In many experiments, the data points collected live in high-dimensional observation spaces, yet can be assigned a set of labels or parameters. In electrophysiological recordings, for instance, the responses of populations of neurons generally depend on mixtures of experimentally controlled parameters. The heterogeneity and diversity of these parameter dependencies can make visualization and int...

We consider a problem involving estimation of a high-dimensional covariance matrix that is the sum of a diagonal matrix and a low-rank matrix, and making a decision based on the resulting estimate. Such problems arise, for example, in portfolio management, where a common approach employs principal component analysis (PCA) to estimate factors used in constructing the low-rank term of the covaria...

Given a set of signals, a classical construction of an optimal truncatable basis for optimally representing the signals, is the principal component analysis (PCA for short) approach. When the information about the signals one would like to represent is a more general property, like smoothness, a different basis should be considered. One example is the Fourier basis which is optimal for represen...

We consider the online version of the well known Principal Component Analysis (PCA) problem. In standard PCA, the input to the problem is a set of vectors X = [x1, . . . , xn] in Rd×n and a target dimension k < d; the output is a set of vectors Y = [y1, . . . , yn] in Rk×n that minimize minΦ ‖X − ΦY ‖F where Φ is restricted to be an isometry. The global minimum of this quantity, OPTk, is obtain...

Efficient and compact representation of images is a fundamental problem in computer vision. Principal Component Analysis (PCA) has been widely used for image representation and has been successfully applied to many computer vision algorithms. In this paper, we propose a method that uses Haar-like binary box functions to span a subspace which approximates the PCA subspace. The proposed method ca...

A novel generalized feature extraction method based on the Expansion Matching (EXM) method and the Karhunen-Loeve (KL) transform is presented. This yields an eecient method to locate a large variety of features with a single pass of parallel ltering operations. The EXM method is used to design optimal detectors for diierent features. The KL representation is used to deene an optimal basis for r...

Although isolated phoneme classification using features from time-domain phase space reconstruction has been investigated recently, the best representation of feature vectors for the discriminability over phoneme classes is still an open question. This paper applies Principal Component Analysis (PCA) to feature vectors from the reconstructed phase space. By using PCA projection, the basis of th...

Individual observations can be very influential when performing classical Principal Component Analysis in a Euclidean space. Robust PCA algorithms detect and neutralize such dominating data points. This paper studies robustness issues for PCA in a kernel induced feature space. The sensitivity of Kernel PCA is characterized by calculating the influence function. A robust Kernel PCA method is pro...

Although isolated phoneme classification using features from time-domain phase space reconstruction has been investigated recently, the best representation of feature vectors for the discriminability over phoneme classes is still an open question. This paper applies Principal Component Analysis (PCA) to feature vectors from the reconstructed phase space. By using PCA projection, the basis of th...

We apply the global Principal Component Analysis (PCA) learning for face recognition tasks. The global unsupervised PCA learning generates a set of plausible visual receptive elds that are ideal for image decomposition during the feature extraction process for recognition. The procedure and results of our approach are illustrated and discussed.