Two Squares Canonical Factorization

نویسندگان

  • Haoyue Bai
  • Frantisek Franek
  • William F. Smyth
چکیده

We present a new combinatorial structure in a string: a canonical factorization for any two squares that occur at the same position and satisfy some size restrictions. We believe that this canonical factorization will have application to related problems such as the New Periodicity Lemma, Crochemore-Rytter Three Squares Lemma, and ultimately the maximum-number-of-runs conjecture.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Projected Alternating Least square Approach for Computation of Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. Methods in alternating least square (ALS) approach usually used to solve this non-convex minimization problem.  At each step of ALS algorithms two convex least square problems should be solved, which causes high com...

متن کامل

The New Periodicity Lemma revisited

Some years ago a New Periodicity Lemma (NPL) was published, showing that the occurrence of two squares at any position i in a string necessarily precludes the occurrence of other squares of specified period in a specified neighbourhood of i. The proof of this lemma was complex, breaking down into 14 subcases, and required that the shorter of the two squares be regular. In this paper we signific...

متن کامل

A regularized kernel CCA contrast function for ICA

A new kernel based contrast function for independent component analysis (ICA) is proposed. This criterion corresponds to a regularized correlation measure in high dimensional feature spaces induced by kernels. The formulation is a multivariate extension of the least squares support vector machine (LS-SVM) formulation to kernel canonical correlation analysis (CCA). The regularization is incorpor...

متن کامل

A Multilevel Block Incomplete Cholesky Preconditioner for Solving Rectangular Sparse Matrices from Linear Least Squares Problems

An incomplete factorization method for preconditioning symmetric positive definite matrices is introduced to solve normal equations. The normal equations are formed as a means to solve rectangular matrices from linear least squares problems. The procedure is based on a block incomplete Cholesky factorization and a multilevel recursive strategy with an approximate Schur complement matrix formed ...

متن کامل

Bayesian exponential family projections for coupled data sources

Exponential family extensions of principal component analysis (EPCA) have received a considerable amount of attention in recent years, demonstrating the growing need for basic modeling tools that do not assume the squared loss or Gaussian distribution. We extend the EPCA model toolbox by presenting the first exponential family multi-view learning methods of the partial least squares and canonic...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2014