The process of placing a separating hyperplane for data classification is normally disconnected from the process of selecting the features to use. An approach for feature selection that is conceptually simple but computationally explosive is to simply apply the hyperplane placement process to all possible subsets of features, selecting the smallest set of features that provides reasonable class...

AdaBoost produces a linear combination of weak hypotheses. It has been observed in practice that the generalization error of the algorithm continues to improve even after all examples are classified correctly by the current linear combination, i.e. by a hyperplane in feature space where each weak hypothesis is a dimension. The improvement is attributed to the experimental observation that the d...

Outline 1 Fixed priority 2 Priority assignment 3 Scheduling analysis 4 A necessary and sufficient test 5 Sensitivity 6 Hyperplane analysis 7 Conclusions 8 Esercizi Calcolo del tempo di risposta Calcolo del tempo di risposta con aperiodici Hyperplane analysis

Sliding mode control strategies are well known for ensuring robustness of the system with respect to disturbance and model uncertainties. For continuous-time plants, they achieve this property by confining state a particular hyperplane in space. Contrary this, discrete-time sliding (DSMC) only drive representative point certain vicinity that hyperplane. In established literature on DSMC, width ...

Understanding the structure of indecomposable $n$-dimensional persistence modules is a difficult problem, yet foundational for studying multipersistence. To this end, Buchet and Escolar showed that any finitely presented rectangular $(n-1)$-dimensional module with finite support hyperplane restriction an module. We extend result to following: If $M$ support, then there exists $M'$ such hyperpla...

Generative Adversarial Nets (GANs) represent an important milestone for effective generative models, which has inspired numerous variants seemingly different from each other. One of the main contributions of this paper is to reveal a unified geometric structure in GAN and its variants. Specifically, we show that the adversarial generative model training can be decomposed into three geometric st...

We attempt to understand visual classification in humans using both psychophysical and machine learning techniques. Frontal views of human faces were used for a gender classification task. Human subjects classified the faces and their gender judgment, reaction time and confidence rating were recorded. Several hyperplane learning algorithms were used on the same classification task using the Pri...

Artin groups are a natural generalization of braid groups and are closely related to Coxeter groups in the following sense. There is a faithful representation of a Coxeter group W as a linear reflection group on a real vector space. The group acts properly and fixes a union of hyperplanes. The W-action extends as a covering space action to the complexified complement of these hyperplanes. The f...