Related papers: Optimized Kernel Entropy Components
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…
Matrix approximations are a key element in large-scale algebraic machine learning approaches. The recently proposed method MEKA (Si et al., 2014) effectively employs two common assumptions in Hilbert spaces: the low-rank property of an…
In this paper, we tackle a significant challenge in PCA: heterogeneity. When data are collected from different sources with heterogeneous trends while still sharing some congruency, it is critical to extract shared knowledge while retaining…
High-dimensional data in the form of tensors are challenging for kernel classification methods. To both reduce the computational complexity and extract informative features, kernels based on low-rank tensor decompositions have been…
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 study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kernel-Principal Component Analysis, manifold and feature space…
Kernel density estimation is a key component of a wide variety of algorithms in machine learning, Bayesian inference, stochastic dynamics and signal processing. However, the unsupervised density estimation technique requires tuning a…
Exposure correction methods aim to adjust the luminance while maintaining other luminance-unrelated information. However, current exposure correction methods have difficulty in fully separating luminance-related and luminance-unrelated…
Kernel density estimation (KDE) is integral to a range of generative and discriminative tasks in machine learning. Drawing upon tools from the multidimensional calculus of variations, we derive an optimal weight function that reduces bias…
We present a method for performing Principal Component Analysis (PCA) on noisy datasets with missing values. Estimates of the measurement error are used to weight the input data such that compared to classic PCA, the resulting eigenvectors…
Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the…
Medical imaging is key in modern medicine. From magnetic resonance imaging (MRI) to microscopic imaging for blood cell detection, diagnostic medical imaging reveals vital insights into patient health. To predict diseases or provide…
Due to the rapid growth of smart agents such as weakly connected computational nodes and sensors, developing decentralized algorithms that can perform computations on local agents becomes a major research direction. This paper considers the…
Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…
Principal Component Analysis (PCA) is one of the most commonly used statistical methods for data exploration, and for dimensionality reduction wherein the first few principal components account for an appreciable proportion of the…
This paper studies the optimality of kernel methods in high-dimensional data clustering. Recent works have studied the large sample performance of kernel clustering in the high-dimensional regime, where Euclidean distance becomes less…
Most of machine learning deals with vector parameters. Ideally we would like to take higher order information into account and make use of matrix or even tensor parameters. However the resulting algorithms are usually inefficient. Here we…
We propose sparseGeoHOPCA, a novel framework for sparse higher-order principal component analysis (SHOPCA) that introduces a geometric perspective to high-dimensional tensor decomposition. By unfolding the input tensor along each mode and…
We are interested in a framework of online learning with kernels for low-dimensional but large-scale and potentially adversarial datasets. We study the computational and theoretical performance of online variations of kernel Ridge…
Incremental versions of batch algorithms are often desired, for increased time efficiency in the streaming data setting, or increased memory efficiency in general. In this paper we present a novel algorithm for incremental kernel PCA, based…