Search results for " dimensionality"
showing 10 items of 129 documents
Sparse Manifold Clustering and Embedding to discriminate gene expression profiles of glioblastoma and meningioma tumors.
2013
Sparse Manifold Clustering and Embedding (SMCE) algorithm has been recently proposed for simultaneous clustering and dimensionality reduction of data on nonlinear manifolds using sparse representation techniques. In this work, SMCE algorithm is applied to the differential discrimination of Glioblastoma and Meningioma Tumors by means of their Gene Expression Profiles. Our purpose was to evaluate the robustness of this nonlinear manifold to classify gene expression profiles, characterized by the high-dimensionality of their representations and the low discrimination power of most of the genes. For this objective, we used SMCE to reduce the dimensionality of a preprocessed dataset of 35 single…
Variability of Classification Results in Data with High Dimensionality and Small Sample Size
2021
The study focuses on the analysis of biological data containing information on the number of genome sequences of intestinal microbiome bacteria before and after antibiotic use. The data have high dimensionality (bacterial taxa) and a small number of records, which is typical of bioinformatics data. Classification models induced on data sets like this usually are not stable and the accuracy metrics have high variance. The aim of the study is to create a preprocessing workflow and a classification model that can perform the most accurate classification of the microbiome into groups before and after the use of antibiotics and lessen the variability of accuracy measures of the classifier. To ev…
A local complexity based combination method for decision forests trained with high-dimensional data
2012
Accurate machine learning with high-dimensional data is affected by phenomena known as the “curse” of dimensionality. One of the main strategies explored in the last decade to deal with this problem is the use of multi-classifier systems. Several of such approaches are inspired by the Random Subspace Method for the construction of decision forests. Furthermore, other studies rely on estimations of the individual classifiers' competence, to enhance the combination in the multi-classifier and improve the accuracy. We propose a competence estimate which is based on local complexity measurements, to perform a weighted average combination of the decision forest. Experimental results show how thi…
Making nonlinear manifold learning models interpretable: The manifold grand tour
2015
Smooth nonlinear topographic maps of the data distribution to guide a Grand Tour visualisation.Prioritisation of data linear views that are most consistent with data structure in the maps.Useful visualisations that cannot be obtained by other more classical approaches. Dimensionality reduction is required to produce visualisations of high dimensional data. In this framework, one of the most straightforward approaches to visualising high dimensional data is based on reducing complexity and applying linear projections while tumbling the projection axes in a defined sequence which generates a Grand Tour of the data. We propose using smooth nonlinear topographic maps of the data distribution to…
Dimensionality reduction via regression on hyperspectral infrared sounding data
2014
This paper introduces a new method for dimensionality reduction via regression (DRR). The method generalizes Principal Component Analysis (PCA) in such a way that reduces the variance of the PCA scores. In order to do so, DRR relies on a deflationary process in which a non-linear regression reduces the redundancy between the PC scores. Unlike other nonlinear dimensionality reduction methods, DRR is easy to apply, it has out-of-sample extension, it is invertible, and the learned transformation is volume-preserving. These properties make the method useful for a wide range of applications, especially in very high dimensional data in general, and for hyperspectral image processing in particular…
A Feature Set Decomposition Method for the Construction of Multi-classifier Systems Trained with High-Dimensional Data
2013
Data mining for the discovery of novel, useful patterns, encounters obstacles when dealing with high-dimensional datasets, which have been documented as the "curse" of dimensionality. A strategy to deal with this issue is the decomposition of the input feature set to build a multi-classifier system. Standalone decomposition methods are rare and generally based on random selection. We propose a decomposition method which uses information theory tools to arrange input features into uncorrelated and relevant subsets. Experimental results show how this approach significantly outperforms three baseline decomposition methods, in terms of classification accuracy.
Incremental Generalized Discriminative Common Vectors for Image Classification.
2015
Subspace-based methods have become popular due to their ability to appropriately represent complex data in such a way that both dimensionality is reduced and discriminativeness is enhanced. Several recent works have concentrated on the discriminative common vector (DCV) method and other closely related algorithms also based on the concept of null space. In this paper, we present a generalized incremental formulation of the DCV methods, which allows the update of a given model by considering the addition of new examples even from unseen classes. Having efficient incremental formulations of well-behaved batch algorithms allows us to conveniently adapt previously trained classifiers without th…
The impact of sample reduction on PCA-based feature extraction for supervised learning
2006
"The curse of dimensionality" is pertinent to many learning algorithms, and it denotes the drastic raise of computational complexity and classification error in high dimensions. In this paper, different feature extraction (FE) techniques are analyzed as means of dimensionality reduction, and constructive induction with respect to the performance of Naive Bayes classifier. When a data set contains a large number of instances, some sampling approach is applied to address the computational complexity of FE and classification processes. The main goal of this paper is to show the impact of sample reduction on the process of FE for supervised learning. In our study we analyzed the conventional PC…
Feature Dimensionality Reduction for Mammographic Report Classification
2016
The amount and the variety of available medical data coming from multiple and heterogeneous sources can inhibit analysis, manual interpretation, and use of simple data management applications. In this paper a deep overview of the principal algorithms for dimensionality reduction is carried out; moreover, the most effective techniques are applied on a dataset composed of 4461 mammographic reports is presented. The most useful medical terms are converted and represented using a TF-IDF matrix, in order to enable data mining and retrieval tasks. A series of query have been performed on the raw matrix and on the same matrix after the dimensionality reduction obtained using the most useful techni…
A hybrid virtual–boundary element formulation for heterogeneous materials
2021
Abstract In this work, a hybrid formulation based on the conjoined use of the recently developed Virtual Element Method (VEM) and the Boundary Element Method (BEM) is proposed for the effective computational analysis of multi-region domains, representative of heterogeneous materials. VEM has been recently developed as a generalisation of the Finite Element Method (FEM) and it allows the straightforward employment of elements of general polygonal shape, maintaining a high level of accuracy. For its inherent features, it allows the use of meshes of general topology, including non-convex elements. On the other hand, BEM is an effective technique for the numerical solution of sets of boundary i…