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Alternative common bases and signal compression for wavelets application in chemometrics
Michele Forina1, Paolo Oliveri, Monica Casale
1Dipartimento di Chimica e Tecnologie Farmaceutiche ed Alimentari, Università di Genova, Via Brigata Salerno 13, 16147 Genova, Italy. forina@dictfa.unige.it
Analytical and Bioanalytical Chemistry
|January 12, 2011
Summary
This study introduces novel common bases for wavelet-based data compression, improving information retention for classification and regression tasks. Alternative bases based on Fisher weights and correlation spectra offer more efficient data representation than traditional variance methods.
Area of Science:
- Data Science
- Chemometrics
- Signal Processing
Background:
- Wavelet-based data compression typically uses common bases derived from variance spectra to retain maximum data variance.
- Representing multiple objects in wavelet space necessitates a common basis, often obtained via variance spectrum or wavelet trees.
Purpose of the Study:
- To propose and evaluate alternative common bases for wavelet space representation in classification and regression.
- To demonstrate that these novel bases can lead to more efficient data compression and information retention.
Main Methods:
- Investigated common bases derived from Fisher weights spectrum for classification.
- Explored common bases from correlation spectrum and Partial Least Squares (PLS) importance for regression.
- Applied Gram-Schmidt supervised orthogonalization to wavelet coefficients as an alternative strategy.
Main Results:
- The proposed alternative common bases showed more efficient information retention compared to variance-based common bases.
- This improved efficiency was observed in both classification and regression problems.
- Alternative strategies like Gram-Schmidt orthogonalization also showed promise.
Conclusions:
- Alternative common bases offer a more efficient approach to wavelet-based data compression than traditional variance-based methods.
- The findings are applicable to both classification and regression tasks, enhancing data representation and analysis.
- This research provides new tools for optimizing data compression in various scientific domains.
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