Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Genetic Algorithms and Machine Learning
Machine Learning
The Journal of Machine Learning Research
Dirichlet aggregation: unsupervised learning towards an optimal metric for proportional data
Proceedings of the 24th international conference on Machine learning
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Proceedings of the ACM International Conference on Image and Video Retrieval
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We consider feature extraction (dimensionality reduction) for compositional data, where the data vectors are constrained to be positive and constant-sum. In real-world problems, the data components (variables) usually have complicated "correlations" while their total number is huge. Such scenario demands feature extraction. That is, we shall de-correlate the components and reduce their dimensionality. Traditional techniques such as the Principle Component Analysis (PCA) are not suitable for these problems due to unique statistical properties and the need to satisfy the constraints in compositional data. This paper presents a novel approach to feature extraction for compositional data. Our method first identifies a family of dimensionality reduction projections that preserve all relevant constraints, and then finds the optimal projection that maximizes the estimated Dirichlet precision on projected data. It reduces the compositional data to a given lower dimensionality while the components in the lower-dimensional space are de-correlated as much as possible. We develop theoretical foundation of our approach, and validate its effectiveness on some synthetic and real-world datasets.