Topic
Invariant (mathematics)
About: Invariant (mathematics) is a research topic. Over the lifetime, 48442 publications have been published within this topic receiving 861923 citations. The topic is also known as: mathematical invariant.
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TL;DR: In this paper, a framework for efficient IV estimators of random effects models with information in levels which can accommodate predetermined variables is presented. But the authors do not consider models with predetermined variables that have constant correlation with the effects.
16,245 citations
Book•
01 Aug 1979
TL;DR: 1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of non negative matrices 4. Symmetric nonnegativeMatrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative methods for linear systems 8. Finite Markov Chains
Abstract: 1. Matrices which leave a cone invariant 2. Nonnegative matrices 3. Semigroups of nonnegative matrices 4. Symmetric nonnegative matrices 5. Generalized inverse- Positivity 6. M-matrices 7. Iterative methods for linear systems 8. Finite Markov Chains 9. Input-output analysis in economics 10. The Linear complementarity problem 11. Supplement 1979-1993 References Index.
6,572 citations
17 Jun 2006
TL;DR: This work presents a method - called Dimensionality Reduction by Learning an Invariant Mapping (DrLIM) - for learning a globally coherent nonlinear function that maps the data evenly to the output manifold.
Abstract: Dimensionality reduction involves mapping a set of high dimensional input points onto a low dimensional manifold so that 'similar" points in input space are mapped to nearby points on the manifold. We present a method - called Dimensionality Reduction by Learning an Invariant Mapping (DrLIM) - for learning a globally coherent nonlinear function that maps the data evenly to the output manifold. The learning relies solely on neighborhood relationships and does not require any distancemeasure in the input space. The method can learn mappings that are invariant to certain transformations of the inputs, as is demonstrated with a number of experiments. Comparisons are made to other techniques, in particular LLE.
4,524 citations
Book•
16 Dec 1981
TL;DR: The first part of the text as discussed by the authors provides an introduction to ergodic theory suitable for readers knowing basic measure theory, including recurrence properties, mixing properties, the Birkhoff Ergodic theorem, isomorphism, and entropy theory.
Abstract: This text provides an introduction to ergodic theory suitable for readers knowing basic measure theory. The mathematical prerequisites are summarized in Chapter 0. It is hoped the reader will be ready to tackle research papers after reading the book. The first part of the text is concerned with measure-preserving transformations of probability spaces; recurrence properties, mixing properties, the Birkhoff ergodic theorem, isomorphism and spectral isomorphism, and entropy theory are discussed. Some examples are described and are studied in detail when new properties are presented. The second part of the text focuses on the ergodic theory of continuous transformations of compact metrizable spaces. The family of invariant probability measures for such a transformation is studied and related to properties of the transformation such as topological traitivity, minimality, the size of the non-wandering set, and existence of periodic points. Topological entropy is introduced and related to measure-theoretic entropy. Topological pressure and equilibrium states are discussed, and a proof is given of the variational principle that relates pressure to measure-theoretic entropies. Several examples are studied in detail. The final chapter outlines significant results and some applications of ergodic theory to other branches of mathematics.
3,550 citations
TL;DR: The high utility of MSERs, multiple measurement regions and the robust metric is demonstrated in wide-baseline experiments on image pairs from both indoor and outdoor scenes.
3,422 citations