Related papers: A Latent Variable Model for Two-Dimensional Canoni…

Principal component analysis (PCA) is a well-established tool in machine learning and data processing. The principal axes in PCA were shown to be equivalent to the maximum marginal likelihood estimator of the factor loading matrix in a…

Latent variable models are an elegant framework for capturing rich probabilistic dependencies in many applications. However, current approaches typically parametrize these models using conditional probability tables, and learning relies…

The Canonical Correlation Analysis (CCA) family of methods is foundational in multiview learning. Regularised linear CCA methods can be seen to generalise Partial Least Squares (PLS) and be unified with a Generalized Eigenvalue Problem…

Recent advances in citation recommendation have improved accuracy by leveraging multi-view representation learning to integrate the various modalities present in scholarly documents. However, effectively combining multiple data views…

Canonical correlation analysis (CCA) is a method for reducing the dimension of data represented using two views. It has been previously used to derive word embeddings, where one view indicates a word, and the other view indicates its…

Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which…

Latent Dirichlet Allocation (LDA) is a popular topic modeling technique for exploring document collections. Because of the increasing prevalence of large datasets, there is a need to improve the scalability of inference of LDA. In this…

Dimensionality reduction algorithms like principal component analysis (PCA) are workhorses of machine learning and neuroscience, but each has well-known limitations. Variants of PCA are simple and interpretable, but not flexible enough to…

In the internet era there has been an explosion in the amount of digital text information available, leading to difficulties of scale for traditional inference algorithms for topic models. Recent advances in stochastic variational inference…

Canonical correlation analysis (CCA) is a technique for finding correlations between different data modalities and learning low-dimensional representations. As fairness becomes crucial in machine learning, fair CCA has gained attention.…

Principal component analysis (PCA) for binary data, known as logistic PCA, has become a popular alternative to dimensionality reduction of binary data. It is motivated as an extension of ordinary PCA by means of a matrix factorization, akin…

We consider the problem of extracting a low-dimensional, linear latent variable structure from high-dimensional random variables. Specifically, we show that under mild conditions and when this structure manifests itself as a linear space…

In many scientific disciplines, the features of interest cannot be observed directly, so must instead be inferred from observed behaviour. Latent variable analyses are increasingly employed to systematise these inferences, and Principal…

Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…

In this paper, we introduce Functional Generalized Canonical Correlation Analysis (FGCCA), a new framework for exploring associations between multiple random processes observed jointly. The framework is based on the multiblock Regularized…

We extend multi-way, multivariate ANOVA-type analysis to cases where one covariate is the view, with features of each view coming from different, high-dimensional domains. The different views are assumed to be connected by having paired…

Despite the fact that they do not consider the temporal nature of data, classic dimensionality reduction techniques, such as PCA, are widely applied to time series data. In this paper, we introduce a factor decomposition specific for time…

Using the linear Gaussian latent variable model as a starting point we relax some of the constraints it imposes by deriving a nonparametric latent feature Gaussian variable model. This model introduces additional discrete latent variables…

Latent semantic analysis (LSA) and correspondence analysis (CA) are two techniques that use a singular value decomposition (SVD) for dimensionality reduction. LSA has been extensively used to obtain low-dimensional representations that…

We propose MNPCA, a novel non-linear generalization of (2D)$^2${PCA}, a classical linear method for the simultaneous dimension reduction of both rows and columns of a set of matrix-valued data. MNPCA is based on optimizing over separate…