Based on classical statistical machine learning methods and statistical learning algorithms for high-dimensional datasets, this dissertation firstly carries out researches and discussions on technologies related to random projection methods, Principal Component Analysis (PCA) method, AdaBoost algorithm, and differential evolution algorithm, and then proposes two new dimensionality reduction algorithms for high-dimensional dataset and improves one existing classical dimensionality reduction algorithm for high-dimensional dataset.
The achievement of this dissertation includes:
1.Proposes a new dimensionality reduction algorithm: JL-PCA;
2.Proposes a new dimensionality reduction algorithm by combination of AdaBoost and Differential Evolution algorithm;
3.Improves one existing deterministic robust PCA method for high-dimensional datasets.
By integrated application of probability and mathematical statistical methods and algorithm design and analysis methods, we carry out theoretical analysis of the newly proposed algorithms and carry out experiments for the proposed algorithms on image analysis and processing problems. The experimental results show that the methods proposed/improved in this dissertation have good performance.