Results 11  20
of
484
Physiological time series analysis: what does regularity quantify
 Am J Physiol
, 1994
"... cal timeseries analysis: what does regularity quantify? Am. J. ..."
Abstract

Cited by 68 (2 self)
 Add to MetaCart
cal timeseries analysis: what does regularity quantify? Am. J.
Generalized Relevance Learning Vector Quantization
 Neural Networks
, 2002
"... We propose a new scheme for enlarging generalized learning vector quantization (GLVQ) with weighting factors for the input dimensions. The factors allow an appropriate scaling of the input dimensions according to their relevance. They are adapted automatically during training according to the specif ..."
Abstract

Cited by 67 (24 self)
 Add to MetaCart
(Show Context)
We propose a new scheme for enlarging generalized learning vector quantization (GLVQ) with weighting factors for the input dimensions. The factors allow an appropriate scaling of the input dimensions according to their relevance. They are adapted automatically during training according to the specific classification task whereby training can be interpreted as stochastic gradient descent on an appropriate error function. This method leads to a more powerful classifier and to an adaptive metric with little extra cost compared to standard GLVQ. Moreover, the size of the weighting factors indicates the relevance of the input dimensions. This proposes a scheme for automatically pruning irrelevant input dimensions. The algorithm is verified on artificial data sets and the iris data from the UCI repository.
Estimating the Intrinsic Dimension of Data with a FractalBased Method
, 2002
"... In this paper, the problem of estimating the intrinsic dimension of a data set is investigated. A fractalbased approach using the GrassbergerProcaccia algorithm is proposed. Since the GrassbergerProcaccia algorithm performs badly on sets of high dimensionality, an empirical procedure, that improv ..."
Abstract

Cited by 58 (2 self)
 Add to MetaCart
In this paper, the problem of estimating the intrinsic dimension of a data set is investigated. A fractalbased approach using the GrassbergerProcaccia algorithm is proposed. Since the GrassbergerProcaccia algorithm performs badly on sets of high dimensionality, an empirical procedure, that improves the original algorithm, has been developed. The procedure has been tested on data sets of known dimensionality and on time series of Santa Fe competition.
Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography
 PHYS. REV. A
, 1991
"... A series of papers has developed a statistical mechanics of neocortical interactions (SMNI), deriving aggregate behavior of experimentally observed columns of neurons from statistical electricalchemical properties of synaptic interactions. While not useful to yield insights at the single neuron lev ..."
Abstract

Cited by 51 (43 self)
 Add to MetaCart
(Show Context)
A series of papers has developed a statistical mechanics of neocortical interactions (SMNI), deriving aggregate behavior of experimentally observed columns of neurons from statistical electricalchemical properties of synaptic interactions. While not useful to yield insights at the single neuron level, SMNI has demonstrated its capability in describing largescale properties of shortterm memory and electroencephalographic (EEG) systematics. The necessity of including nonlinear and stochastic structures in this development has been stressed. In this paper, a more stringent test is placed on SMNI: The algebraic and numerical algorithms previously developed in this and similar systems are brought to bear to fit large sets of EEG and evoked potential data being collected to investigate genetic predispositions to alcoholism and to extract brain “signatures” of shortterm memory. Using the numerical algorithm of Very Fast Simulated ReAnnealing, it is demonstrated that SMNI can indeed fit this data within experimentally observed ranges of its underlying neuronalsynaptic parameters, and use the quantitative modeling results to examine physical neocortical mechanisms to discriminate between highrisk and lowrisk populations genetically predisposed to alcoholism. Since this first study is a control to span relatively long time epochs, similar to earlier attempts to establish such correlations, this discrimination is inconclusive because of other neuronal activity which can mask such effects. However, the SMNI model is shown to be consistent
Exceptional Events as Evidence for Determinism
 Physica D
, 1994
"... By focusing attention on close returns of a trajectory to itself, the existence of deterministic dynamics underlying a time series can be detected even in very short data sets. This provides a practical means of detecting determinism in moderatedimensional (e.g. ß 7) noisy systems, or lowdimension ..."
Abstract

Cited by 50 (3 self)
 Add to MetaCart
(Show Context)
By focusing attention on close returns of a trajectory to itself, the existence of deterministic dynamics underlying a time series can be detected even in very short data sets. This provides a practical means of detecting determinism in moderatedimensional (e.g. ß 7) noisy systems, or lowdimensional systems with large Lyapunov exponents such as computer random number generators. A large variety of methods have been developed to reconstruct dynamics from measured time series, and to characterize dynamics in terms of predictability or dynamical invariants such as the correlation dimension or spectrum of Lyapunov exponents. These characterizations are often applied to experimental or field time series in order to decide whether the data are consistent with a lowdimensional deterministic mechanism, or a stochastic (or extremely highdimensional, hence, effectively stochastic) mechanism. Limits on the power of these methods arise from finite and often small lengths of data sets and measu...
Multifractal Processes
, 1999
"... This paper has two main objectives. First, it develops the multifractal formalism in a context suitable for both, measures and functions, deterministic as well as random, thereby emphasizing an intuitive approach. Second, it carefully discusses several examples, such as the binomial cascades and sel ..."
Abstract

Cited by 41 (6 self)
 Add to MetaCart
This paper has two main objectives. First, it develops the multifractal formalism in a context suitable for both, measures and functions, deterministic as well as random, thereby emphasizing an intuitive approach. Second, it carefully discusses several examples, such as the binomial cascades and selfsimilar processes with a special eye on the use of wavelets. Particular attention is given to a novel class of multifractal processes which combine the attractive features of cascades and selfsimilar processes. Statistical properties of estimators as well as modelling issues are addressed.
Chaotic Mixing of Tracer and Vorticity by Modulated Travelling Rossby Waves
 Astrophys. Fluid Dyn
, 1991
"... We consider the mixing of passive tracers and vorticity by temporally fluctuating large scale flows in two dimensions. In analyzing this problem, we employ modern developments stemming from properties of Hamiltonian chaos in the particle trajectories; these developments generally come under the head ..."
Abstract

Cited by 40 (3 self)
 Add to MetaCart
(Show Context)
We consider the mixing of passive tracers and vorticity by temporally fluctuating large scale flows in two dimensions. In analyzing this problem, we employ modern developments stemming from properties of Hamiltonian chaos in the particle trajectories; these developments generally come under the heading &quot;chaotic advection &quot; or &quot;lagrangian turbulence. &quot; A review of the salient properties of this kind of mixing, and the mathematics used to analyze it, is presented in the context of passive tracer mixing by a vacillating barotropic Rossby wave. We then take up the characterization of subtler aspects of the mixing. It is shown the chaotic advection produces very nonlocal mixing which cannot be represented by eddy diffusivity. Also, the power spectrum of the tracer field is found to be k1 at shortwaves
Intrinsic dimensionality estimation of submanifolds in rd
 In ICML
, 2005
"... We present a new method to estimate the intrinsic dimensionality of a submanifold M in Rd from random samples. The method is based on the convergence rates of a certain Ustatistic on the manifold. We solve at least partially the question of the choice of the scale of the data. Moreover the proposed ..."
Abstract

Cited by 39 (3 self)
 Add to MetaCart
We present a new method to estimate the intrinsic dimensionality of a submanifold M in Rd from random samples. The method is based on the convergence rates of a certain Ustatistic on the manifold. We solve at least partially the question of the choice of the scale of the data. Moreover the proposed method is easy to implement, can handle large data sets and performs very well even for small sample sizes. We compare the proposed method to two standard estimators on several artificial as well as real data sets. 1.
Curvilinear Distance Analysis versus Isomap
 Proceedings of ESANN’2002, 10th European Symposium on Artificial Neural Networks
, 2000
"... Dimension reduction techniques are widely used for the analysis and visualization of complex sets of data. This paper compares two nonlinear projection methods: Isomap and Curvilinear Distance Analysis. ..."
Abstract

Cited by 35 (12 self)
 Add to MetaCart
(Show Context)
Dimension reduction techniques are widely used for the analysis and visualization of complex sets of data. This paper compares two nonlinear projection methods: Isomap and Curvilinear Distance Analysis.
Manifold denoising
 Advances in Neural Information Processing Systems (NIPS) 19
, 2006
"... We consider the problem of denoising a noisily sampled submanifold M in R d, where the submanifold M is a priori unknown and we are only given a noisy point sample. The presented denoising algorithm is based on a graphbased diffusion process of the point sample. We analyze this diffusion process us ..."
Abstract

Cited by 35 (1 self)
 Add to MetaCart
(Show Context)
We consider the problem of denoising a noisily sampled submanifold M in R d, where the submanifold M is a priori unknown and we are only given a noisy point sample. The presented denoising algorithm is based on a graphbased diffusion process of the point sample. We analyze this diffusion process using recent results about the convergence of graph Laplacians. In the experiments we show that our method is capable of dealing with nontrivial highdimensional noise. Moreover using the denoising algorithm as preprocessing method we can improve the results of a semisupervised learning algorithm. 1