The problems of finding alternative clusterings and avoiding bias have gained popularity over the last years. In this paper we put the focus on the quality of these alternative clusterings, proposing two approaches based in the use of negative constraints in conjunction with spectral clustering techniques. The first approach tries to introduce these constraints in the core of the constrained no...

This paper introduces an additive fuzzy clustering model for similarity data as oriented towards representation and visualization of activities of research organizations in a hierarchical taxonomy of the field. We propose a one-by-one cluster extracting strategy which leads to a version of spectral clustering approach for similarity data. The derived fuzzy clustering method, FADDIS, is experime...

Although spectral clustering has enjoyed considerable empirical success in machine learning, its theoretical properties are not yet fully developed. We analyze the performance of a spectral algorithm for hierarchical clustering and show that on a class of hierarchically structured similarity matrices, this algorithm can tolerate noise that grows with the number of data points while still perfec...

In an era of big data, face images captured in social media and forensic investigations, etc., generally lack labels, while the number identities (clusters) may range from a few dozen to thousands. Therefore, it is practical importance cluster large unlabeled into efficient or even exact identities, which can avoid image labeling by hand. Here, we propose adaptive facial imagery clustering that...

Spectral clustering and path-based clustering are two recently developed clustering approaches that have delivered impressive results in a number of challenging clustering tasks. However, they are not robust enough against noise and outliers in the data. In this paper, based on M-estimation from robust statistics, we develop a robust path-based spectral clustering method by defining a robust pa...

We study L bounds on spectral projections for the Laplace operator on compact Riemannian manifolds, restricted to small frequency dependent neighborhoods of submanifolds. In particular, if λ is a frequency and the size of the neigborhood is O(λ−δ), then new sharp estimates are established when δ ≥ 1, while for 0 ≤ δ ≤ 1/2, Sogge’s estimates [17] turn out to be optimal. In the intermediate regio...

A hierarchical scheme for clustering data is presented which applies to spaces with a high number of dimension (N D > 3). The data set is first reduced to a smaller set of partitions (multi-dimensional bins). Multiple clustering techniques are used, including spectral clustering, however, new techniques are also introduced based on the path length between partitions that are connected to one an...

In a recent paper Gunnells, Scott and Walden have determined the complete spectrum of the Schreier graph on the symmetric group corresponding to the Young subgroup Sn−2 × S2 and generated by initial reversals. In particular they find that the first nonzero eigenvalue, or spectral gap, of the Laplacian is always 1, and report that “empirical evidence” suggests that this also holds for the corres...

We consider the problem of variation of spectral subspaces for linear self-adjoint operators with emphasis on the case of off-diagonal perturbations. We prove a number of new optimal results on the shift of the spectrum and obtain (sharp) estimates on the norm of the difference of two spectral projections associated with isolated parts of the spectrum of the perturbed and unperturbed operators ...