Uncertainty-Aware Principal Component Analysis

@article{Grtler2020UncertaintyAwarePC,
  title={Uncertainty-Aware Principal Component Analysis},
  author={Jochen G{\"o}rtler and Thilo Spinner and Dirk Streeb and Daniel Weiskopf and Oliver Deussen},
  journal={IEEE Transactions on Visualization and Computer Graphics},
  year={2020},
  volume={26},
  pages={822-831}
}
We present a technique to perform dimensionality reduction on data that is subject to uncertainty. [] Key Method We derive a representation of the PCA sample covariance matrix that respects potential uncertainty in each of the inputs, building the mathematical foundation of our new method: uncertainty-aware PCA. In addition to the accuracy and performance gained by our approach over sampling-based strategies, our formulation allows us to perform sensitivity analysis with regard to the uncertainty in the data…

Figures from this paper

UAC: An Uncertainty-Aware Face Clustering Algorithm
TLDR
An uncertainty-aware clustering algorithm is proposed, UAC, which explicitly leverages uncertainty information during clustering to decide when a pair of faces are similar or when a predicted cluster should be discarded and produces significantly better clusters by leveraging uncertainty in face images.
The State of the Art in Enhancing Trust in Machine Learning Models with the Use of Visualizations
TLDR
This survey is intended to be beneficial for visualization researchers whose interests involve making ML models more trustworthy, as well as researchers and practitioners from other disciplines in their search for effective visualization techniques suitable for solving their tasks with confidence and conveying meaning to their data.
Uncertainty Visualization: Concepts, Methods, and Applications in Biological Data Visualization
  • D. Weiskopf
  • Computer Science
    Frontiers in Bioinformatics
  • 2022
TLDR
Components are discussed that are relevant for handling and visualizing uncertainty introduced with the original data and at later stages in the pipeline, which shows the importance of making the stages of the pipeline aware of uncertainty and allowing them to propagate uncertainty.
Shape in Medical Imaging: International Workshop, ShapeMI 2020, Held in Conjunction with MICCAI 2020, Lima, Peru, October 4, 2020, Proceedings
TLDR
An algorithm to register sets of points or oriented points through arbitrarily composed sets of transformations so as to allow the construction of context-specific deformation spaces, which is generic with respect to the choice of transformations.
Intelligent Recognition and Analysis of Negative Emotions of Undergraduates Under COVID-19
Background The outbreak and spread of COVID-19 has brought a tremendous impact on undergraduates' study and life, and also caused anxiety, depression, fear and loneliness among undergraduates. If
A Novel Human-Machine Collaboration Model of an Ankle Joint Rehabilitation Robot Driven by EEG Signals
TLDR
Experiments show that the human-machine collaboration model used can show higher accuracy of intention recognition, thereby increasing the satisfaction of using AJRR and truly realizes patient-oriented rehabilitation training.
A class-driven approach to dimension embedding
  • F. Aydın
  • Computer Science
    Expert Syst. Appl.
  • 2022
Learning discriminative representation for image classification

References

SHOWING 1-10 OF 55 REFERENCES
On Consistency and Sparsity for Principal Components Analysis in High Dimensions
  • I. Johnstone, A. Lu
  • Computer Science, Mathematics
    Journal of the American Statistical Association
  • 2009
TLDR
A simple algorithm for selecting a subset of coordinates with largest sample variances is provided, and it is shown that if PCA is done on the selected subset, then consistency is recovered, even if p(n) ≫ n.
Bayesian principal component analysis
Principal component analysis (PCA) is a dimensionality reduction modeling technique that transforms a set of process variables by rotating their axes of representation. Maximum likelihood PCA (MLPCA)
On Bayesian PCA: Automatic Dimensionality Selection and Analytic Solution
TLDR
This paper investigates whether VB-PCA is really the best choice from the viewpoints of computational efficiency and ADS, and shows that ADS is not the unique feature of VB -PCA—PB- PCA is also actually equipped with ADS.
Robust linear dimensionality reduction
  • Y. Koren, L. Carmel
  • Computer Science
    IEEE Transactions on Visualization and Computer Graphics
  • 2004
We present a novel family of data-driven linear transformations, aimed at finding low-dimensional embeddings of multivariate data, in a way that optimally preserves the structure of the data. The
Accounting for probe-level noise in principal component analysis of microarray data
TLDR
A new model-based approach to PCA that takes into account the variances associated with each gene in each experiment is proposed and it is shown how the model can be used to 'denoise' a microarray dataset leading to improved expression profiles and tighter clustering across profiles.
Probabilistic Principal Component Analysis
Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based on a probability model. We demonstrate how the principal axes of a set of
Principal component analysis with missing values: a comparative survey of methods
TLDR
The case where some of the data values are missing is studied and a review of methods which accommodate PCA to missing data is proposed and several techniques to consider or estimate (impute) missing values in PCA are presented.
DimReader: Axis lines that explain non-linear projections
TLDR
DimReader is a technique that recovers readable axes from non-linear dimensionality reduction techniques based on analyzing infinitesimal perturbations of the dataset with respect to variables of interest, and is efficient and easily integrated into programs written in modern programming languages.
Gaussian Cubes: Real-Time Modeling for Visual Exploration of Large Multidimensional Datasets
TLDR
Gaussian Cubes is contributed, which significantly improves on state-of-the-art systems by providing interactive modeling capabilities, which include but are not limited to linear least squares and principal components analysis (PCA).
A comparison of three methods for principal component analysis of fuzzy interval data
...
...