Related papers: Stability of Partitions Induced by Nearest-Center …
We consider the model introduced by Bilu and Linial (2010), who study problems for which the optimal clustering does not change when distances are perturbed. They show that even when a problem is NP-hard, it is sometimes possible to obtain…
We consider the problem of center-based clustering in low-dimensional Euclidean spaces under the perturbation stability assumption. An instance is $\alpha$-stable if the underlying optimal clustering continues to remain optimal even when…
Clustering under most popular objective functions is NP-hard, even to approximate well, and so unlikely to be efficiently solvable in the worst case. Recently, Bilu and Linial \cite{Bilu09} suggested an approach aimed at bypassing this…
Recently, there has been substantial interest in clustering research that takes a beyond worst-case approach to the analysis of algorithms. The typical idea is to design a clustering algorithm that outputs a near-optimal solution, provided…
Motivated by the fact that distances between data points in many real-world clustering instances are often based on heuristic measures, Bilu and Linial~\cite{BL} proposed analyzing objective based clustering problems under the assumption…
The gravitation interaction between particles is taken into account in central configuration model. After that, the resonance perturbation of the particle of the central configuration by distant satellite is considered in the restricted…
Questions of noise stability play an important role in hardness of approximation in computer science as well as in the theory of voting. In many applications, the goal is to find an optimizer of noise stability among all possible partitions…
We study the critical behavior of low-frequency vibrations of packings with pinned particles near the jamming point. Soft modes form a plateau in the density of states and its frequency is controlled by the contact number as the ordinary…
We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around…
The performance of decision policies and prediction models often deteriorates when applied to environments different from the ones seen during training. To ensure reliable operation, we analyze the stability of a system under distribution…
The Standard Simplex Conjecture and the Plurality is Stablest Conjecture are two conjectures stating that certain partitions are optimal with respect to Gaussian and discrete noise stability respectively. These two conjectures are natural…
The $k$-center problem is a canonical and long-studied facility location and clustering problem with many applications in both its symmetric and asymmetric forms. Both versions of the problem have tight approximation factors on worst case…
We introduce a perturbation expansion for athermal systems that allows an exact determination of displacement fields away from the crystalline state as a response to disorder. We show that the displacement fields in energy minimized…
Under natural assumptions, an unstable equilibrium of a difference equation can be stabilized by a bounded multiplicative noise, identically distributed at each step. This includes stabilization of an otherwise unstable positive equilibrium…
We study the instabilities of a harmonic oscillator subject to additive and dichotomous multiplicative noise, focussing on the dependance of the instability threshold on the mass. For multiplicative noise in the damping, the instability…
We study theoretically and numerically how hard frictionless particles in random packings can rearrange. We demonstrate the existence of two distinct unstable non-linear modes of rearrangement, both associated with the opening and the…
The stability of a rotating fluid disk to the formation of spiral arms is studied in the tightwinding approximation in the linear regime. The dispersion relation for spirals that was derived by Bertin et al. is shown to contain a new,…
A theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution is suggested. The reason for the clustering instability is a combined effect of the particles inertia…
This paper considers gravitational perturbations in geometrically thin disks with rotation curves dominated by a central object, but with substantial contributions from magnetic pressure and tension. The treatment is general, but the…
Although consistency is a minimum requirement of any estimator, little is known about consistency of the mean partition approach in consensus clustering. This contribution studies the asymptotic behavior of mean partitions. We show that…