English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In recent work, we proposed a distributed Banach-Picard iteration (DBPI) thatallows a set of agents, linked by a communication network, to find a fixedpoint of a locally contractive (LC) map that is the average of individual mapsheld by said agents. In this work, we build upon the DBPI and its local linearconvergence (LLC) guarantees to make several contributions. We show thatSanger's algorithm for principal component analysis (PCA) corresponds to theiteration of an LC map that can be written as the average of local maps, eachmap known to each agent holding a subset of the data. Similarly, we show that avariant of the expectation-maximization (EM) algorithm for parameter estimationfrom noisy and faulty measurements in a sensor network can be written as theiteration of an LC map that is the average of local maps, each available atjust one node. Consequently, via the DBPI, we derive two distributed algorithms- distributed EM and distributed PCA - whose LLC guarantees follow from thosethat we proved for the DBPI. The verification of the LC condition for EM ischallenging, as the underlying operator depends on random samples, thus the LCcondition is of probabilistic nature.

Distributed Banach-Picard Iteration: Application to Distributed EM and Distributed PCA