KPCA denoising and the pre-image problem revisited

Teixeira, António; Tomé, Ana Maria; Stadlthanner, K.; Lang, Elmar

doi:10.1016/j.dsp.2007.08.001

Cited by 53 publications

(29 citation statements)

References 11 publications

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“…Later it was claimed that a more efficient starting point would be the mean of a certain number of neighbors of the point to be de-noised [16]. Dambreville et al [4] proposed a modification of the method developed by Mika et al utilizing feature space distances.…”

Section: Overview Of Existing Algorithmsmentioning

confidence: 99%

Regularized Pre-image Estimation for Kernel PCA De-noising

Abrahamsen

Hansen

2010

J Sign Process Syst

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The main challenge in de-noising by kernel Principal Component Analysis (PCA) is the mapping of de-noised feature space points back into input space, also referred to as "the pre-image problem". Since the feature space mapping is typically not bijective, preimage estimation is inherently illposed. As a consequence the most widely used estimation schemes lack stability. A common way to stabilize such estimates is by augmenting the cost function by a suitable constraint on the solution values. For de-noising applications we here propose Tikhonov input space distance regularization as a stabilizer for pre-image estimation, or sparse reconstruction by Lasso regularization in cases where the main objective is to improve the visual simplicity. We perform extensive experiments on the USPS digit modeling problem to evaluate the stability of three widely used pre-image estimators. We show that the previous methods lack stability in the is non-linear regime, however, by applying our proposed input space distance regularizer the estimates are stabilized with a limited sacrifice in terms of de-noising efficiency. Furthermore, we show how sparse reconstruction can lead to improved visual quality of the estimated pre-image.

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Section: Overview Of Existing Algorithmsmentioning

confidence: 99%

Regularized Pre-image Estimation for Kernel PCA De-noising

Abrahamsen

Hansen

2010

J Sign Process Syst

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“…Thus, the ERP signals were decomposed into details D1-D7 and one final approximation, A7. The detail coefficients D7, D6, D5 and approximation coefficients A7 were chosen as feature parameters, which respectively corresponded to theta (4-7 Hz), alpha (8-15 Hz), beta (16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31), and delta(0.5-4 Hz) rhythms. For each electrode, Fz, Cz and Pz, the WCs of 64 dimensions were obtained.…”

Section: Feature Extraction Based On Wavelet Transformmentioning

confidence: 99%

“…In recent years, Kernel-based nonlinear feature extraction and classification algorithms become a hot research direction in machine learning field [18]. Successful applications of kernel-based algorithm have been reported in various fields [19,20].…”

Section: Introductionmentioning

confidence: 99%

A New Approach for Concealed Information Identification Based on ERP Assessment

2011

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Recently, numerous concealed information test (CIT) studies have been done with event related potential (ERP) for its sufficient validity in applied use. In this study, a new approach based on wavelet coefficients (WCs) and kernel learning algorithm is proposed to identify concealed information. Totally 16 subjects went through the designed CIT paradigm and the multichannel electroencephalogram (EEG) signals were recorded. Then, the high-dimensional WCs of ERP in delta, theta, alpha and beta rhythms were extracted. For the analysis of the data, kernel principle component analysis (KPCA) and a support vector machines (SVM) classifier are implemented. The results show that WCs features are significant differences between concealed information and irrelevant information (P < 0.05). The KPCA is able to effectively reduce feature dimensionalities and increase generalization performance of SVM. A high accuracy (93.6%) in recognizing concealed information and irrelevant information is achieved, which indicates the combination KPCA and SVM may provide a useful tool for detecting the concealed information.

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“…Instead [10] suggested to initialize the fixed-point iteration scheme in the solution found by the distance method in [3]. Later it was claimed that a more efficient starting point would be the mean of a certain number of neighbors of the point to be de-noised [11]. In [4] a modification of the method developed in [1], utilizing feature space distances was proposed.…”

Section: Overview Of Existing Algorithmsmentioning

confidence: 99%

Input space regularization stabilizes pre-images for kernel PCA de-noising

Abrahamsen

Hansen

2009

2009 IEEE International Workshop on Machine Learning for Signal Processing

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Solution of the pre-image problem is key to efficient nonlinear de-noising using kernel Principal Component Analysis. Pre-image estimation is inherently ill-posed for typical kernels used in applications and consequently the most widely used estimation schemes lack stability. For de-noising applications we propose input space distance regularization as a stabilizer for pre-image estimation. We perform extensive experiments on the USPS digit modeling problem to evaluate the stability of three widely used pre-image estimators. We show that the previous methods lack stability when the feature mapping is non-linear, however, by applying a simple input space distance regularizer we can reduce variability with very limited sacrifice in terms of de-noising efficiency.

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KPCA denoising and the pre-image problem revisited

Cited by 53 publications

References 11 publications

Regularized Pre-image Estimation for Kernel PCA De-noising

Regularized Pre-image Estimation for Kernel PCA De-noising

A New Approach for Concealed Information Identification Based on ERP Assessment

Input space regularization stabilizes pre-images for kernel PCA de-noising

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