Euclidean Partitions Optimizing Noise Stability
نویسنده
چکیده
The Standard Simplex Conjecture of Isaksson and Mossel [12] asks for the partition {Ai}i=1 of R into k ≤ n + 1 pieces of equal Gaussian measure of optimal noise stability. That is, for ρ > 0, we maximize k ∑
منابع مشابه
On the comparison and representation of fuzzy partitions
A fuzzy partition assigns to each among n objects a distribution over a categories. Elementary linear algebraic methods permit to introduce and investigate concepts and properties such as a) variance and inertia decomposition; b) coarseand fine-graining (nestedness); c) iteration of fuzzy partitions; d) stability of a group in regard to another partition; e) (euclidean embeddable) dissimilariti...
متن کاملLow Correlation Noise Stability of Symmetric Sets
We study the Gaussian noise stability of subsets A of Euclidean space satisfying A = −A. It is shown that an interval centered at the origin, or its complement, maximizes noise stability for small correlation, among symmetric subsets of the real line of fixed Gaussian measure. In the plane, we show that a ball or its complement locally maximizes noise stability for small correlation, among symm...
متن کاملA numerical distance based on fuzzy partitions
This work studies a new distance function which takes into account expert knowledge by making use of fuzzy partitions. It considers the symbolic distances between concepts and is equivalent to the Euclidean distance for regular partitions made of triangular membership functions. Its behaviour is investigated in comparison with that of the Euclidean distance and its interest is shown for cluster...
متن کاملNoise Stability Is Computable and Approximately Low-Dimensional
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 of R for n ≥ 1 to k parts with given Gaussian measures μ1, . . . , μk. We call a partition -optimal, if its noise stability is optimal up to an additive . I...
متن کاملA New Fuzzy Noise-Rejection Data Partitioning Algorithm with Revised Mahalanobis Distance
Fuzzy C-Means (FCM) and hard clustering are the most common tools for data partitioning. However, the presence of noisy observations in the data may cause generation of completely unreliable partitions from these clustering algorithms. Also, application of the Euclidean distance in FCM only produces spherical clusters. In this paper, a new noise-rejection clustering algorithm based on Mahalanob...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1211.7138 شماره
صفحات -
تاریخ انتشار 2012