Statistics – Machine Learning
Scientific paper
2011-03-31
S. Girard & S. Iovleff. "Auto-associative models, nonlinear Principal component analysis, manifolds and projection pursuit", L
Statistics
Machine Learning
Scientific paper
In this paper, auto-associative models are proposed as candidates to the generalization of Principal Component Analysis. We show that these models are dedicated to the approximation of the dataset by a manifold. Here, the word "manifold" refers to the topology properties of the structure. The approximating manifold is built by a projection pursuit algorithm. At each step of the algorithm, the dimension of the manifold is incremented. Some theoretical properties are provided. In particular, we can show that, at each step of the algorithm, the mean residuals norm is not increased. Moreover, it is also established that the algorithm converges in a finite number of steps. Some particular auto-associative models are exhibited and compared to the classical PCA and some neural networks models. Implementation aspects are discussed. We show that, in numerous cases, no optimization procedure is required. Some illustrations on simulated and real data are presented.
Girard Stéphane
Iovleff Serge
No associations
LandOfFree
Auto-associative models, nonlinear Principal component analysis, manifolds and projection pursuit does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Auto-associative models, nonlinear Principal component analysis, manifolds and projection pursuit, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Auto-associative models, nonlinear Principal component analysis, manifolds and projection pursuit will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-245282