title: Regularized Least Squares Cancer classifiers from DNA microarray data.
abstract: BACKGROUND
  The advent of the technology of DNA microarrays constitutes an epochal change in the classification and discovery of different types of cancer because the information provided by DNA microarrays allows an approach to the problem of cancer analysis from a quantitative rather than qualitative point of view. Cancer classification requires well founded mathematical methods which are able to predict the status of new specimens with high significance levels starting from a limited number of data. In this paper we assess the performances of Regularized Least Squares (RLS) classifiers, originally proposed in regularization theory, by comparing them with Support Vector Machines (SVM), the state-of-the-art supervised learning technique for cancer classification by DNA microarray data. The performances of both approaches have been also investigated with respect to the number of selected genes and different gene selection strategies.
  
  
  RESULTS
  We show that RLS classifiers have performances comparable to those of SVM classifiers as the Leave-One-Out (LOO) error evaluated on three different data sets shows. The main advantage of RLS machines is that for solving a classification problem they use a linear system of order equal to either the number of features or the number of training examples. Moreover, RLS machines allow to get an exact measure of the LOO error with just one training.
  
  
  CONCLUSIONS
  RLS classifiers are a valuable alternative to SVM classifiers for the problem of cancer classification by gene expression data, due to their simplicity and low computational complexity. Moreover, RLS classifiers show generalization ability comparable to the ones of SVM classifiers also in the case the classification of new specimens involves very few gene expression levels.
authors.affiliation: Istituto di Studi sui Sistemi Intelligenti per I'Automazione, CNR, Via Amendola 122/D-I, 70126 Bari, Italy. ancona@ba.issia.cnr.it
authors.forename: Nicola
authors.initials: N
authors.lastname: Ancona
authors.forename: Rosalia
authors.initials: R
authors.lastname: Maglietta
authors.forename: Annarita
authors.initials: A
authors.lastname: D'Addabbo
authors.forename: Sabino
authors.initials: S
authors.lastname: Liuni
authors.forename: Graziano
authors.initials: G
authors.lastname: Pesole
mesh_terms: D000465:Algorithms; D016000:Cluster Analysis; D019295:Computational Biology / Q000379:methods*; D003198:Computer Simulation; D016002:Discriminant Analysis; D020869:Gene Expression Profiling; D015972:Gene Expression Regulation, Neoplastic; D006801:Humans; D016018:Least-Squares Analysis; D008957:Models, Genetic; D015233:Models, Statistical; D009369:Neoplasms / Q000235:genetics*; D017711:Nonlinear Dynamics; D020411:Oligonucleotide Array Sequence Analysis / Q000379:methods*; D010363:Pattern Recognition, Automated; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D016415:Sequence Alignment; D012984:Software