Global Dimensionality Reduction Research Articles

Dimensionality Reduction Based on Low Rank Representation

Dimensionality Reduction is a common way to solve the problem of 'curse of dimensions', especially for im- age processing. Among all these methods, the linear methods are believed to have better performance in actual databases. This paper proposes a novel unsupervised linear dimensionality reduction method that based on low rank representation which aims at finding the subspace structure of the original data sets. This method named LRRDR tries to preserve the subspace structure of the original data therefore is better than the global dimensionality reduction methods like PCA. The experiments compare PCA, NPE, LRRDR and SPP and the results show that LRRDR outperforms the other methods.

Improved Gini-Index Algorithm to Correct Feature-Selection Bias in Text Classification

This paper presents an improved Gini-Index algorithm to correct feature-selection bias in text classification. Gini-Index has been used as a split measure for choosing the most appropriate splitting attribute in decision tree. Recently, an improved Gini-Index algorithm for feature selection, designed for text categorization and based on Gini-Index theory, was introduced, and it has proved to be better than the other methods. However, we found that the Gini-Index still shows a feature selection bias in text classification, specifically for unbalanced datasets having a huge number of features. The feature selection bias of the Gini-Index in feature selection is shown in three ways: 1) the Gini values of low-frequency features are low (on purity measure) overall, irrespective of the distribution of features among classes, 2) for high-frequency features, the Gini values are always relatively high and 3) for specific features belonging to large classes, the Gini values are relatively lower than those belonging to small classes. Therefore, to correct that bias and improve feature selection in text classification using Gini-Index, we propose an improved Gini-Index (I-GI) algorithm with three reformulated Gini-Index expressions. In the present study, we used global dimensionality reduction (DR) and local DR to measure the goodness of features in feature selections. In experimental results for the I-GI algorithm, we obtained unbiased feature values and eliminated many irrelevant general features while retaining many specific features. Furthermore, we could improve the overall classification performances when we used the local DR method. The total averages of the classification performance were increased by 19.4%, 15.9%, 3.3%, 2.8% and 2.9% (kNN) in Micro-F1, 14%, 9.8%, 9.2%, 3.5% and 4.3% (SVM) in Micro-F1, 20%, 16.9%, 2.8%, 3.6% and 3.1% (kNN) in Macro-F1, 16.3%, 14%, 7.1%, 4.4%, 6.3% (SVM) in Macro-F1, compared with tf*idf, χ2, Information Gain, Odds Ratio and the existing Gini-Index methods according to each classifier.

General Cost Models for Evaluating Dimensionality Reduction in High-Dimensional Spaces

Similarity search usually encounters a serious problem in the high-dimensional space, known as the curse of dimensionality. In order to speed up the retrieval efficiency, most previous approaches reduce the dimensionality of the entire data set to a fixed lower value before building indexes (referred to as global dimensionality reduction (GDR)). More recent works focus on locally reducing the dimensionality of data to different values (called the local dimensionality reduction (LDR)). In addition, random projection is proposed as an approximate dimensionality reduction (ADR) technique to answer the approximate similarity search instead of the exact one. However, so far little work has formally evaluated the effectiveness and efficiency of GDR, LDR, and ADR for the range query. Motivated by this, in this paper, we propose general cost models for evaluating the query performance over the reduced data sets by GDR, LDR, and ADR, in light of which we introduce a novel (A)LDR method, partitioning based on randomized search (PRANS). It can achieve high retrieval efficiency with the guarantee of optimality given by the formal models. Finally, a B+-tree index is constructed over the reduced partitions for fast similarity search. Extensive experiments validate the correctness of our cost models on both real and synthetic data sets and demonstrate the efficiency and effectiveness of the proposed PRANS method.

Locally adaptive metrics for clustering high dimensional data

Clustering suffers from the curse of dimensionality, and similarity functions that use all input features with equal relevance may not be effective. We introduce an algorithm that discovers clusters in subspaces spanned by different combinations of dimensions via local weightings of features. This approach avoids the risk of loss of information encountered in global dimensionality reduction techniques, and does not assume any data distribution model. Our method associates to each cluster a weight vector, whose values capture the relevance of features within the corresponding cluster. We experimentally demonstrate the gain in perfomance our method achieves with respect to competitive methods, using both synthetic and real datasets. In particular, our results show the feasibility of the proposed technique to perform simultaneous clustering of genes and conditions in gene expression data, and clustering of very high-dimensional data such as text data.

Local Dimensionality Reduction and Supervised Learning Within Natural Clusters for Biomedical Data Analysis

Inductive learning systems were successfully applied in a number of medical domains. Nevertheless, the effective use of these systems often requires data preprocessing before applying a learning algorithm. This is especially important for multidimensional heterogeneous data presented by a large number of features of different types. Dimensionality reduction (DR) is one commonly applied approach. The goal of this paper is to study the impact of natural clustering--clustering according to expert domain knowledge--on DR for supervised learning (SL) in the area of antibiotic resistance. We compare several data-mining strategies that apply DR by means of feature extraction or feature selection with subsequent SL on microbiological data. The results of our study show that local DR within natural clusters may result in better representation for SL in comparison with the global DR on the whole data.

Local dimensionality reduction

In automatic pattern recognition applications, numerous features that describe the classes are obtained in an attempt to ensure accurate classification of unknown observations. These features or dimensions must be reduced to a smaller number before classification schemes can be applied, because classifiers become computationally and analytically unmanageable in high dimensions. Principal components and Fisher’s Linear Discriminant offer global dimensionality reduction within the framework of linear algebra applied to covariance matrices. This report describes local methods that use both mixture models and nearest neighbor calculations to construct local versions of these methods. These new versions for local dimensionality reduction will provide increased classification accuracy in lower dimensions.