Maximum Margin Clustering for State Decomposition of Metastable Systems

When studying a metastable dynamical system, a prime concern is how to decompose the phase space into a set of metastable states. Unfortunately, the metastable state decomposition based on simulation or experimental data is still a challenge. The most popular and simplest approach is geometric clustering which is developed based on the classical clustering technique. However, the prerequisites of this approach are: (1) data are obtained from simulations or experiments which are in global equilibrium and (2) the coordinate system is appropriately selected. Recently, the kinetic clustering approach based on phase space discretization and transition probability estimation has drawn much attention due to its applicability to more general cases, but the choice of discretization policy is a difficult task. In this paper, a new decomposition method designated as maximum margin metastable clustering is proposed, which converts the problem of metastable state decomposition to a semi-supervised learning problem so that the large margin technique can be utilized to search for the optimal decomposition without phase space discretization. Moreover, several simulation examples are given to illustrate the effectiveness of the proposed method

Fuzzy spectral clustering methods for textual data

Nowadays, the development of advanced information technologies has determined an increase in the production of textual data. This inevitable growth accentuates the need to advance in the identification of new methods and tools able to efficiently analyse such kind of data. Against this background, unsupervised classification techniques can play a key role in this process since most of this data is not classified. Document clustering, which is used for identifying a partition of clusters in a corpus of documents, has proven to perform efficiently in the analyses of textual documents and it has been extensively applied in different fields, from topic modelling to information retrieval tasks. Recently, spectral clustering methods have gained success in the field of text classification. These methods have gained popularity due to their solid theoretical foundations which do not require any specific assumption on the global structure of the data. However, even though they prove to perform well in text classification problems, little has been done in the field of clustering. Moreover, depending on the type of documents analysed, it might be often the case that textual documents do not contain only information related to a single topic: indeed, there might be an overlap of contents characterizing different knowledge domains. Consequently, documents may contain information that is relevant to different areas of interest to some degree. The first part of this work critically analyses the main clustering algorithms used for text data, involving also the mathematical representation of documents and the pre-processing phase. Then, three novel fuzzy versions of spectral clustering algorithms for text data are introduced. The first one exploits the use of fuzzy K-medoids instead of K-means. The second one derives directly from the first one but is used in combination with Kernel and Set Similarity (KS2M), which takes into account the Jaccard index. Finally, in the third one, in order to enhance the clustering performance, a new similarity measure S∗ is proposed. This last one exploits the inherent sequential nature of text data by means of a weighted combination between the Spectrum string kernel function and a measure of set similarity. The second part of the thesis focuses on spectral bi-clustering algorithms for text mining tasks, which represent an interesting and partially unexplored field of research. In particular, two novel versions of fuzzy spectral bi-clustering algorithms are introduced. The two algorithms differ from each other for the approach followed in the identification of the document and the word partitions. Indeed, the first one follows a simultaneous approach while the second one a sequential approach. This difference leads also to a diversification in the choice of the number of clusters. The adequacy of all the proposed fuzzy (bi-)clustering methods is evaluated by experiments performed on both real and benchmark data sets

Towards flow cytometry data clustering on graphics processing units

Like many modern techniques for scientific analysis, flow cytometry produces massive amounts of data that must be analyzed and clustered intelligently to be useful. Current manual binning techniques are cumbersome and limited in both the quality and quantity of analyses produced. To address the quality of results, a new framework applying two different sets of clustering algorithms and inference methods are implemented. The two methods investigated are fuzzy c-means and minimum description length inference and k-medoids with BIC. These approaches lend themselves to large scale parallel processing. To address the computational demands, the Nvidia CUDA framework and Tesla architecture are utilized. The resulting performance demonstrated 1-2 orders of magnitude improvement over an equivalent sequential version. The quality of results is promising and motivates further research and development in this direction