The Priberam Machine Learning Lunch Seminars are a series of informal meetings which occur every two weeks at Instituto Superior Técnico, in Lisbon. It works as a discussion forum involving different research groups, from IST and elsewhere. Its participants are interested in areas such as (but not limited to): statistical machine learning, signal processing, pattern recognition, computer vision, natural language processing, computational biology, neural networks, control systems, reinforcement learning, or anything related (even if vaguely) with machine learning.

The seminars last for about one hour (including time for discussion and questions) and revolve around the general topic of Machine Learning. The speaker is a volunteer who decides the topic of her presentation. Past seminars have included presentations about state-of-the-art research, surveys and tutorials, practicing a conference talk, presenting a challenging problem and asking for help, and illustrating an interesting application of Machine Learning such as a prototype or finished product.

Presenters can have any background: undergrads, graduate students, academic researchers, company staff, etc. Anyone is welcome both to attend the seminar as well as to present it. Ocasionally we will have invited speakers. See below for a list of all seminars, including the speakers, titles and abstracts.

Note: The seminars are held at lunch-time, and include delicious free food.

Feel free to join our mailing list, where seminar topics are announced beforehand. You may also visit the mailing list webpage. Anyone can attend the seminars; no registration is necessary. If you would like to present something, please send us an email.

The seminars are usually held every other Tuesday, from 1 PM to 2 PM, at the IST campus in Alameda. This sometimes changes due to availability of the speakers, so check regularly!

Tuesday, February 4th 2014, 13h00 - 14h00

Renato Negrinho (IT)

Shape Representation via Symmetric Polynomials: A Complete Invariant Inspired by the Bispectrum

Room EA4 (Torre Norte)

Instituto Superior Técnico - Alameda


We address the representation of two-dimensional shapes in its most general form, i.e., arbitrary sets of points. Examples of these shapes arise in multiple situations, in the form of sparse sets of representative landmarks, or dense sets of image edge points. Our goal are recognition tasks, where the key is balancing two contradicting demands: shapes that differ by rigid transformations or point relabeling should have the same representation (invariance), but geometrically distinct shapes should have different representations (completeness). We introduce a new shape representation that marries properties of the symmetric polynomials and the bispectrum. Like the power spectrum, the bispectrum is insensitive to signal shifts; however, unlike the power spectrum, the bispectrum is complete. Particular sets of symmetric polynomials, the so-called elementary ones and the power sums, are complete and invariant to variable relabeling. We show that these polynomials of the shape points depend on the shape orientation in a way that enables interpreting them in the frequency domain and building from them a bispectrum. The result is a shape representation that is complete and invariant to rigid transformations and point relabeling.

We describe the shape representation problem in a very general way by using concepts of group theory. The concept of shape is determined by the definition of the required shape-preserving transformations (e.g., point relabeling and/or geometric ones) through group actions. Shapes are then identified with the orbits of the actions of those groups and shape representation amounts to representing those orbits. This way, as pretended, elements that belong to the same orbit have the same representation and elements that belong to different orbits have different representations. The proposed shape representation attains this goal.

We describe how the proposed representation can be efficiently computed from the shape points using dynamic programming and end by describing experiments that illustrate the proved properties.


Bio: Renato Negrinho received a M.Sc degree in Electrical and Computer Engineering from Instituto Superior Técnico, Portugal, in 2013. He currently holds a research scholarship and is working on NLP and Machine Learning problems under the supervision of André Martins at Priberam. He is interested in machine learning, optimization and the application of mathematics in general to solve difficult problems in science.