Related papers: History PCA: A New Algorithm for Streaming PCA
We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…
We study the problem of solving semidefinite programs (SDP) in the streaming model. Specifically, $m$ constraint matrices and a target matrix $C$, all of size $n\times n$ together with a vector $b\in \mathbb{R}^m$ are streamed to us…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
We consider the classic Euclidean $k$-median and $k$-means objective on data streams, where the goal is to provide a $(1+\varepsilon)$-approximation to the optimal $k$-median or $k$-means solution, while using as little memory as possible.…
Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…
Robust PCA methods are typically batch algorithms which requires loading all observations into memory before processing. This makes them inefficient to process big data. In this paper, we develop an efficient online robust principal…
We initiate the study of biological neural networks from the perspective of streaming algorithms. Like computers, human brains suffer from memory limitations which pose a significant obstacle when processing large scale and dynamically…
This paper describes some applications of an incremental implementation of the principal component analysis (PCA). The algorithm updates the transformation coefficients matrix on-line for each new sample, without the need to keep all the…
Partitioning graphs into blocks of roughly equal size is widely used when processing large graphs. Currently there is a gap in the space of available partitioning algorithms. On the one hand, there are streaming algorithms that have been…
A streaming algorithm to compute the spectral proper orthogonal decomposition (SPOD) of stationary random processes is presented. As new data becomes available, an incremental update of the truncated eigenbasis of the estimated…
This paper considers the problem of estimating the principal eigenvector of a covariance matrix from independent and identically distributed data samples in streaming settings. The streaming rate of data in many contemporary applications…
We study high-dimensional robust statistics tasks in the streaming model. A recent line of work obtained computationally efficient algorithms for a range of high-dimensional robust estimation tasks. Unfortunately, all previous algorithms…
Sparse Principal Component Analysis (Sparse PCA) is a pivotal tool in data analysis and dimensionality reduction. However, Sparse PCA is a challenging problem in both theory and practice: it is known to be NP-hard and current exact methods…
Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…
We introduce a novel algorithm to perform graph clustering in the edge streaming setting. In this model, the graph is presented as a sequence of edges that can be processed strictly once. Our streaming algorithm has an extremely low memory…
In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…
Stochastic algorithms are well-known for their performance in the era of big data. In convex optimization, stochastic algorithms have been studied in depth and breadth. However, the current body of research on stochastic algorithms for…
The number of triangles (hereafter denoted by $\Delta$) is an important metric to analyze massive graphs. It is also used to compute clustering coefficient in networks. This paper proposes a new algorithm called PES (Priority Edge Sampling)…
Transformer models serve as the backbone of many state-ofthe-art language models, and most use the scaled dot-product attention (SDPA) mechanism to capture relationships between tokens. However, the straightforward implementation of SDPA…
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…