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From Common Information to Canonical Correlation Analysis and Beyond: Bridging Information Theory, Signal Processing, and Machine Learning

Paris A. Karakasis, Walid Saad · 2026 · Entropy

DOI: 10.3390/e28101161 · cited by 0 works (OpenAlex) · open-access PDF

Spanish

Muchos problemas en el procesamiento de señales, el aprendizaje automático y la neuroimagen proporcionan varias mediciones observadas conjuntamente de partes de un proceso, cada una mezclando un componente común a todos ellos con un componente privado a sí mismo, y requieren que el componente común se recupere sin supervisión. Este problema ha sido estudiado en varias comunidades, en gran parte de forma independiente. Este tutorial presenta los principales resultados y herramientas de análisis de correlación canónica (CCA), introducido por Hotelling en una exposición única. Los teóricos de la información propusieron dos conceptos de información común, debido a Gács y Körner y a Wyner. Los ingenieros desarrollaron métodos de subespacio para las agrupaciones de sensores y las comunicaciones multiusuarios para diseñar receptores multiview. Este tutorial presenta los principales resultados y cada una de las herr

Machine translation (Meta M2M100); the English original follows.

Abstract

Many problems in signal processing, machine learning, and neuroimaging provide several jointly observed measurements of one process, each mixing a component common to all of them with a component private to itself, and require the common component to be recovered without supervision. This problem has been studied in several communities, largely independently. Statisticians proposed canonical correlation analysis (CCA), introduced by Hotelling in 1936. Information theorists proposed two notions of common information, due to Gács and Körner and to Wyner. Engineers developed subspace methods for sensor arrays and multiuser communications to design multiview receivers. This tutorial presents the main results and tools each community developed for this problem in a single exposition, and explains the connections that emerge where they meet, distinguishing exact equivalences from special cases and analogies. We develop the information-theoretic foundation from first principles. We then introduce CCA and its extension to several views, followed by the engineering thread from blind multiuser detection to CCA as a blind receiver. Next, we turn to nonlinear CCA, covering kernel, deep, and probabilistic formulations, the conditions under which the common factor is identifiable, and connections to self-supervised learning. We conclude with a discussion of further extensions and open directions. The exposition is self-contained, so that readers from each of these communities can follow the parts developed by the others.

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Topics: Canonical correlation, Probabilistic logic, Computer science, Artificial intelligence, Bridging (networking), Subspace topology

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