A filtering technique for Markov chains with applications to spectral embedding
نویسندگان
چکیده
منابع مشابه
A filtering technique for Markov chains with applications to spectral embedding
Spectral methods have proven to be a highly effective tool in understanding the intrinsic geometry of a high-dimensional data set {xi}ni=1 ⊂ Rd. The key ingredient is the construction of a Markov chain on the set, where transition probabilities depend on the distance between elements, for example where for every 1 ≤ j ≤ n the probability of going from xj to xi is proportional to pij ∼ exp ( − 1...
متن کاملMarkov Chains and Spectral Clustering
The importance of Markov chains in modeling diverse systems, including biological, physical, social and economic systems, has long been known and is well documented. More recently, Markov chains have proven to be effective when applied to internet search engines such as Google’s PageRank model [7], and in data mining applications wherein data trends are sought. It is with this type of Markov ch...
متن کاملMarkov Chains and Applications
In this paper I provide a quick overview of Stochastic processes and then quickly delve into a discussion of Markov Chains. There is some assumed knowledge of basic calculus, probability, and matrix theory. I build up Markov Chain theory towards a limit theorem. I prove the Fundamental Theorem of Markov Chains relating the stationary distribution to the limiting distribution. I then employ this...
متن کاملA Class of Markov Chains with No Spectral Gap
In this paper we extend the results of the research started in [6] and [7], in which Karlin-McGregor diagonalization of certain reversible Markov chains over countably infinite general state spaces by orthogonal polynomials was used to estimate the rate of convergence to a stationary distribution. We use a method of Koornwinder [5] to generate a large and interesting family of random walks whic...
متن کاملMixing Times with Applications to Perturbed Markov Chains
A measure of the “mixing time” or “time to stationarity” in a finite irreducible discrete time Markov chain is considered. The statistic η π i ij j m j m = = ∑ 1 , where {πj} is the stationary distribution and mij is the mean first passage time from state i to state j of the Markov chain, is shown to be independent of the state i that the chain starts in (so that ηi = η for all i), is minimal i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2016
ISSN: 1063-5203
DOI: 10.1016/j.acha.2015.08.010