Effective PCA for high-dimension, low-sample-size data with singular value decomposition of cross data matrix

Yata, Kazuyoshi; Aoshima, Makoto

doi:10.1016/j.jmva.2010.04.006

Cited by 62 publications

(54 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to study the performance of the two-stage procedure given by (12) and (13), we used computer simulations. Our goal was to construct a 95% givenbandwidth confidence region, R N .…”

Section: Simulationmentioning

confidence: 99%

“…We divided each type into two groups with respect to the relapse as follows: (a) π 1 : B-cell with the relapse (n 1 = 50 samples); (b) π 2 : B-cell without the relapse (n 2 = 26 samples); (c) π 3 : T-cell with the relapse (n 3 = 15 samples); and (d) π 4 : T-cell without the relapse (n 4 = 9 samples). Table 2 Required sample size and coverage probability given by (12) and (13) …”

Section: Examplementioning

confidence: 99%

See 1 more Smart Citation

Asymptotic Normality for Inference on Multisample, High-Dimensional Mean Vectors Under Mild Conditions

Aoshima

Yata

2013

Methodol Comput Appl Probab

Self Cite

View full text Add to dashboard Cite

In this paper, we consider the asymptotic normality for various inference problems on multisample and high-dimensional mean vectors. We verify that the asymptotic normality of concerned statistics is proved under mild conditions for high-dimensional data. We show that the asymptotic normality can be justified theoretically and numerically even for non-Gaussian data. We introduce the extended cross-data-matrix (ECDM) methodology to construct an unbiased estimator at a reasonable computational cost. With the help of the asymptotic normality, we show that the concerned statistics given by ECDM can ensure consistency properties for inference on multisample and high-dimensional mean vectors. We give several applications such as confidence regions for high-dimensional mean vectors, confidence intervals for the squared norm and the test of multisample mean vectors. We also provide sample size determination so as to satisfy prespecified accuracy on inference. Finally, we give several examples by using a microarray data set.

show abstract

“…In order to study the performance of the two-stage procedure given by (12) and (13), we used computer simulations. Our goal was to construct a 95% givenbandwidth confidence region, R N .…”

Section: Simulationmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Asymptotic Normality for Inference on Multisample, High-Dimensional Mean Vectors Under Mild Conditions

Aoshima

Yata

2013

Methodol Comput Appl Probab

Self Cite

View full text Add to dashboard Cite

show abstract

“…Actually, one cannot handle the noise space by S D for high-dimension, non-Gaussian data. In order to handle the two-sample problem for high-dimensional non-Gaussian data, we shall consider applying the CDM method given by Yata and Aoshima (2010). …”

Section: Noise Space For High-dimensional Non-gaussian Datamentioning

confidence: 99%

“…The cross-data-matrix (CDM) methodology is high-dimensional Principal Component Analysis developed by Yata and Aoshima (2010). Again, throughout this section, we omit the population index to avoid confusion.…”

Section: Bias-corrected Cdm Estimatormentioning

confidence: 99%

See 1 more Smart Citation

A High-Dimensional Two-Sample Test for Non-Gaussian Data under a Strongly Spiked Eigenvalue Model

Ishii

2017

JJSS

View full text Add to dashboard Cite

In this paper, we discuss two-sample tests for high-dimension, non-Gaussian data. We suppose that two classes have a strongly spiked eigenvalue model. First, we investigate the noise space for high-dimension, non-Gaussian data. A two-sample test is proposed by using the cross-data-matrix (CDM) methodology and its power is derived under some regularity conditions when the dimension is very large. We discuss the validity of assumptions. We check the performance of the proposed twosample test procedure by simulations. Finally, we demonstrate the proposed twosample test in actual data analyses.

show abstract

Reflections of the real‐world in the unreal, using simulation to design complex real‐world validation studies for spectroscopy

Beattie¹

2021

J Raman Spectroscopy

View full text Add to dashboard Cite

Increasing use of real-world experiments embeds scientific study in settings relevant to everyday life but brings a number of complications. Traditional study design has evaluated experimental risk based on a limited number of factors that are tightly controlled while others are standardised. In real-world data, many unstandardised factors risk confounding the study in unanticipated ways. Some simulation tools and processes are evaluated for use in capturing current knowledge of complex scenarios to evaluate validation of multivariate models in real-world settings. Further, it examines the value of probing the range of uncertainty of the assumptions used to build the model. Copulas simulate correlation of multiple underlying factors where the web of causal interactions cannot be untangled. These factors influence the biochemical status of an individual, determining what pathways are activated in that individual. The final biochemical status of the individuals is then transformed into Raman spectroscopic, reference and pathological measurements. Evaluating different validation scenarios (same population, subset of that population and a new population) allows evaluation of the risks of the model being deployed for different intended uses. Technical factors are stress tested to determine the analytical bottlenecks. Individual socio-economic factors are stress tested todetermine the leverage that current uncertainty has on the risks to the validation study. Use of simulation was able to identify the limitations of the current model for new scenarios and also to assess the specific changes in expected sensitivity versus specificity in the new populations, which would be relevant for benefit risk analysis.

show abstract

Effective PCA for high-dimension, low-sample-size data with singular value decomposition of cross data matrix

Cited by 62 publications

References 11 publications

Asymptotic Normality for Inference on Multisample, High-Dimensional Mean Vectors Under Mild Conditions

Asymptotic Normality for Inference on Multisample, High-Dimensional Mean Vectors Under Mild Conditions

A High-Dimensional Two-Sample Test for Non-Gaussian Data under a Strongly Spiked Eigenvalue Model

Reflections of the real‐world in the unreal, using simulation to design complex real‐world validation studies for spectroscopy

Contact Info

Product

Resources

About