### Abstract

Original language | Undefined |
---|---|

Pages (from-to) | 127-139 |

Number of pages | 14 |

Journal | IEEE transactions on pattern analysis and machine intelligence |

Volume | 36 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2014 |

### Keywords

- SCS-Safety
- variance correction
- ApplicationsApplications and Expert Knowledge-Intensive SystemsArtificial IntelligenceComputational models of visionComputer visionComputing MethodologiesFace and gesture recognitionImage Processing and Computer VisionImage RepresentationLearningMachine learningMathematics of ComputingModel Validation and AnalysisModelingModelsMultidimensionalMultivariate statisticsPattern RecognitionProbability and StatisticsSimulationVisualization
- EWI-23367
- High dimensional verification
- Eigenwise correction
- METIS-297651
- PrincipleComponent Analysis
- IR-86200
- Marˇcenko Pastur equation
- Euclidean distance
- Fixed point eigenvalue correction
- eigenvalue bias correction

### Cite this

}

*IEEE transactions on pattern analysis and machine intelligence*, vol. 36, no. 1, pp. 127-139. https://doi.org/10.1109/TPAMI.2013.93

**Likelihood ratio based verification in high dimensional spaces.** / Hendrikse, A.J.; Veldhuis, Raymond N.J.; Spreeuwers, Lieuwe Jan.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Likelihood ratio based verification in high dimensional spaces

AU - Hendrikse, A.J.

AU - Veldhuis, Raymond N.J.

AU - Spreeuwers, Lieuwe Jan

N1 - eemcs-eprint-23367

PY - 2014/1

Y1 - 2014/1

N2 - The increase of the dimensionality of data sets often lead to problems during estimation, which are denoted as the curse of dimensionality. One of the problems of Second Order Statistics (SOS) estimation in high dimensional data is that the resulting covariance matrices are not full rank, so their inversion, needed for example in verification systems based on the likelihood ratio, is an ill posed problem, known as the singularity problem. A classical solution to this problem is the projection of the data onto a lower dimensional subspace using Principle Component Analysis (PCA) and it is assumed that any further estimation on this dimension reduced data is free from the effects of the high dimensionality. Using theory on SOS estimation in high dimensional spaces, we show that the solution with PCA is far from optimal in verification systems if the high dimensionality is the sole source of error. For moderate dimensionality it is already outperformed by solutions based on euclidean distances and it breaks down completely if the dimensionality becomes very high.We propose a new method,the fixed point eigenwise correction, which does not have these disadvantages and performs close to optimal.

AB - The increase of the dimensionality of data sets often lead to problems during estimation, which are denoted as the curse of dimensionality. One of the problems of Second Order Statistics (SOS) estimation in high dimensional data is that the resulting covariance matrices are not full rank, so their inversion, needed for example in verification systems based on the likelihood ratio, is an ill posed problem, known as the singularity problem. A classical solution to this problem is the projection of the data onto a lower dimensional subspace using Principle Component Analysis (PCA) and it is assumed that any further estimation on this dimension reduced data is free from the effects of the high dimensionality. Using theory on SOS estimation in high dimensional spaces, we show that the solution with PCA is far from optimal in verification systems if the high dimensionality is the sole source of error. For moderate dimensionality it is already outperformed by solutions based on euclidean distances and it breaks down completely if the dimensionality becomes very high.We propose a new method,the fixed point eigenwise correction, which does not have these disadvantages and performs close to optimal.

KW - SCS-Safety

KW - variance correction

KW - ApplicationsApplications and Expert Knowledge-Intensive SystemsArtificial IntelligenceComputational models of visionComputer visionComputing MethodologiesFace and gesture recognitionImage Processing and Computer VisionImage RepresentationLearningMachine l

KW - EWI-23367

KW - High dimensional verification

KW - Eigenwise correction

KW - METIS-297651

KW - PrincipleComponent Analysis

KW - IR-86200

KW - Marˇcenko Pastur equation

KW - Euclidean distance

KW - Fixed point eigenvalue correction

KW - eigenvalue bias correction

U2 - 10.1109/TPAMI.2013.93

DO - 10.1109/TPAMI.2013.93

M3 - Article

VL - 36

SP - 127

EP - 139

JO - IEEE transactions on pattern analysis and machine intelligence

JF - IEEE transactions on pattern analysis and machine intelligence

SN - 0162-8828

IS - 1

ER -