We propose a novel hierarchical clustering algorithm for data-sets in which only pairwise distances between the points are provided. The classical Hungarian method is an efficient algorithm for solving the problem of minimal-weight cycle cover. We utilize the Hungarian method as the basic building block of our clustering algorithm. The disjoint cycles, produced by the Hungarian method, are view...

k-means clustering is a popular approach to clustering. It is easy to implement and intuitive but has the disadvantage of being sensitive to initialization due to an underlying non-convex optimization problem. In this paper, we derive an equivalent formulation of k-means clustering. The formulation takes the form of a `0-regularized least squares problem. We then propose a novel convex, relaxed...

clustering is a widespread data analysis and data mining technique in many fields of study such as engineering, medicine, biology and the like. the aim of clustering is to collect data points. in this paper, a cultural algorithm (ca) is presented to optimize partition with n objects into k clusters. the ca is one of the effective methods for searching into the problem space in order to find a n...

Constrained spectral clustering is a semi-supervised learning problem that aims at incorporating userdefined constraints in spectral clustering. Typically, there are two kinds of constraints: (i) must-link, and (ii) cannot-link. These constraints represent prior knowledge indicating whether two data objects should be in the same cluster or not; thereby aiding in clustering. In this paper, we pr...

Spectral Clustering (SC) is a widely used data clustering method which first learns a low-dimensional embedding U of data by computing the eigenvectors of the normalized Laplacian matrix, and then performs k-means on U> to get the final clustering result. The Sparse Spectral Clustering (SSC) method extends SC with a sparse regularization on UU> by using the block diagonal structure prior of UU>...

association rules are among important techniques in data mining which are used for extracting hidden patterns and knowledge in large volumes of data. association rules help individuals and organizations take strategic decisions and improve their business processes. extracted association rules from a database contain important and confidential information that if published, the privacy of indivi...

We present a numerical algorithm for nonnegative matrix factorization (NMF) problems under noisy separability. An NMF problem under separability can be stated as one of finding all vertices of the convex hull of data points. The research interest of this paper is to find the vectors as close to the vertices as possible in a situation in which noise is added to the data points. Our algorithm is ...

Prototype-based methods are commonly used in cluster analysis and the results may be highly dependent on the prototype used. In this paper, we propose a two-level fuzzy clustering method that involves adaptively expanding and merging convex polytopes, where the convex polytopes are considered as a “flexible” prototype. Therefore, the dependency on the use of a specified prototype can be elimina...