Related papers: A Category Space Approach to Supervised Dimensiona…
This paper proposes a novel kernel approach to linear dimension reduction for supervised learning. The purpose of the dimension reduction is to find directions in the input space to explain the output as effectively as possible. The…
We propose a method for the approximation of high- or even infinite-dimensional feature vectors, which play an important role in supervised learning. The goal is to reduce the size of the training data, resulting in lower storage…
This paper introduces a novel framework for dynamic classification in high dimensional spaces, addressing the evolving nature of class distributions over time or other index variables. Traditional discriminant analysis techniques are…
When performing classification tasks, raw high dimensional features often contain redundant information, and lead to increased computational complexity and overfitting. In this paper, we assume the data samples lie on a single underlying…
Representing images and videos with Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, has been shown to yield high discriminative power in many visual recognition tasks.…
The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…
The kernel matrix used in kernel methods encodes all the information required for solving complex nonlinear problems defined on data representations in the input space using simple, but implicitly defined, solutions. Spectral analysis on…
We encounter a bottleneck when we try to borrow the strength of classical classifiers to classify functional data. The major issue is that functional data are intrinsically infinite dimensional, thus classical classifiers cannot be applied…
The paper introduces a new efficient nonlinear one-class classifier formulated as the Rayleigh quotient criterion optimisation. The method, operating in a reproducing kernel Hilbert space, minimises the scatter of target distribution along…
Unsupervised machine learning lacks ground truth by definition. This poses a major difficulty when designing metrics to evaluate the performance of such algorithms. In sharp contrast with supervised learning, for which plenty of quality…
We investigate the minimization of a quadratic function over Stiefel manifolds (the set of all orthogonal $r$- frames in $\mathbf{R}^n$), which has applications in high-dimensional semi-supervised classification tasks. To reduce the…
Representing images and videos with Symmetric Positive Definite (SPD) matrices and considering the Riemannian geometry of the resulting space has proven beneficial for many recognition tasks. Unfortunately, computation on the Riemannian…
In complex visual recognition tasks it is typical to adopt multiple descriptors, that describe different aspects of the images, for obtaining an improved recognition performance. Descriptors that have diverse forms can be fused into a…
The effectiveness of Symmetric Positive Definite (SPD) manifold features has been proven in various computer vision tasks. However, due to the non-Euclidean geometry of these features, existing Euclidean machineries cannot be directly used.…
Face verification is a problem approached in the literature mainly using nonlinear class-specific subspace learning techniques. While it has been shown that kernel-based Class-Specific Discriminant Analysis is able to provide excellent…
It is proven that encoding images and videos through Symmetric Positive Definite (SPD) matrices, and considering the Riemannian geometry of the resulting space, can lead to increased classification performance. Taking into account manifold…
A particularly interesting instance of supervised learning with kernels is when each training example is associated with two objects, as in pairwise classification (Brunner et al., 2012), and in supervised learning of preference relations…
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…
Representing images by compact codes has proven beneficial for many visual recognition tasks. Most existing techniques, however, perform this coding step directly in image feature space, where the distributions of the different classes are…
Dimensionality reduction is often used as an initial step in data exploration, either as preprocessing for classification or regression or for visualization. Most dimensionality reduction techniques to date are unsupervised; they do not…