# Notes on Expected Computational Cost of Classifiers Cascade: A Geometric View

### Dariusz Sychel, Przemysław Klęsk, Aneta Bera

#### Abstract

A cascade of classifiers, working within a detection procedure, extracts and uses different number of features depending on the window under analysis. Windows with background regions can be typically recognized as negative with just a few features, whereas windows with target objects (or resembling them) might require thousands of features. The central point of attention for this paper is a quantity that describes the average computational cost of an operating cascade, namely—the expected value of the number of features the cascade uses. This quantity can be calculated explicitly knowing the probability distribution underlying the data and the properties of a particular cascade (detection and false alarm rates of its stages), or it can be accurately estimated knowing just the latter. We show three purely geometric examples that demonstrate how training a cascade with sensitivity / FAR constraints imposed per each stage can lead to non-optimality in terms of the computational cost. We do not propose a particular algorithm to overcome the pitfalls of stage-wise training, instead, we sketch an intuition showing that non-greedy approaches can improve the resulting cascades.

Download#### Paper Citation

#### in Harvard Style

Sychel D., Klęsk P. and Bera A. (2018). **Notes on Expected Computational Cost of Classifiers Cascade: A Geometric View**.In *Proceedings of the 7th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,* ISBN 978-989-758-276-9, pages 103-114. DOI: 10.5220/0006585301030114

#### in Bibtex Style

@conference{icpram18,

author={Dariusz Sychel and Przemysław Klęsk and Aneta Bera},

title={Notes on Expected Computational Cost of Classifiers Cascade: A Geometric View},

booktitle={Proceedings of the 7th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,},

year={2018},

pages={103-114},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006585301030114},

isbn={978-989-758-276-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 7th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,

TI - Notes on Expected Computational Cost of Classifiers Cascade: A Geometric View

SN - 978-989-758-276-9

AU - Sychel D.

AU - Klęsk P.

AU - Bera A.

PY - 2018

SP - 103

EP - 114

DO - 10.5220/0006585301030114