3,625 research outputs found
Training Support Vector Machines Using Frank-Wolfe Optimization Methods
Training a Support Vector Machine (SVM) requires the solution of a quadratic
programming problem (QP) whose computational complexity becomes prohibitively
expensive for large scale datasets. Traditional optimization methods cannot be
directly applied in these cases, mainly due to memory restrictions.
By adopting a slightly different objective function and under mild conditions
on the kernel used within the model, efficient algorithms to train SVMs have
been devised under the name of Core Vector Machines (CVMs). This framework
exploits the equivalence of the resulting learning problem with the task of
building a Minimal Enclosing Ball (MEB) problem in a feature space, where data
is implicitly embedded by a kernel function.
In this paper, we improve on the CVM approach by proposing two novel methods
to build SVMs based on the Frank-Wolfe algorithm, recently revisited as a fast
method to approximate the solution of a MEB problem. In contrast to CVMs, our
algorithms do not require to compute the solutions of a sequence of
increasingly complex QPs and are defined by using only analytic optimization
steps. Experiments on a large collection of datasets show that our methods
scale better than CVMs in most cases, sometimes at the price of a slightly
lower accuracy. As CVMs, the proposed methods can be easily extended to machine
learning problems other than binary classification. However, effective
classifiers are also obtained using kernels which do not satisfy the condition
required by CVMs and can thus be used for a wider set of problems
Fusion of Head and Full-Body Detectors for Multi-Object Tracking
In order to track all persons in a scene, the tracking-by-detection paradigm
has proven to be a very effective approach. Yet, relying solely on a single
detector is also a major limitation, as useful image information might be
ignored. Consequently, this work demonstrates how to fuse two detectors into a
tracking system. To obtain the trajectories, we propose to formulate tracking
as a weighted graph labeling problem, resulting in a binary quadratic program.
As such problems are NP-hard, the solution can only be approximated. Based on
the Frank-Wolfe algorithm, we present a new solver that is crucial to handle
such difficult problems. Evaluation on pedestrian tracking is provided for
multiple scenarios, showing superior results over single detector tracking and
standard QP-solvers. Finally, our tracker ranks 2nd on the MOT16 benchmark and
1st on the new MOT17 benchmark, outperforming over 90 trackers.Comment: 10 pages, 4 figures; Winner of the MOT17 challenge; CVPRW 201
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