scholarly journals CBIR Feature Vector Dimension Reduction with Eigenvectors of Covariance Matrix using Row, Column and Diagonal Mean Sequences

2010 ◽  
Vol 3 (12) ◽  
pp. 39-46 ◽  
Author(s):  
Dr. H.B. Kekre ◽  
Sudeep D. Thepade ◽  
Akshay Maloo
Keyword(s):  
Dimension Reduction ◽  
Covariance Matrix ◽  
Feature Vector ◽  
Vector Dimension

scholarly journals Reducing Dimensions of the Feature Vector of an Image Based on Blocking-DCT

2021 ◽  
Author(s):  
Farah Torkamani Azar
Keyword(s):  
Dimension Reduction ◽  
Feature Vector

Two approach for dimension reduction of a DCT block of an image to extracting features are provided.

scholarly journals A Novel Hybrid Dimension Reduction Technique for Undersized High Dimensional Gene Expression Data Sets Using Information Complexity Criterion for Cancer Classification

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Esra Pamukçu ◽  
Hamparsum Bozdogan ◽  
Sinan Çalık
Keyword(s):  
Gene Expression ◽  
Dimension Reduction ◽  
Covariance Matrix ◽  
Gene Expression Data ◽  
Information Criterion ◽  
Data Sets ◽  
Expression Data ◽  
Akaike's Information Criterion ◽  
Akaike’S Information Criterion ◽  
Probabilistic Pca

Gene expression data typically are large, complex, and highly noisy. Their dimension is high with several thousand genes (i.e., features) but with only a limited number of observations (i.e., samples). Although the classical principal component analysis (PCA) method is widely used as a first standard step in dimension reduction and in supervised and unsupervised classification, it suffers from several shortcomings in the case of data sets involving undersized samples, since the sample covariance matrix degenerates and becomes singular. In this paper we address these limitations within the context of probabilistic PCA (PPCA) by introducing and developing a new and novel approach using maximum entropy covariance matrix and its hybridized smoothed covariance estimators. To reduce the dimensionality of the data and to choose the number of probabilistic PCs (PPCs) to be retained, we further introduce and develop celebrated Akaike’s information criterion (AIC), consistent Akaike’s information criterion (CAIC), and the information theoretic measure of complexity (ICOMP) criterion of Bozdogan. Six publicly available undersized benchmark data sets were analyzed to show the utility, flexibility, and versatility of our approach with hybridized smoothed covariance matrix estimators, which do not degenerate to perform the PPCA to reduce the dimension and to carry out supervised classification of cancer groups in high dimensions.

The regularization method in the classification task according to given examples

2019 ◽  
Vol 7(25) (3-4) ◽  
pp. 3-13
Author(s):  
Włodzimierz Kwiatkowski
Keyword(s):  
Covariance Matrix ◽  
Regularization Method ◽  
Feature Vector ◽  
Statistical Properties ◽  
Classification Task ◽  
The Given ◽  
Direct Use

The article considers the problem of classification based on the given examples of classes. As a feature vector, a complete characteristic of object is assumed. The peculiarity of the problem being solved is that the number of examples of the class may be less than the dimension of the feature vector, and also most of the coordinates of the feature vector can be correlated. As a consequence, the feature covariance matrix calculated for the cluster of examples may be singular or ill-conditioned. This disenable a direct use of metrics based on this covariance matrix. The article presents a regularization method involving the additional use of statistical properties of the environment.

Study of Face Feature Extraction and Recognition Techniques Based on Wavelet Analysis

2014 ◽  
Vol 1030-1032 ◽  
pp. 1810-1813
Author(s):  
Xin Wang ◽  
He Pan
Keyword(s):  
Face Recognition ◽  
Wavelet Decomposition ◽  
Feature Vector ◽  
Recognition Performance ◽  
Image Database ◽  
Face Image ◽  
Support Vector ◽  
Svm Model ◽  
Feature Based ◽  
Vector Dimension

Face recognition is a research hotspot of pattern recognition and artificial intelligence. This paper presents a method of extract face feature based on Wavelet. First, reduce vector dimension by wavelet decomposition of the image, second, train the multi class support vector machine (SVM) model by face feature vector extracted and make face recognition finally. The experiments on ORL face image database of the algorithm shows the superiority of the proposed algorithm in terms of recognition performance.

scholarly journals A SUB-VECTOR WEIGHTING SCHEME FOR IMAGE RETRIEVAL WITH RELEVANCE FEEDBACK

2002 ◽  
Vol 02 (02) ◽  
pp. 199-213
Author(s):  
LEI WANG ◽  
KAP LUK CHAN ◽  
XUEJIAN XIONG
Keyword(s):  
Image Retrieval ◽  
Covariance Matrix ◽  
Relevance Feedback ◽  
Feature Vector ◽  
Weighting Scheme ◽  
Subjective Perception ◽  
Mutual Correlation ◽  
Final Score ◽  
Low Dimensional ◽  
High Level

In image retrieval with relevance feedback, feature components are weighted to reflect the high-level concepts, and a user's subjective perception, embodied in the images labelled by the user in the feedback. However, the number of labelled images is often small and the covariance matrix needed for weighting will be singular. For this reason, the commonly used methods discard the mutual correlation among the feature components completely and use a diagonal covariance matrix. In this paper, a sub-vector weighting scheme is proposed. This scheme partitions a multi-dimensional visual feature vector into multiple low-dimensional sub-vectors. The singularity of the covariance matrix for each sub-vector can be avoided due to the lower dimensionality of the sub-vectors. Thus, the mutual correlation in each sub-vector can be retained for weighting and an optimally weighted similarity metric can be applied on each sub-vector. The similarity scores obtained from different sub-vectors are combined, as the final score, to rank the database images. Experimental results demonstrated that the proposed weighting scheme can significantly improve the efficacy of image retrieval with relevance feedback.

scholarly journals Dimension reduction of high-dimensional dataset with missing values

2019 ◽  
Vol 13 ◽  
pp. 174830261986744
Author(s):  
Ran Zhang ◽  
Bin Ye ◽  
Peng Liu
Keyword(s):  
Principal Component Analysis ◽  
Dimension Reduction ◽  
Covariance Matrix ◽  
Incomplete Data ◽  
Missing Values ◽  
Principal Component ◽  
High Dimensional ◽  
Data Handling ◽  
Handling Methods ◽  
Lasso Estimator

Nowadays, datasets containing a very large number of variables or features are routinely generated in many fields. Dimension reduction techniques are usually performed prior to statistically analyzing these datasets in order to avoid the effects of the curse of dimensionality. Principal component analysis is one of the most important techniques for dimension reduction and data visualization. However, datasets with missing values arising in almost every field will produce biased estimates and are difficult to handle, especially in the high dimension, low sample size settings. By exploiting a Lasso estimator of the population covariance matrix, we propose to regularize the principal component analysis to reduce the dimensionality of dataset with missing data. The Lasso estimator of covariance matrix is computationally tractable by solving a convex optimization problem. To illustrate the effectiveness of our method on dimension reduction, the principal component directions are evaluated by the metrics of Frobenius norm and cosine distance. The performances are compared with other incomplete data handling methods such as mean substitution and multiple imputation. Simulation results also show that our method is superior to other incomplete data handling methods in the context of discriminant analysis of real world high-dimensional datasets.

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