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We describe visual classification by a hierarchy of semantic fragments. In fragment-based classification, objects within a class are represented by common sub-structures selected during training. Here we propose two extensions to the basic fragment-based scheme. The first extension is the extraction and use of feature hierarchies. We describe a method that automatically constructs complete feature hierarchies from image examples, and show that features constructed hierarchically are significantly more informative and better for classification compared with similar non-hierarchical features. The second extension is the use of so-called semantic fragments to represent object parts. The goal of a semantic fragment is to represent the different possible appearances of a given object part. The visual appearance of such object parts can differ substantially, and therefore traditional image similarity-based methods are inappropriate for the task. We show how the method can automatically learn the part structure of a new domain, identify the main parts, and how their appearance changes across objects in the class. We discuss the implications of these extensions to object classification and recognition. Joint work with Prof. Shimon Ullman. ©2006 Microsoft Corporation. All rights reserved.

Well we're back, and in true aussie fashion we are fucking late. Oh well, I'm sure our one fan will be consoled by the fact that this may possibly be our most Australian podcast yet, if only for the mention of Stack Hats. If you don't know what they are you led a deprived and sad life. Anyways, on with the show! Shit we talk about: - STACKHATS!! - We love old school games - Silent Hill Homecoming, it aint no 5 - Sam and Max = God - Scratch that, Mike Patton = God - Duke Forever, RIP - Ahhhh, [url=http://gamingisstupid.com/2009/05/06/the-chair-story-revival/]that chair story[/url]. - We get pissy about Ghostbusters, then at eachother - Where the fuck is our MvC2 demo? - The RC Spotlight: Tits in games. Seriously. - Dillinger Drops his phone number again. Somebody call the bastard. - Listener questions yaaaaayyyy! - AnimuCast! - I know too much about Luchadores Intro Music: Bionic Commando: Rearmed OST - Power Plant Break Music: Selkies the endless obsessions - Between The Buried And Me. 8Bit Version by [url=http://www.youtube.com/user/xTwilightxxPrincessx]xtwilightxxprincessx[/url] Outro Music: Bulb - Illustrated 8 Test

Classification of Animals • Language: Hebrew • Author: Ashur Cherry (Toronto, Canada) Hebrew Language Publications are Dedicated in Honour of Professor Binyamin Geva

Classification of Animals • Language: Hebrew • Author: Ashur Cherry (Toronto, Canada) Hebrew Language Publications are Dedicated in Honour of Professor Binyamin Geva

Classification of Animals • Language: Hebrew • Author: Ashur Cherry (Toronto, Canada) Hebrew Language Publications are Dedicated in Honour of Professor Binyamin Geva

Classification of Animals • Language: Hebrew • Author: Ashur Cherry (Toronto, Canada) Hebrew Language Publications are Dedicated in Honour of Professor Binyamin Geva

Classification of Animals • Language: Hebrew • Author: Ashur Cherry (Toronto, Canada) Hebrew Language Publications are Dedicated in Honour of Professor Binyamin Geva

Classification of Animals • Language: Hebrew • Author: Ashur Cherry (Toronto, Canada) Hebrew Language Publications are Dedicated in Honour of Professor Binyamin Geva

Classification of Animals • Language: Hebrew • Author: Ashur Cherry (Toronto, Canada) Hebrew Language Publications are Dedicated in Honour of Professor Binyamin Geva

Classification of Animals • Language: Hebrew • Author: Ashur Cherry (Toronto, Canada) Hebrew Language Publications are Dedicated in Honour of Professor Binyamin Geva

The performance of a modulation classifier is highly sensitive to channel signal-to-noise ratio (SNR). In this paper, we focus on amplitude-phase modulations and propose a modulation classification framework based on centralized data fusion using multiple radios and the hybrid maximum likelihood (ML) approach. In order to alleviate the computational complexity associated with ML estimation, we adopt the Expectation Maximization (EM) algorithm. Due to SNR diversity, the proposed multi-radio framework provides robustness to channel SNR. Numerical results show the superiority of the proposed approach with respect to single radio approaches as well as to modulation classifiers using moments based estimators.

The performance of a modulation classifier is highly sensitive to channel signal-to-noise ratio (SNR). In this paper, we focus on amplitude-phase modulations and propose a modulation classification framework based on centralized data fusion using multiple radios and the hybrid maximum likelihood (ML) approach. In order to alleviate the computational complexity associated with ML estimation, we adopt the Expectation Maximization (EM) algorithm. Due to SNR diversity, the proposed multi-radio framework provides robustness to channel SNR. Numerical results show the superiority of the proposed approach with respect to single radio approaches as well as to modulation classifiers using moments based estimators.

We investigate detection, classification, and prognostication of osteosarcoma using artificial intelligence.

The study will be a replication of Maria Abascal´s study "Contraction as a Response to Group Threat: Demographic Decline and Whites’ Classification of People Who Are Ambiguously White" in the German context. Participants willl be shown a graph, depicting the increasing share of migrants in Germany, through a time period with varying length. Later on, participants will be shown faces with ambiguous German appearance, of which they should assess, whether they have a migration background or not.

Overview In Thayer & Stevens (2021), we conducted two experiments investigating the effects of human-animal interaction (HAI) on affect and cognition. In these experiments, participants experienced cognitive (working memory, attentional control) tasks before and after either a three-minute exposure to a dog (HAI condition) or a control task. Self-report measures of affect (mood, anxiety, stress) were collected repeatedly throughout the sessions. While interacting with a dog influenced measures of affect, they did not influence cognition. In addition to the affect and cognition measures, participants wore an Empatica E4 to record heart rate, electrodermal activity, body temperature, etc. However, we did not analyze these data, as the sampling rate was too low for robust measures of heart rate variability (Malik et al. 1996, Laborde et al. 2017). Arce & Gehringer (2021) have investigated machine learning algorithms that take Empatica E4 data and classify whether participants were experiencing stress induction. This offers the opportunity to apply the machine learning algorithms developed to classify stress to the Thayer & Stevens (2021) data and address two specific aims: 1. Assess the predictive accuracy of the machine learning algorithms in classifying intervention exposure 2. Determine which features are most important in classifying exposure Research questions 1. How accurately can machine learning algorithms classify stress intervention exposure? 2. Which algorithms best predict stress intervention exposure? 3. Does the accelerometer data act as a naive feature that gives extra weighting to the different affect states? 4. Which features best predict passive and active stress intervention exposures?

The current study is part of the innovative training network ETUDE (Encompassing Training in fUnctional Disorders across Europe; https://etude-itn.eu/), ultimately aiming to improve the understanding of mechanisms, diagnosis, treatment and stigmatization of Functional Disorders (5). Project 5: Predictive validity of diagnostic criteria of FD used in mental health care. ETUDE programme website https://etude-itn.eu/

We digitized and uploaded this film from the Orgone Cinema 16mm Archive Email us at [email protected] if you have questions about the footage and are interested in using it in your project

Pre-registration for a meta-analysis of the relationship between the after-effects of job insecurity and job insecurity.

Protocol for future scoping review investigating speech pathology interventions for multilingual people with aphasia across the ICF.

Protocol for future scoping review investigating speech pathology interventions for multilingual people with aphasia across the ICF.

Protocol for future scoping review investigating speech pathology interventions for multilingual people with aphasia across the ICF.

In the first section we recall some basic notions on Lie algebras. In a second time we study the algebraic variety of complex $n$-dimensional Lie algebras. We present different notions of deformations : Gerstenhaber deformations, pertubations, valued deformations and we use these tools to study some properties of this variety. Finaly we introduce the concept of rigidity and we present some results on the class of rigid Lie algebras.

We derive integrable discrete systems which are contiguity relations of two equations in the Painlev\'e-Gambier classification depending on some parameter. These studies extend earlier work where the contiguity relations for the six transcendental Painlev\'e equations were obtained. In the case of the Gambier equation we give the contiguity relations for both the continuous and the discrete system.

We classify Lie-Poisson brackets that are formed from Lie algebra extensions. The problem is relevant because many physical systems owe their Hamiltonian structure to such brackets. A classification involves reducing all brackets to a set of normal forms, independent under coordinate transformations, and is achieved with the techniques of Lie algebra cohomology. For extensions of order less than five, we find that the number of normal forms is small and they involve no free parameters. A special extension, known as the Leibniz extension, is shown to be the unique ``maximal'' extension. We derive a general method of finding Casimir invariants of Lie-Poisson bracket extensions. The Casimir invariants of all brackets of order less than five are explicitly computed, using the concept of `coextension.' We obtain the Casimir invariants of Leibniz extensions of arbitrary order. We also offer some physical insight into the nature of the Casimir invariants of compressible reduced magnetohydrodynamics. We make use of the methods developed to study the stability of extensions for given classes of Hamiltonians. This helps to elucidate the distinction between semidirect extensions and those involving cocycles. For compressible reduced magnetohydrodynamics, we find the cocycle has a destabilizing effect on the steady-state solutions.

Group classification of the generalized complex Ginzburg-Landau equations is presented. An approach to group classification of systems of reaction-diffusion equations with general diffusion matrix is developed.

Generalized quantum statistics such as para-statistics is usually characterized by certain triple relations. In the case of para-Fermi statistics these relations can be associated with the orthogonal Lie algebra B_n=so(2n+1); in the case of para-Bose statistics they are associated with the Lie superalgebra B(0|n)=osp(1|2n). In a previous paper, a mathematical definition of ``a generalized quantum statistics associated with a classical Lie algebra G'' was given, and a complete classification was obtained. Here, we consider the definition of ``a generalized quantum statistics associated with a basic classical Lie superalgebra G''. Just as in the Lie algebra case, this definition is closely related to a certain Z-grading of G. We give in this paper a complete classification of all generalized quantum statistics associated with the basic classical Lie superalgebras A(m|n), B(m|n), C(n) and D(m|n).

Generalized quantum statistics such as para-statistics is usually characterized by certain triple relations. In the case of para-Fermi statistics these relations can be associated with the orthogonal Lie algebra B_n=so(2n+1); in the case of para-Bose statistics they are associated with the Lie superalgebra B(0|n)=osp(1|2n). In a previous paper, a mathematical definition of ``a generalized quantum statistics associated with a classical Lie algebra G'' was given, and a complete classification was obtained. Here, we consider the definition of ``a generalized quantum statistics associated with a basic classical Lie superalgebra G''. Just as in the Lie algebra case, this definition is closely related to a certain Z-grading of G. We give in this paper a complete classification of all generalized quantum statistics associated with the basic classical Lie superalgebras A(m|n), B(m|n), C(n) and D(m|n).

This paper reports about an approach to the classification of proteins' primary structures taking advantage of the Self Organizing Maps algorithm and of a numerical coding of the aminoacids based upon their physico-chemical properties. Hydrophobicity, volume, surface area, hydrophilicity, bulkiness, refractivity and polarity were subjected to a Principal Component Analysis and the first two principal components, explaining 84.8 % of the total observed variability, were used to cluster the aminoacids into 4 or 5 classes through a k-means algorithm. This leads to an economical representation of the primary structures which, in the construction of the input vectors for the Self Organizing Maps algorithm, allows the consideration of up to tri- and tetrapeptides' frequency matrices with minimal computational overload. In comparison with previously explored conditions, namely symbolic coding of aminoacids and dipeptides frequencies, no significant improvement was observed in the classification of 69 cytochromes of the c type, characterized by a high degree of structural and functional similarity, while a substantial improvement occurred in the case of a data set including quite heterogeneous primary structures.

A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if they are present in the unknown regression function $f_0$. An idealized one-dimensional problem is considered in detail. The proposed nonparametric prior uses random split points to partition the unit interval into a random number of pieces. This prior is found to provide a consistent estimate of the regression function in the $\L^p$ topology, for any $1 \leq p < \infty$, and for arbitrary measurable $f_0:[0,1] \to [0,1]$. A Markov chain Monte Carlo (MCMC) implementation is outlined and analyzed. Simulation experiments are conducted to show that the proposed estimate compares favorably with a variety of conventional estimators. A striking resemblance between the posterior mean estimate and the bagged CART estimate is noted and discussed. For higher dimensions, a generalized prior is introduced which employs a random Voronoi partition of the covariate-space. The resulting estimate displays promise on a two-dimensional problem, and extends with a minimum of additional computational effort to arbitrary metric spaces.

The linear finite irreducible representations of the algebra of the 1D $N$-Extended Supersymmetric Quantum Mechanics are discussed in terms of their "connectivity" (a symbol encoding information on the graphs associated to the irreps). The classification of the irreducible representations with the same fields content and different connectivity is presented up to $N\leq 8$.

We present a classification of $W$ algebras and superalgebras arising in Abelian as well as non Abelian Toda theories. Each model, obtained from a constrained WZW action, is related with an $Sl(2)$ subalgebra (resp. $OSp(1|2)$ superalgebra) of a simple Lie algebra (resp. superalgebra) $\cg$. However, the determination of an $U(1)_Y$ factor, commuting with $Sl(2)$ (resp. $OSp(1|2)$), appears, when it exists, particularly useful to characterize the corresponding $W$ algebra. The (super) conformal spin contents of each $W$ (super)algebra is performed. The class of all the superconformal algebras (i.e. with conformal spins $s\leq2$) is easily obtained as a byproduct of our general results.

Misprints in the definition of semiclassical tau-function and in the formulae (3.40b) and (4.20) are corrected.

We find a relation between the spectrum of solitons of massive $N=2$ quantum field theories in $d=2$ and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling dimensions be real imposes restrictions on the soliton numbers and leads to a classification program for symmetric $N=2$ conformal theories and their massive deformations in terms of a suitable generalization of Dynkin diagrams (which coincides with the A--D--E Dynkin diagrams for minimal models). The Landau-Ginzburg theories are a proper subset of this classification. In the particular case of LG theories we relate the soliton numbers with intersection of vanishing cycles of the corresponding singularity; the relation between soliton numbers and the scaling dimensions in this particular case is a well known application of Picard-Lefschetz theory.

Microarray data consists of mRNA expression levels of thousands of genes under certain conditions. A difference in the expression level of a gene at two different conditions/phenotypes, such as cancerous versus non-cancerous, one subtype of cancer versus another, before versus after a drug treatment, is indicative of the relevance of that gene to the difference of the high-level phenotype. Each gene can be ranked by its ability to distinguish the two conditions. We study how the single-gene classification ability decreases with its rank (a Zipf's plot). Power-law function in the Zipf's plot is observed for the four microarray datasets obtained from various cancer studies. This power-law behavior in the Zipf's plot is reminiscent of similar power-law curves in other natural and social phenomena (Zipf's law). However, due to our choice of the measure of importance in classification ability, i.e., the maximized likelihood in a logistic regression, the exponent of the power-law function is a function of the sample size, instead of a fixed value close to 1 for a typical example of Zipf's law. The presence of this power-law behavior is important for deciding the number of genes to be used for a discriminant microarray data analysis.

This article explores \Z_2-graded L_\infinity algebra structures on a 2|1-dimensional vector space. The reader should note that our convention on the parities is the opposite of the usual one, because we define our structures on the symmetric coalgebra of the parity reversion of a space, so our 2|1-dimensional L_\infinity algebras correspond to the usual 1|2-dimensional algebras. We give a complete classification of all structures with a nonzero degree 1 term. We also classify all degree 2 codifferentials, which is the same as a classification of all 1|2-dimensional Z_2-graded Lie algebras. For each of these algebra structures, we calculate the cohomology and a miniversal deformation.

There are 339 combinatorial types of generic metrics on six points. They correspond to the 339 regular triangulations of the second hypersimplex \Delta(6,2), which also has 14 non-regular triangulations.

Prediction error is critical to assessing the performance of statistical methods and selecting statistical models. We propose the cross-validation and approximated cross-validation methods for estimating prediction error under a broad q-class of Bregman divergence for error measures which embeds nearly all of the commonly used loss functions in regression, classification procedures and machine learning literature. The approximated cross-validation formulas are analytically derived, which facilitate fast estimation of prediction error under the Bregman divergence. We then study a data-driven optimal bandwidth selector for the local-likelihood estimation that minimizes the overall prediction error or equivalently the covariance penalty. It is shown that the covariance penalty and cross-validation methods converge to the same mean-prediction-error-criterion. We also propose a lower-bound scheme for computing the local logistic regression estimates and demonstrate that it is as simple and stable as the local least-squares regression estimation. The algorithm monotonically enhances the target local-likelihood and converges. The idea and methods are extended to the generalized varying-coefficient models and semiparametric models.

We extend the symbolic representation to the ring of N=1 supersymmetric differential polynomials, and demonstrate that operations on the ring, such as the super derivative, Frechet derivative and super commutator, can be carried out in the symbolic way. Using the symbolic representation, we classify scalar $\lambda$-homogeneous N=1 supersymmetric evolutionary equations with nonzero linear term when $\lambda>0$ for arbitrary order and give a comprehensive description of all such integrable equations.

Social media tend to be rife with rumours while new reports are released piecemeal during breaking news. Interestingly, one can mine multiple reactions expressed by social media users in those situations, exploring their stance towards rumours, ultimately enabling the flagging of highly disputed rumours as being potentially false. In this work, we set out to develop an automated, supervised classifier that uses multi-task learning to classify the stance expressed in each individual tweet in a rumourous conversation as either supporting, denying or questioning the rumour. Using a classifier based on Gaussian Processes, and exploring its effectiveness on two datasets with very different characteristics and varying distributions of stances, we show that our approach consistently outperforms competitive baseline classifiers. Our classifier is especially effective in estimating the distribution of different types of stance associated with a given rumour, which we set forth as a desired characteristic for a rumour-tracking system that will warn both ordinary users of Twitter and professional news practitioners when a rumour is being rebutted.

Information on the spectral types of stars is of great interest in view of the exploitation of space-based imaging surveys. In this article, we investigate the classification of stars into spectral types using only the shape of their diffraction pattern in a single broad-band image. We propose a supervised machine learning approach to this endeavour, based on principal component analysis (PCA) for dimensionality reduction, followed by artificial neural networks (ANNs) estimating the spectral type. Our analysis is performed with image simulations mimicking the Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) in the F606W and F814W bands, as well as the Euclid VIS imager. We first demonstrate this classification in a simple context, assuming perfect knowledge of the point spread function (PSF) model and the possibility of accurately generating mock training data for the machine learning. We then analyse its performance in a fully data-driven situation, in which the training would be performed with a limited subset of bright stars from a survey, and an unknown PSF with spatial variations across the detector. We use simulations of main-sequence stars with flat distributions in spectral type and in signal-to-noise ratio, and classify these stars into 13 spectral subclasses, from O5 to M5. Under these conditions, the algorithm achieves a high success rate both for Euclid and HST images, with typical errors of half a spectral class. Although more detailed simulations would be needed to assess the performance of the algorithm on a specific survey, this shows that stellar classification from single-band images is well possible.

Roughly speaking, an ideal immersion of a Riemannian manifold into a real space form is an isometric immersion which produces the least possible amount of tension from the ambient space at each point of the submanifold. The main purpose of this paper is to completely classify all non-minimal ideal submanifolds of real space forms with type number $\leq 2$.

We propose a high dimensional classification method that involves nonparametric feature augmentation. Knowing that marginal density ratios are the most powerful univariate classifiers, we use the ratio estimates to transform the original feature measurements. Subsequently, penalized logistic regression is invoked, taking as input the newly transformed or augmented features. This procedure trains models equipped with local complexity and global simplicity, thereby avoiding the curse of dimensionality while creating a flexible nonlinear decision boundary. The resulting method is called Feature Augmentation via Nonparametrics and Selection (FANS). We motivate FANS by generalizing the Naive Bayes model, writing the log ratio of joint densities as a linear combination of those of marginal densities. It is related to generalized additive models, but has better interpretability and computability. Risk bounds are developed for FANS. In numerical analysis, FANS is compared with competing methods, so as to provide a guideline on its best application domain. Real data analysis demonstrates that FANS performs very competitively on benchmark email spam and gene expression data sets. Moreover, FANS is implemented by an extremely fast algorithm through parallel computing.

We employ a simple potential model to analyse the effects which a Regge trajectory, correlating with a bound or a metastable state at zero angular momentum, has on an integral cross section. A straightforward modification of the Mulholland formula of Macek et al is proposed for more efficient separation of the resonance contribution.

Let $X\subset \P^N$ be a nondegenerate irreducible closed subvariety of dimension $n$ over the field of complex numbers and let $SX\subset\P^N$ be its secant variety. $X\subset\P^N$ is called `secant defective' if $\dim(SX)$ is strictly less than the expected dimension $2n+1$. In \cite{Z1}, F.L. Zak showed that for a secant defective manifold necessarily $N\le{n+2 \choose n}-1$ and that the Veronese variety $v_2(\P^n)$ is the only boundary case. Recently R. Mu$\tilde{\textrm{n}}$oz, J. C. Sierra, and L. E. Sol\'a Conde classified secant defective varieties next to this extremal case in \cite{MSS}. In this paper, we will consider secant defective manifolds $X\subset\P^N$ of dimension $n$ with $N={n+2 \choose n}-1-\epsilon$ for $\epsilon\ge0$. First, we will prove that $X$ is a $LQEL$-manifold of type $\delta=1$ for $\epsilon\le n-2$ (see Theorem \ref{main_thm}) by showing that the tangential behavior of $X$ is good enough to apply Scorza lemma. Then we will completely describe the above manifolds by using the classification of conic-connected manifolds given in \cite{IR1}. Our method generalizes previous results in \cite{Z1,MSS}.

A linkage diagram is obtained from the Carter diagram $\Gamma$ by adding an extra root $\gamma$, so that the resulting subset of roots is linearly independent. With every linkage diagram we associate the linkage label vector $\gamma^{\nabla}$, similar to Dynkin labels. The linkage diagrams connected under the action of the group $W^{\vee}_{S}$ constitute the the linkage system $\mathscr{L}(\Gamma)$. For any simply-laced Carter diagram, the system $\mathscr{L}(\Gamma)$ is constructed. To obtain linkage diagrams $\theta^{\nabla}$, we use an easily verifiable criterion: $\mathscr{B}^{\vee}_{\Gamma}(\theta^{\nabla}) < 2$, where $\mathscr{B}^{\vee}_{\Gamma}$ is the inverse quadratic form associated with $\Gamma$. A Dynkin diagram $\Gamma'$ such that rank($\Gamma'$) = rank($\Gamma$) + 1 and any $\Gamma$-associated root subset $S$ lies in $\varPhi(\Gamma')$, is said to be the Dynkin extension. The linkage system $\mathscr{L}(\Gamma)$ is the union of $\Gamma_i$-components $\mathscr{L}_{\Gamma_i}(\Gamma)$ taken for all Dynkin extensions of $\Gamma

We prove that every vertically nearly separately continuous function defined on a product of a strong PP-space and a topological space and with values in a strongly $\sigma$-metrizable space with a special stratification, is a pointwise limit of continuous functions.

We classify all monomial planar Cremona maps by multidegree using recent methods developed by Aluffi. Following the main result, we prove several more properties of the set of these maps, and also extend the results to the more general `r.c. monomial' maps.

Ribbon 2-knotted objects are locally flat embeddings of surfaces in 4-space which bound immersed 3-manifolds with only ribbon singularities. They appear as topological realizations of welded knotted objects, which is a natural quotient of virtual knot theory. In this paper we consider ribbon tubes and ribbon torus-links, which are natural analogues of string links and links, respectively. We show how ribbon tubes naturally act on the reduced free group, and how this action classifies ribbon tubes up to link-homotopy, that is when allowing each component to cross itself. At the combinatorial level, this provides a classification of welded string links up to self-virtualization. This generalizes a result of Habegger and Lin on usual string links, and the above-mentioned action on the reduced free group can be refined to a general "virtual extension" of Milnor invariants. As an application, we obtain a classification of ribbon torus-links up to link-homotopy.

We have analyzed ISO SWS 01 observations for 61 proto-planetary nebulae candidates and classified their spectra according to their dominant chemistry. On the basis of our classification and the more general classification of SWS 01 spectra by Kraemer et al. (2002) we discuss the connection between proto-planetary nebulae candidates and planetary nebulae, with emphasis on possible precursors of planetary nebulae with [WR] central stars.

We consider high-dimensional multi-class classification of normal vectors, where unlike standard assumptions, the number of classes may be also large. We derive the (non-asymptotic) conditions on effects of significant features, and the low and the upper bounds for distances between classes required for successful feature selection and classification with a given accuracy. Furthermore, we study an asymptotic setup where the number of classes is growing with the dimension of feature space and sample sizes. To the best of our knowledge, our paper is the first to study this important model. In particular, we present an interesting and, at first glance, somewhat counter-intuitive phenomenon that the precision of classification can improve as the number of classes grows. This is due to more accurate feature selection since even weak significant features, which are not sufficiently strong to be manifested in a coarse classification, can nevertheless have a strong impact when the number of classes is large. We consider both the case of the known and the unknown covariance matrix. The performance of the procedure is demonstrated on simulated and real-data examples.