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 many applications, such as classification of images or videos, it is ofinterest to develop a framework for tensor data instead of an ad-hoc way oftransforming data to vectors due to the computational and under-samplingissues. In this paper, we study convergence and statistical properties oftwo-dimensional canonical correlation analysis \citep{Lee2007Two} under anassumption that data come from a probabilistic model. We show that carefullyinitialized the power method converges to the optimum and provide a finitesample bound. Then we extend this framework to tensor-valued data and proposethe higher-order power method, which is commonly used in tensor decomposition,to extract the canonical directions. Our method can be used effectively in alarge-scale data setting by solving the inner least squares problem with astochastic gradient descent, and we justify convergence via the theory ofLojasiewicz's inequalities without any assumption on data generating processand initialization. For practical applications, we further develop (a) aninexact updating scheme which allows us to use the state-of-the-art stochasticgradient descent algorithm, (b) an effective initialization scheme whichalleviates the problem of local optimum in non-convex optimization, and (c) adeflation procedure for extracting several canonical components. Empiricalanalyses on challenging data including gene expression and air pollutionindexes in Taiwan, show the effectiveness and efficiency of the proposedmethodology. Our results fill a missing, but crucial, part in the literature ontensor data.

Tensor Canonical Correlation Analysis with Convergence and Statistical Guarantees