Hierarchical and Non-Hierarchical Linear and Non-Linear Clustering Methods to “Shakespeare Authorship Question”

Clustering is a data mining task devoted to the automatic grouping of data based on mutual similarity. Clustering in high-dimensional spaces is a recurrent problem in many domains. It affects time complexity, space complexity, scalability and accuracy of clustering methods. Highdimensional non-linear datausually live in different low dimensional subspaces hidden in the original space. As high‐dimensional objects appear almost alike, new approaches for clustering are required. This research has focused on developing Mathematical models, techniques and clustering algorithms specifically for high‐dimensional data. The innocent growth in the fields of communication and technology, there is tremendous growth in high dimensional data spaces. As the variant of dimensions on high dimensional non-linear data increases, many clustering techniques begin to suffer from the curse of dimensionality, de-grading the quality of the results. In high dimensional non-linear data, the data becomes very sparse and distance measures become increasingly meaningless. The principal challenge for clustering high dimensional data is to overcome the “curse of dimensionality”. This research work concentrates on devising an enhanced algorithm for clustering high dimensional non-linear data.

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Sparse and Low-Rank Subspace Data Clustering with Manifold Regularization Learned by Local Linear Embedding

Applied Sciences ◽

10.3390/app8112175 ◽

2018 ◽

Vol 8 (11) ◽

pp. 2175 ◽

Cited By ~ 1

Author(s):

Ye Yang ◽

Yongli Hu ◽

Fei Wu

Keyword(s):

Data Clustering ◽

Spectral Clustering ◽

Subspace Clustering ◽

Low Rank ◽

Clustering Methods ◽

Local Linear Embedding ◽

Local Linear ◽

Non Linear ◽

Laplacian Graph ◽

Linear Embedding

Data clustering is an important research topic in data mining and signal processing communications. In all the data clustering methods, the subspace spectral clustering methods based on self expression model, e.g., the Sparse Subspace Clustering (SSC) and the Low Rank Representation (LRR) methods, have attracted a lot of attention and shown good performance. The key step of SSC and LRR is to construct a proper affinity or similarity matrix of data for spectral clustering. Recently, Laplacian graph constraint was introduced into the basic SSC and LRR and obtained considerable improvement. However, the current graph construction methods do not well exploit and reveal the non-linear properties of the clustering data, which is common for high dimensional data. In this paper, we introduce the classic manifold learning method, the Local Linear Embedding (LLE), to learn the non-linear structure underlying the data and use the learned local geometry of manifold as a regularization for SSC and LRR, which results the proposed LLE-SSC and LLE-LRR clustering methods. Additionally, to solve the complex optimization problem involved in the proposed models, an efficient algorithm is also proposed. We test the proposed data clustering methods on several types of public databases. The experimental results show that our methods outperform typical subspace clustering methods with Laplacian graph constraint.

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Fuzzy clustering methods for identifying and modelling of non-linear control strategies

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1177/095965180121500502 ◽

2001 ◽

Vol 215 (5) ◽

pp. 437-452 ◽

Cited By ~ 3

Author(s):

I S Akkizidis ◽

G N Roberts

Keyword(s):

Fuzzy Clustering ◽

Control Strategies ◽

Linear Control ◽

Clustering Methods ◽

Non Linear ◽

Fuzzy Clustering Methods

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B. The Non-Linear Calculations for Pulsating Stars

Symposium - International Astronomical Union ◽

10.1017/s0074180900019008 ◽

1967 ◽

Vol 28 ◽

pp. 105-176

Author(s):

Robert F. Christy

Keyword(s):

Major Part ◽

Afternoon Session ◽

Discussion Session ◽

Pulsating Stars ◽

Fourth Symposium ◽

Non Linear ◽

Considerable Discussion ◽

Informal Approach ◽

Preceding Session

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)

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