Lecture

Linear Classification: Signal Processing

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In course

NX-421: Neural signals and signal processing

Understanding, processing, and analysis of signals and images obtained from the central and peripheral nervous system ...

Description

This lecture covers linear classification in signal processing, focusing on solving least-squares problems, the need for regularization, and the inclusion of bias terms in linear predictions. It also delves into feature extraction for fMRI classification, the structure of linear classifiers, loss functions, cross-validation techniques, and the popularity of linear classifiers in fMRI analysis. The instructor discusses the spatial scales exploited by multivariate pattern analysis (MVPA) and the hyperacuity hypothesis, which explores fine-grained spatial details in fMRI data.

Instructors (2)

Dimitri Nestor Alice Van De Ville

Expertise Brain and spinal cord imaging, signal and image processing, network science, dynamic systems Teaching & PhD PhD Students Alexandre Cionca, Chun Hei Michael Chan, Flavia Petruso, Bassam El Rawas, Nikolaos Molochidis, Christophe Pascal Jérémie Chênes, Fabrice Jean Guibert, Alessio Siviglia, Ekansh Sareen, Beatrice Lugli Past EPFL PhD Students Djano Kandaswamy, Fikret Isik Karahanoglu, Nora Leonardi, Zafer Dogan, Jeffrey Adam Kasten, Naghmeh Ghazaleh, Rotem Roza Kopel, Daniela Maria Zöller, Thomas

Silvestro Micera

Short biographical sketch Silvestro Micera received the University degree (Laurea) in Electrical Engineering from the University of Pisa, in 1996, and the Ph.D. degree in Biomedical Engineering from the Scuola Superiore Sant'Anna, in 2000. From 2000 to 2009, he has been an Assistant Professor of BioRobotics at the Scuola Superiore Sant'Anna where he is now the Head of the Neural Engineering group. In 2007 he was a Visiting Scientist at the Massachusetts Institute of Technology, Cambridge, USA with a Fulbri

Official source

Related concepts (32)

Statistical classification

In statistics, classification is the problem of identifying which of a set of categories (sub-populations) an observation (or observations) belongs to. Examples are assigning a given email to the "spam" or "non-spam" class, and assigning a diagnosis to a given patient based on observed characteristics of the patient (sex, blood pressure, presence or absence of certain symptoms, etc.). Often, the individual observations are analyzed into a set of quantifiable properties, known variously as explanatory variables or features.

Linear discriminant analysis

Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification.

Regularized least squares

Regularized least squares (RLS) is a family of methods for solving the least-squares problem while using regularization to further constrain the resulting solution. RLS is used for two main reasons. The first comes up when the number of variables in the linear system exceeds the number of observations. In such settings, the ordinary least-squares problem is ill-posed and is therefore impossible to fit because the associated optimization problem has infinitely many solutions.

Linear least squares

Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression, including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals. Numerical methods for linear least squares include inverting the matrix of the normal equations and orthogonal decomposition methods. The three main linear least squares formulations are: Ordinary least squares (OLS) is the most common estimator.

Naive Bayes classifier

In statistics, naive Bayes classifiers are a family of simple "probabilistic classifiers" based on applying Bayes' theorem with strong (naive) independence assumptions between the features (see Bayes classifier). They are among the simplest Bayesian network models, but coupled with kernel density estimation, they can achieve high accuracy levels. Naive Bayes classifiers are highly scalable, requiring a number of parameters linear in the number of variables (features/predictors) in a learning problem.

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