COMPUTERVISION RESEARCHSCIENTIST

RESEARCHSCIENTIST

This page presents some educational projects.

This library implements common matrix decompositions in PHP. Based on the library, a demonstration application provides the theoretical background and may be used to compute these matrix decompositions. The following table provides an overview:

Decomposition | Factorization | Applicable for | Runtime |
---|---|---|---|

LU | $A = LU$ | $A \in \mathbb{R}^{n \times n}$, $A$ regular | $\mathcal{O}(\frac{1}{3}n^3)$ |

Cholesky | $A = LDL^T$ | $A \in \mathbb{R}^{n \times n}$, $A$ symmetric and positive definite | $\mathcal{O}(\frac{1}{6}n^3)$ |

QR: Givens Rotations | $A = QR$ | $A \in \mathbb{R}^{m \times n}$ | $\mathcal{O}(\frac{4}{3}n^3)$ |

QR: Householder Transformations | $A = QR$ | $A \in \mathbb{R}^{m \times n}$ | $\mathcal{O}(\frac{2}{3}n^3)$ |

The demonstration application is available on GitHub as well, however, as separate repository.

PHP Matrix Decompositions on GitHub Demonstration Application Demonstration Application on GitHub- davidstutz 9cb2ab7 Minor fix.
- davidstutz 09a2f1e Tests running!
- davidstutz 1c72765 Fixed routing and updated matrix decompositions library.

This library implements the Simplex algorithm in PHP as discussed in [1] and the course Linear and Integer Programming on Coursera.

PHP Simplex on GitHub- davidstutz 2c1a042 Added example and usage details.
- davidstutz d76b9c8 Additional test data for dictionaries that need to be initialized. Tested initialization!
- davidstutz 5ebb9a2 Additional test data and working on initialization.

- [1] R. J. Vanderbei.
*Linear Programming: Foundations and Extensions*. Springer, 2001.

This is a MatLab implementation of a two-layer perceptron, that is a neural network with one input, one hidden and one output layer. The implementation was assessed using the MNIST dataset.

Further details on neural networks can be found in my seminar paper: Seminar Paper "Introduction to Neural Networks".

MatLab Two-Layer Perceptron on GitHub- davidstutz 153b0c4 Added note to mini-batch training, thanks to @Myasuka.
- davidstutz 141b44e Initial commit including sources and README.

A simple application demonstrating the use of several of my Kohana modules together with Kohana 3.1, 3.2 and 3.3.6 (see the corresponding branches in the below GitHub repository). Figure 1 shows some screenshots of the application. The following modules are included in the applications:

Kohana Demo on GitHub- davidstutz 153b0c4 Added note to mini-batch training, thanks to @Myasuka.
- davidstutz 141b44e Initial commit including sources and README.

What is

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