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Dimensionality reduction is a topic of recent interest. In this paper, we present the classification constrained dimensionality reduction (CCDR) algorithm to account for label information. The algorithm can account for multiple classes as…

We propose a strategy to compress and store large volumes of scientific data represented on unstructured grids. Approaches utilizing tensor decompositions for data compression have already been proposed. Here, data on a structured grid is…

A critical challenge for modern system design is meeting the overwhelming performance, storage, and communication bandwidth demand of emerging applications within a tightly bound power budget. As both the time and power, hence the energy,…

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

Compressed file formats are the corner stone of efficient data storage and transmission, yet their potential for representation learning remains largely underexplored. We introduce TEMPEST (TransformErs froM comPressed rEpreSenTations), a…

How should statistical procedures be designed so as to be scalable computationally to the massive datasets that are increasingly the norm? When coupled with the requirement that an answer to an inferential question be delivered within a…

In several applications, input samples are more naturally represented in terms of similarities between each other, rather than in terms of feature vectors. In these settings, machine-learning algorithms can become very computationally…

Tensor data are increasingly available in many application domains. We develop several tensor decomposition methods for binary tensor data. Different from classical tensor decompositions for continuous-valued data with squared error loss,…

In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…

On-device machine learning is often constrained by limited storage, particularly in continuous data collection scenarios. This paper presents an empirical study on storage-aware learning, focusing on the trade-off between data quantity and…

Many real-world data are naturally represented as a sparse reorderable matrix, whose rows and columns can be arbitrarily ordered (e.g., the adjacency matrix of a bipartite graph). Storing a sparse matrix in conventional ways requires an…

Deep neural networks (DNNs) have enabled impressive breakthroughs in various artificial intelligence (AI) applications recently due to its capability of learning high-level features from big data. However, the current demand of DNNs for…

We consider a binary supervised learning classification problem where instead of having data in a finite-dimensional Euclidean space, we observe measures on a compact space $\mathcal{X}$. Formally, we observe data $D_N = (\mu_1, Y_1),…

Multimodal representation learning produces high-dimensional embeddings that align diverse modalities in a shared latent space. While this enables strong generalization, it also introduces scalability challenges, both in terms of storage…

It is common for researchers to record long, multiple time series from experiments or calculations. But sometimes there are no good models for the systems or no applicable mathematical theorems that can tell us when there are basic…

Recent work in Deep Learning has re-imagined the representation of data as functions mapping from a coordinate space to an underlying continuous signal. When such functions are approximated by neural networks this introduces a compelling…

In this article, we investigate several structured deep learning models for crop type classification on multi-spectral time series. In particular, our aim is to assess the respective importance of spatial and temporal structures in such…

Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, assumed unknown. In practice one may have access to dimensionality-reduced observations of the…

This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…

Modeling of multidimensional signal using tensor is more convincing than representing it as a collection of matrices. The tensor based approaches can explore the abundant spatial and temporal structures of the mutlidimensional signal. The…