Search results for "subspace"
showing 10 items of 164 documents
Some classes of topological quasi *-algebras
2001
The completion $\overline{A}[\tau]$ of a locally convex *-algebra $A [ \tau ]$ with not jointly continuous multiplication is a *-vector space with partial multiplication $xy$ defined only for $x$ or $y \in A_{0}$, and it is called a topological quasi *-algebra. In this paper two classes of topological quasi *-algebras called strict CQ$^*$-algebras and HCQ$^*$-algebras are studied. Roughly speaking, a strict CQ$^*$-algebra (resp. HCQ$^*$-algebra) is a Banach (resp. Hilbert) quasi *-algebra containing a C$^*$-algebra endowed with another involution $\sharp$ and C$^*$-norm $\| \|_{\sharp}$. HCQ$^*$-algebras are closely related to left Hilbert algebras. We shall show that a Hilbert space is a H…
Smooth surjections and surjective restrictions
2017
Given a surjective mapping $f : E \to F$ between Banach spaces, we investigate the existence of a subspace $G$ of $E$, with the same density character as $F$, such that the restriction of $f$ to $G$ remains surjective. We obtain a positive answer whenever $f$ is continuous and uniformly open. In the smooth case, we deduce a positive answer when $f$ is a $C^1$-smooth surjection whose set of critical values is countable. Finally we show that, when $f$ takes values in the Euclidean space $\mathbb R^n$, in order to obtain this result it is not sufficient to assume that the set of critical values of $f$ has zero-measure.
Feature Selection for Ensembles of Simple Bayesian Classifiers
2002
A popular method for creating an accurate classifier from a set of training data is to train several classifiers, and then to combine their predictions. The ensembles of simple Bayesian classifiers have traditionally not been a focus of research. However, the simple Bayesian classifier has much broader applicability than previously thought. Besides its high classification accuracy, it also has advantages in terms of simplicity, learning speed, classification speed, storage space, and incrementality. One way to generate an ensemble of simple Bayesian classifiers is to use different feature subsets as in the random subspace method. In this paper we present a technique for building ensembles o…
Null Space Based Image Recognition Using Incremental Eigendecomposition
2011
An incremental approach to the discriminative common vector (DCV) method for image recognition is considered. Discriminative projections are tackled in the particular context in which new training data becomes available and learned subspaces may need continuous updating. Starting from incremental eigendecomposition of scatter matrices, an efficient updating rule based on projections and orthogonalization is given. The corresponding algorithm has been empirically assessed and compared to its batch counterpart. The same good properties and performance results of the original method are kept but with a dramatic decrease in the computation needed.
Ensemble Feature Selection Based on Contextual Merit and Correlation Heuristics
2001
Recent research has proven the benefits of using ensembles of classifiers for classification problems. Ensembles of diverse and accurate base classifiers are constructed by machine learning methods manipulating the training sets. One way to manipulate the training set is to use feature selection heuristics generating the base classifiers. In this paper we examine two of them: correlation-based and contextual merit -based heuristics. Both rely on quite similar assumptions concerning heterogeneous classification problems. Experiments are considered on several data sets from UCI Repository. We construct fixed number of base classifiers over selected feature subsets and refine the ensemble iter…
ERP denoising in multichannel EEG data using contrasts between signal and noise subspaces
2009
Abstract In this paper, a new method intended for ERP denoising in multichannel EEG data is discussed. The denoising is done by separating ERP/noise subspaces in multidimensional EEG data by a linear transformation and the following dimension reduction by ignoring noise components during inverse transformation. The separation matrix is found based on the assumption that ERP sources are deterministic for all repetitions of the same type of stimulus within the experiment, while the other noise sources do not obey the determinancy property. A detailed derivation of the technique is given together with the analysis of the results of its application to a real high-density EEG data set. The inter…
Multilinear Fourier multipliers related to time–frequency localization
2013
We consider multilinear multipliers associated in a natural way with localization operators. Boundedness and compactness results are obtained. In particular, we get a geometric condition on a subset A⊂R2d which guarantees that, for a fixed synthesis window ψ∈L2(Rd), the family of localization operators Lφ,ψA obtained when the analysis window φ varies on the unit ball of L2(Rd) is a relatively compact set of compact operators.
Multi-class pairwise linear dimensionality reduction using heteroscedastic schemes
2010
Accepted version of an article published in the journal: Pattern Recognition. Published version on Sciverse: http://dx.doi.org/10.1016/j.patcog.2010.01.018 Linear dimensionality reduction (LDR) techniques have been increasingly important in pattern recognition (PR) due to the fact that they permit a relatively simple mapping of the problem onto a lower-dimensional subspace, leading to simple and computationally efficient classification strategies. Although the field has been well developed for the two-class problem, the corresponding issues encountered when dealing with multiple classes are far from trivial. In this paper, we argue that, as opposed to the traditional LDR multi-class schemes…
p-VARIATION OF VECTOR MEASURES WITH RESPECT TO BILINEAR MAPS
2008
AbstractWe introduce the spaces Vℬp(X) (respectively 𝒱ℬp(X)) of the vector measures ℱ:Σ→X of bounded (p,ℬ)-variation (respectively of bounded (p,ℬ)-semivariation) with respect to a bounded bilinear map ℬ:X×Y →Z and show that the spaces Lℬp(X) consisting of functions which are p-integrable with respect to ℬ, defined in by Blasco and Calabuig [‘Vector-valued functions integrable with respect to bilinear maps’, Taiwanese Math. J. to appear], are isometrically embedded in Vℬp(X). We characterize 𝒱ℬp(X) in terms of bilinear maps from Lp′×Y into Z and Vℬp(X) as a subspace of operators from Lp′(Z*) into Y*. Also we define the notion of cone absolutely summing bilinear maps in order to describe t…
Rates of convergence to equilibrium for collisionless kinetic equations in slab geometry
2017
This work deals with free transport equations with partly diffuse stochastic boundary operators in slab geometry. Such equations are governed by stochastic semigroups in $L^{1}$ spaces$.\ $We prove convergence to equilibrium at the rate $O\left( t^{-\frac{k}{2(k+1)+1}}\right) \ (t\rightarrow +\infty )$ for $L^{1}$ initial data $g$ in a suitable subspace of the domain of the generator $T$ where $k\in \mathbb{N}$ depends on the properties of the boundary operators near the tangential velocities to the slab. This result is derived from a quantified version of Ingham's tauberian theorem by showing that $F_{g}(s):=\lim_{\varepsilon \rightarrow 0_{+}}\left( is+\varepsilon -T\right) ^{-1}g$ exists…