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Combining the linear canonical transform and the Riesz transform, we introduce the linear canonical Riesz transform (for short, LCRT), which is further proved to be a linear canonical multiplier. Using this LCRT multiplier, we conduct…
The linear canonical transform (LCT) was extended to complex-valued parameters, called complex LCT, to describe the complex amplitude propagation through lossy or lossless optical systems. Bargmann transform is a special case of the complex…
This article reviews recent developments in multiresolution analysis which make it a powerful tool for the systematic treatment of the multiple length-scales inherent in the electronic structure of matter. Although the article focuses on…
Canonical Correlation Analysis (CCA) is a multivariate technique that takes two datasets and forms the most highly correlated possible pairs of linear combinations between them. Each subsequent pair of linear combinations is orthogonal to…
By deriving influence functions related to multiple-set linear canonical analysis (MSLCA) we show that the classical version of this analysis, based on empirical covariance operators, is not robust. Then, we introduce a robust version of…
Generalized canonical correlation analysis (GCCA) aims at finding latent low-dimensional common structure from multiple views (feature vectors in different domains) of the same entities. Unlike principal component analysis (PCA) that…
Lorentz-equivariant neural networks are becoming the leading architectures for high-energy physics. Current implementations rely on specialized layers, limiting architectural choices. We introduce Lorentz Local Canonicalization (LLoCa), a…
This paper considers canonical correlation analysis for two longitudinal variables that are possibly sampled at different time resolutions with irregular grids. We modeled trajectories of the multivariate variables using random effects and…
The offset linear canonical transform encompassing the numerous integral transforms, is a promising tool for analyzing non-stationary signals with more degrees of freedom. In this paper, we generalize the windowed offset linear canonical…
We present an algorithm using transformation groups and their irreducible representations to generate an orthogonal basis for a signal in the vector space of the signal. It is shown that multiresolution analysis can be done with amplitudes…
Transformers have emerged as a preferred model for many tasks in natural langugage processing and vision. Recent efforts on training and deploying Transformers more efficiently have identified many strategies to approximate the…
Multimodal Transformers serve as the backbone for state-of-the-art vision-language models, yet their quadratic attention complexity remains a critical barrier to scalability. In this work, we investigate the viability of Linear Attention…
Tensor canonical correlation analysis (TCCA) has garnered significant attention due to its effectiveness in capturing high-order correlations in multi-view learning. However, existing TCCA methods often underemphasize the characterization…
The linear canonical wavelet transform has been shown to be a valuable and powerful time-frequency analyzing tool for optics and signal processing. In this article, we propose a novel transform called quaternion linear canonical wavelet…
The main purpose of this work is to identify invariant quadratic operators associated with Linear Canonical Transformations (LCTs) which could play important roles in physics. LCTs are considered in many fields. In quantum theory, they can…
Lattice reduction (LR) is a preprocessing technique for multiple-input multiple-output (MIMO) symbol detection to achieve better bit error-rate (BER) performance. In this paper, we propose a customized homogeneous multiprocessor for LR. The…
We present a novel multiview canonical correlation analysis model based on a variational approach. This is the first nonlinear model that takes into account the available graph-based geometric constraints while being scalable for processing…
We examine Deep Canonically Correlated LSTMs as a way to learn nonlinear transformations of variable length sequences and embed them into a correlated, fixed dimensional space. We use LSTMs to transform multi-view time-series data…
Canonical Correlation Analysis (CCA) is a linear representation learning method that seeks maximally correlated variables in multi-view data. Non-linear CCA extends this notion to a broader family of transformations, which are more powerful…
As a time-shifted and frequency-modulated version of the linear canonical transform (LCT), the offset linear canonical transform (OLCT) provides a more general framework of most existing linear integral transforms in signal processing and…