In this chapter, we present two approaches for clustering spatial functional data. The first one is the model-based that uses concept of density random variables. second hierarchical based on univariate statistics data such as mode or mean. These take into account features data: observations are spatially close and share a common distribution associated methodologies illustrated by an applicati...

This paper addresses the problem of robust matrix rootclustering analysis. The considered matrices are complex and subject to both polytopic and parameter-dependent normbounded uncertainties. The clustering regions are unions of convex and possibly disjoint and nonsymmetric subregions of the complex plane. The proposed clustering conditions are formulated through an approach based upon Linear M...

A blind classification algorithm is presented that uses hyperdimensional geometric algorithms to locate a hypothesis, in the form of a convex polytope or hyper-sphere. The convex polytope geometric model provides a well-fitted class representation that does not require training with instances of opposing classes. Further, the classification algorithm creates models for as many training classes ...

The goal of hierarchical clustering is to construct a cluster tree, which can be viewed as the modal structure of a density. For this purpose, we use a convex optimization program that can efficiently estimate a family of hierarchical dense sets in high-dimensional distributions. We further extend existing graph-based methods to approximate the cluster tree of a distribution. By avoiding direct...

Abstract. Prototypical data clustering is known to su↵er from poor initializations. Recently, a semidefinite relaxation has been proposed to overcome this issue and to enable the use of convex programming instead of ad-hoc procedures. Unfortunately, this relaxation does not extend to the more involved case where clusters are defined by parametric models, and where the computation of means has t...

Invariance and representation learning are important precursors to modeling and classification tools particularly for non-Euclidean spaces such as images, strings and nonvectorial data. This article proposes a method for learning invariances in data while jointly estimating a model. The technique results in a convex programming problem with a consistent and unique solution. Representation varia...

<p>In response to the abnormal data mining in dam safety monitoring, and based on traditional spectral clustering, this paper presents an anomaly detection method improved clustering. This applies a distance density adaptive similarity measure. The natural eigenvalue is introduced adaptively select neighbors of points, redefined be combined with k-nearest neighbor. Furthermore, shared nei...

this paper uses integrated data envelopment analysis (dea) models to rank all extreme and non-extreme efficient decision making units (dmus) and then applies integrated dea ranking method as a criterion to modify genetic algorithm (ga) for finding pareto optimal solutions of a multi objective programming (mop) problem. the researchers have used ranking method as a shortcut way to modify ga to d...

Clustering is a relevant problem in machine learning where the main goal is to locate meaningful partitions of unlabeled data. In the case of labeled data, a related problem is supervised clustering, where the objective is to locate classuniform clusters. Most current approaches to supervised clustering optimize a score related to cluster purity with respect to class labels. In particular, we p...