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Principal component analysis (PCA) is a widely used dimension reduction method, but its performance is known to be non-robust to outliers. Recently, product-PCA (PPCA) has been shown to possess the efficiency-loss free ordering-robustness…

A new dimension reduction method based on Gaussian finite mixtures is proposed as an extension to sliced inverse regression (SIR). The model-based SIR (MSIR) approach allows the main limitation of SIR to be overcome, i.e., failure in the…

We address the problem of sufficient dimension reduction for feature matrices, which arises often in sensor network localization, brain neuroimaging, and electroencephalography analysis. In general, feature matrices have both row- and…

Dimensionality reduction is a critical step in scaling machine learning pipelines. Principal component analysis (PCA) is a standard tool for dimensionality reduction, but performing PCA over a full dataset can be prohibitively expensive. As…

Large high-dimensional datasets are becoming more and more popular in an increasing number of research areas. Processing the high dimensional data incurs a high computational cost and is inherently inefficient since many of the values that…

Layover separation has been fundamental to many synthetic aperture radar applications, such as building reconstruction and biomass estimation. Retrieving the scattering profile along the mixed dimension (elevation) is typically solved by…

Despite many applications, dimensionality reduction in the $\ell_1$-norm is much less understood than in the Euclidean norm. We give two new oblivious dimensionality reduction techniques for the $\ell_1$-norm which improve exponentially…

Dimensional reduction techniques have long been used to visualize the structure and geometry of high dimensional data. However, most widely used techniques are difficult to interpret due to nonlinearities and opaque optimization processes.…

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…

For many years, a combination of principal component analysis (PCA) and independent component analysis (ICA) has been used for blind source separation (BSS). However, it remains unclear why these linear methods work well with real-world…

Motivated by applications in high-dimensional data analysis where strong signals often stand out easily and weak ones may be indistinguishable from the noise, we develop a statistical framework to provide a novel categorization of the data…

Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of…

Dimension reduction is increasingly applied to high-dimensional biomedical data to improve its interpretability. When datasets are reduced to two dimensions, each observation is assigned an x and y coordinates and is represented as a point…

In high-dimensional prediction problems, where the number of features may greatly exceed the number of training instances, fully Bayesian approach with a sparsifying prior is known to produce good results but is computationally challenging.…

Reliable forward uncertainty quantification in engineering requires methods that account for aleatory and epistemic uncertainties. In many applications, epistemic effects arising from uncertain parameters and model form dominate prediction…

Perfect Electric Conductors (PECs) are imaged integrating the subspace-based optimizationmethod (SOM) within the iterative multi-scaling scheme (IMSA). Without a-priori information on the number or/and the locations of the scatterers and…

Eigenspaces of covariance matrices play an important role in statistical machine learning, arising in variety of modern algorithms. Quantitatively, it is convenient to describe the eigenspaces in terms of spectral projectors. This work…

Anomaly and similarity detection in multidimensional series have a long history and have found practical usage in many different fields such as medicine, networks, and finance. Anomaly detection is of great appeal for many different…

Multi-view data provides complementary information on the same set of observations, with multi-omics and multimodal sensor data being common examples. Analyzing such data typically requires distinguishing between shared (joint) and unique…

Recently, Tibshirani et al. (2016) proposed a method for making inferences about parameters defined by model selection, in a typical regression setting with normally distributed errors. Here, we study the large sample properties of this…