance of the dimension to the cluster. Using fuzzy techniques for subspace clus...

As a prolific research area in data mining, subspace clustering and related problems induced a vast amount of proposed solutions. However, many publications compare a new proposition – if at all – with one or two competitors or even with a so called “näıve” ad hoc solution but fail to clarify the exact problem definition. As a consequence, even if two solutions are thoroughly compared experimen...