Publications related to Estimating the Intrinsic Dimension of Data with a Fractal-Based Method

Low-rank Matrix Approximation Using Point-wise Operators

Extracting low dimensional structure from high dimensional data arises in many applications such as machine learning, statistical pattern recognition, wireless sensor networks, and data compression. If the data is restricted to a lower dimensional subspace ...

Institute of Electrical and Electronics Engineers2012

Using sketch-map coordinates to analyze and bias molecular dynamics simulations

Michele Ceriotti, Gareth Aneurin Tribello, Michele Parrinello

When examining complex problems, such as the folding of proteins, coarse grained descriptions of the system drive our investigation and help us to rationalize the results. Oftentimes collective variables (CVs), derived through some chemical intuition about ...

National Academy of Sciences2012

Semi-supervised dimensionality reduction for analyzing high-dimensional data with constraints

Sofien Bouaziz

In this paper, we present a novel semi-supervised dimensionality reduction technique to address the problems of inefficient learning and costly computation in coping with high-dimensional data. Our method named the dual subspace projections (DSP) embeds hi ...

Elsevier2012

Learning Low-Dimensional Signal Models

Volkan Cevher

Sampling, coding, and streaming even the most essential data, e.g., in medical imaging and weather-monitoring applications, produce a data deluge that severely stresses the avail able analog-to-digital converter, communication bandwidth, and digital-storag ...

Institute of Electrical and Electronics Engineers2011

On the spectral estimates for Schrödinger type operators. The case of small local dimension

The behavior of the discrete spectrum of the Schr"odinger operator

-\D - V

, in quite a general setting, up to a large extent is determined by the behavior of the corresponding heat kernel

P(t;x,y)

as

t\to 0

and

t\to\infty

. If this behavior is powe ...

2010

Distributed Similarity Search in High Dimensions Using Locality Sensitive Hashing

Karl Aberer, Sebastian Michel, Parisa Haghani

In this paper we consider distributed K-Nearest Neighbor (KNN) search and range query processing in high dimensional data. Our approach is based on Locality Sensitive Hashing (LSH) which has proven very efficient in answering KNN queries in centralized set ...

2009

Pattern Recognition using Higher-Order Local Autocorrelation Coefficients

Jean-Philippe Thiran, Vlad Popovici

The autocorrelations have been previously used as features for 1D or 2D signal classification in a wide range of applications, like texture classification, face detection and recognition, EEG signal classification, and so on. However, in almost all the cas ...

2004

Estimating the Intrinsic Dimension of Data with a Fractal-Based Method

Alessandro Vinciarelli

In this paper, the problem of estimating the Intrinsic Dimension of a data set is investigated. A fractal-based approach using the Grassberger-Procaccia algorithm is proposed. Since the Grassberger-Procaccia algorithm performs badly on sets of high dimensi ...

2002

PCA in Autocorrelation Space

Jean-Philippe Thiran, Vlad Popovici

The use of higher order autocorrelations as features for pattern classification has been usually restricted to second or third orders due to high computational costs. Since the autocorrelation space is a high dimensional space we are interested in reducing ...

SPIE2002

Intrinsic dimension estimation of data: an approach based on Grassberger-Procaccia's algorithm

Alessandro Vinciarelli

In this paper the problem of estimating the intrinsic dimension of a data set is investigated. An approach based on the Grassberger-Procaccia's algorithm has been studied. Since this algorithm does not yield accurate measures in high-dimensional data sets, ...

2001

Estimating the Intrinsic Dimension of Data with a Fractal-Based Method

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Low-rank Matrix Approximation Using Point-wise Operators

Using sketch-map coordinates to analyze and bias molecular dynamics simulations

Semi-supervised dimensionality reduction for analyzing high-dimensional data with constraints

Learning Low-Dimensional Signal Models

On the spectral estimates for Schrödinger type operators. The case of small local dimension

Distributed Similarity Search in High Dimensions Using Locality Sensitive Hashing

Pattern Recognition using Higher-Order Local Autocorrelation Coefficients

Estimating the Intrinsic Dimension of Data with a Fractal-Based Method

PCA in Autocorrelation Space

Intrinsic dimension estimation of data: an approach based on Grassberger-Procaccia's algorithm

Low-rank Matrix Approximation Using Point-wise Operators

PCA in Autocorrelation Space

Estimating the Intrinsic Dimension of Data with a Fractal-Based Method

Intrinsic dimension estimation of data: an approach based on Grassberger-Procaccia's algorithm

Using sketch-map coordinates to analyze and bias molecular dynamics simulations

Pattern Recognition using Higher-Order Local Autocorrelation Coefficients

On the spectral estimates for Schrödinger type operators. The case of small local dimension

Semi-supervised dimensionality reduction for analyzing high-dimensional data with constraints

Distributed Similarity Search in High Dimensions Using Locality Sensitive Hashing

Learning Low-Dimensional Signal Models