Related papers: Efficient Estimation of Unique Components in Indep…
Spatial Independent Component Analysis (ICA) decomposes the time by space functional MRI (fMRI) matrix into a set of 1-D basis time courses and their associated 3-D spatial maps that are optimized for mutual independence. When applied to…
Independent component analysis (ICA) is widely used to separate mixed signals and recover statistically independent components. However, in non-human primate neuroimaging studies, most ICA-recovered spatial maps are often dense. To extract…
We analyze the dynamics of an online algorithm for independent component analysis in the high-dimensional scaling limit. As the ambient dimension tends to infinity, and with proper time scaling, we show that the time-varying joint empirical…
We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a…
Independent Component Analysis (ICA) offers interpretable semantic components of embeddings. While ICA theory assumes that embeddings can be linearly decomposed into independent components, real-world data often do not satisfy this…
Principal Component Analysis (PCA) is a ubiquitous tool with many applications in machine learning including feature construction, subspace embedding, and outlier detection. In this paper, we present an algorithm for computing the top…
This study utilizes Independent Component Analysis (ICA) to unveil a consistent semantic structure within embeddings of words or images. Our approach extracts independent semantic components from the embeddings of a pre-trained model by…
Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…
The Independent Component Analysis (ICA) algorithm is implemented as a neural network for separating signals of different origin in astrophysical sky maps. Due to its self-organizing capability, it works without prior assumptions on the…
Here, a separation theorem about Independent Subspace Analysis (ISA), a generalization of Independent Component Analysis (ICA) is proven. According to the theorem, ISA estimation can be executed in two steps under certain conditions. In the…
We introduce coroICA, confounding-robust independent component analysis, a novel ICA algorithm which decomposes linearly mixed multivariate observations into independent components that are corrupted (and rendered dependent) by hidden…
Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…
Independent component analysis (ICA) is a fundamental statistical tool used to reveal hidden generative processes from observed data. However, traditional ICA approaches struggle with the rotational invariance inherent in Gaussian…
Independent component analysis (ICA) is a method to extract a set of time-series data using ``statistical independency" of each component. We applied ICA to extract gravitational wave (GW) signals directly from the detector data. Our idea…
This paper proposes a novel method of independent component analysis (ICA), which we name higher-order tensor ICA (HOT-ICA). HOT-ICA is a tensor ICA that makes effective use of the signal categories represented by the axes of a separating…
Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and thus, various robust PCA methods have been proposed.…
Principal component analysis (PCA) is by far the most widespread tool for unsupervised learning with high-dimensional data sets. Its application is popularly studied for the purpose of exploratory data analysis and online process…
Principal Component Analysis (PCA) is a popular method for dimension reduction and has attracted an unfailing interest for decades. More recently, kernel PCA (KPCA) has emerged as an extension of PCA but, despite its use in practice, a…