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Assessing local influence in principal component analysis with application to haematology study data.
Wing K Fung1, Hong Gu, Liming Xiang
1Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong. wingfung@hku.hk
Statistics in Medicine
|November 10, 2006
Summary
Principal Component Analysis (PCA) is sensitive to outliers in high-dimensional data. This study introduces methods to assess this sensitivity, improving outlier detection in medical and health studies.
Area of Science:
- Statistics
- Biostatistics
- Data Science
Background:
- High-dimensional data are common in medical and health studies.
- Principal Component Analysis (PCA) is widely used for dimensionality reduction.
- Standard PCA is sensitive to abnormal observations (outliers).
Purpose of the Study:
- To develop methods for assessing local influence in PCA.
- To identify influential observations in high-dimensional datasets.
- To enhance the robustness of PCA in medical and health research.
Main Methods:
- Local influence assessment using generalized influence functions.
- Application of case-weights and additive perturbation schemes.
- Analysis of perturbation schemes and generalized influence function approach.
Main Results:
- Identified directions of largest joint local influence for eigenvalues.
- Demonstrated that these directions are determined by observation score values.
- Provided an approximate cut-off point for identifying influential observations.
- Applied methods to haematology data, revealing new insights.
Conclusions:
- The proposed methods effectively assess PCA sensitivity to outliers.
- The findings aid in identifying influential observations in complex datasets.
- This work contributes to more reliable data analysis in health studies.
