Pattern Analysis and Applications

, Volume 18, Issue 2, pp 247–261 | Cite as

Generalized multi-scale stacked sequential learning for multi-class classification

  • Eloi Puertas
  • Sergio Escalera
  • Oriol Pujol
Theoretical Advances


In many classification problems, neighbor data labels have inherent sequential relationships. Sequential learning algorithms take benefit of these relationships in order to improve generalization. In this paper, we revise the multi-scale sequential learning approach (MSSL) for applying it in the multi-class case (MMSSL). We introduce the error-correcting output codesframework in the MSSL classifiers and propose a formulation for calculating confidence maps from the margins of the base classifiers. In addition, we propose a MMSSL compression approach which reduces the number of features in the extended data set without a loss in performance. The proposed methods are tested on several databases, showing significant performance improvement compared to classical approaches.


Stacked sequential learning Multi-scale Error-correct output codes (ECOC) Contextual classification 

Abbreviation List


Set of samples


Set of labels


A sample


A label


A classifier


A prediction from a classifier


A final prediction from a chain of classifiers


Extended set


Neighborhood relationship function


Neighborhood model features




Neighborhood parameterization


Number of elements in the neighborhood window


Number of scales


Set of different classes in a multi-class problem

\(\hat{F}(\mathbf{x}, c)\)

A prediction confidence map


Number of classes in a multi-class problem


Number of dichotomizers


Parameter of a Gaussian filter

Set of scales defined by σ parameters


A dichotomizer


ECOC coding matrix


A class codeword in ECOC framework


A sample prediction codeword in ECOC framework


Margin for a prediction of sample x


Constant which governs transition in a sigmoidean function


Number of iterations in an ADABoost classifier


A soft distance


Normalization parameter for soft distance δ


A multidimensional isotropic gaussian filter with zero mean and σ standard deviation


A set of partitions of classes


A partition of groups of classes


A symbol in a partition codeword


A partition codeword


The mean ranking for each system configurations


The total number of experiments


The total number of system configuration


Friedman statistic value



This work has been supported in part by the projects TIN2009-14404-C02, IMSERSO Mediminder and Rercercaixa 2011 Remedi.


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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Dept. Matemàtica Aplicada i AnàlisiUniversitat de BarcelonaBarcelonaSpain
  2. 2.Computer Vision CenterBellaterraSpain

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