| 1. |
- Borga, Magnus, et al.
(författare)
-
A Unified Approach to PCA, PLS, MLR and CCA
- 1997
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper presents a novel algorithm for analysis of stochastic processes. The algorithm can be used to find the required solutions in the cases of principal component analysis (PCA), partial least squares (PLS), canonical correlation analysis (CCA) or multiple linear regression (MLR). The algorithm is iterative and sequential in its structure and uses on-line stochastic approximation to reach an equilibrium point. A quotient between two quadratic forms is used as an energy function and it is shown that the equilibrium points constitute solutions to the generalized eigenproblem.
|
|
| 2. |
|
|
| 3. |
- Knutsson, Hans, et al.
(författare)
-
Generalized Eigenproblem for Stochastic Process Covariances
- 1996
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper presents a novel algorithm for finding the solution of the generalized eigenproblem where the matrices involved contain expectation values from stochastic processes. The algorithm is iterative and sequential to its structure and uses on-line stochastic approximation to reach an equilibrium point. A quotient between two quadratic forms is suggested as an energy function for this problem and is shown to have zero gradient only at the points solving the eigenproblem. Furthermore it is shown that the algorithm for the generalized eigenproblem can be used to solve three important problems as special cases. For a stochastic process the algorithm can be used to find the directions for maximal variance, covariance, and canonical correlation as well as their magnitudes.
|
|
| 4. |
- Knutsson, Hans, et al.
(författare)
-
Learning Canonical Correlations
- 1995
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper presents a novel learning algorithm that finds the linear combination of one set of multi-dimensional variates that is the best predictor, and at the same time finds the linear combination of another set which is the most predictable. This relation is known as the canonical correlation and has the property of being invariant with respect to affine transformations of the two sets of variates. The algorithm successively finds all the canonical correlations beginning with the largest one. It is shown that canonical correlations can be used in computer vision to find feature detectors by giving examples of the desired features. When used on the pixel level, the method finds quadrature filters and when used on a higher level, the method finds combinations of filter output that are less sensitive to noise compared to vector averaging.
|
|
| 5. |
- Knutsson, Hans, 1950-, et al.
(författare)
-
Learning Multidimensional Signal Processing
- 1998
-
Ingår i: Proceedings of the 14th International Conference on Pattern Recognition, vol 2. - Linköping, Sweden : Linköping University, Department of Electrical Engineering. ; , s. 1416-1420
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper presents our general strategy for designing learning machines as well as a number of particular designs. The search for methods allowing a sufficient level of adaptivity are based on two main principles: 1. Simple adaptive local models and 2. Adaptive model distribution. Particularly important concepts in our work is mutual information and canonical correlation. Examples are given on learning feature descriptors, modeling disparity, synthesis of a global 3-mode model and a setup for reinforcement learning of online video coder parameter control.
|
|
| 6. |
- Landelius, Tomas, et al.
(författare)
-
On-Line Singular Value Decomposition of Stochastic Process Covariances
- 1995
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper presents novel algorithms for finding the singular value decomposition (SVD) of a general covariance matrix by stochastic approximation. General in the sense that also non-square, between sets, covariance matrices are dealt with. For one of the algorithms, convergence is shown using results from stochastic approximation theory. Proofs of this sort, establishing both the point of equilibrium and its domain of attraction, have been reported very rarely for stochastic, iterative feature extraction algorithms.
|
|
| 7. |
- Landelius, Tomas, et al.
(författare)
-
Reinforcement Learning Trees
- 1996
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Two new reinforcement learning algorithms are presented. Both use a binary tree to store simple local models in the leaf nodes and coarser global models towards the root. It is demonstrated that a meaningful partitioning into local models can only be accomplished in a fused space consisting of both input and output. The first algorithm uses a batch like statistic procedure to estimate the reward functions in the fused space. The second one uses channel coding to represent the output- and input vectors allowing a simple iterative algorithm based on competing subsystems. The behaviors of both algorithms are illustrated in a preliminary experiment.
|
|
