相关论文: Locally linear embedding: dimension reduction of m…

Design-space dimensionality reduction is essential to mitigate the cost of high-fidelity simulation-based optimization, especially when dealing with high-dimensional geometric parameterizations. Traditional linear techniques, such as…

Semantic text representation is a fundamental task in the field of natural language processing. Existing text embedding (e.g., SimCSE and LLM2Vec) have demonstrated excellent performance, but the values of each dimension are difficult to…

We propose a new supervised dimensionality reduction technique called Supervised Linear Centroid-Encoder (SLCE), a linear counterpart of the nonlinear Centroid-Encoder (CE) \citep{ghosh2022supervised}. SLCE works by mapping the samples of a…

Embedding representations power machine intelligence in many applications, including recommendation systems, but they are space intensive -- potentially occupying hundreds of gigabytes in large-scale settings. To help manage this outsized…

In this paper, we study the problem of hyperspectral pixel classification based on the recently proposed architectures for compressive whisk-broom hyperspectral imagers without the need to reconstruct the complete data cube. A clear…

Dense retrievers encode queries and documents and map them in an embedding space using pre-trained language models. These embeddings need to be high-dimensional to fit training signals and guarantee the retrieval effectiveness of dense…

The objective in extreme multi-label learning is to train a classifier that can automatically tag a novel data point with the most relevant subset of labels from an extremely large label set. Embedding based approaches make training and…

Our aim is to evaluate fundamental parameters from the analysis of the electromagnetic spectra of stars. We may use $10^3$-$10^5$ spectra; each spectrum being a vector with $10^2$-$10^4$ coordinates. We thus face the so-called "curse of…

We show how perceptual embeddings of the visual system can be constructed at inference-time with no training data or deep neural network features. Our perceptual embeddings are solutions to a weighted least squares (WLS) problem, defined at…

We revisit the problem of fair representation learning by proposing Fair Partial Least Squares (PLS) components. PLS is widely used in statistics to efficiently reduce the dimension of the data by providing representation tailored for the…

High dimensional data can contain multiple scales of variance. Analysis tools that preferentially operate at one scale can be ineffective at capturing all the information present in this cross-scale complexity. We propose a multiscale joint…

The Johnson-Lindenstrauss (JL) lemma is a fundamental result in dimensionality reduction, ensuring that any finite set $X \subseteq \mathbb{R}^d$ can be embedded into a lower-dimensional space $\mathbb{R}^k$ while approximately preserving…

This paper investigates the problem of selecting the embedding dimension for large heterogeneous networks that have weakly distinguishable community structure. For a broad family of embeddings based on normalized adjacency matrices, we…

In meteorology, finding similar weather patterns or analogs in historical datasets can be useful for data assimilation, forecasting, and postprocessing. In climate science, analogs in historical and climate projection data are used for…

We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity…

Feature representation is an important aspect of remote-sensing based image classification. While deep convolutional neural networks are able to effectively amalgamate information, large numbers of parameters often make learned features…

Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known…

When performing classification tasks, raw high dimensional features often contain redundant information, and lead to increased computational complexity and overfitting. In this paper, we assume the data samples lie on a single underlying…

In this note we discuss a common misconception, namely that embeddings are always used to reduce the dimensionality of the item space. We show that when we measure dimensionality in terms of information entropy then the embedding of sparse…

Dimensionality reduction is a fundamental task in modern data science. Several projection methods specifically tailored to take into account the non-linearity of the data via local embeddings have been proposed. Such methods are often based…