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1

Linear discriminant analysis with a generalization of the Moore–Penrose pseudoinverse

Górecki T., Łuczak M.

International Journal of Applied Mathematics and Computer Science

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2013

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Vol. 23, no. 2

463--471

EN

The Linear Discriminant Analysis (LDA) technique is an important and well-developed area of classification, and to date many linear (and also nonlinear) discrimination methods have been put forward. A complication in applying LDA to real data occurs when the number of features exceeds that of observations. In this case, the covariance estimates do not have full rank, and thus cannot be inverted. There are a number of ways to deal with this problem. In this paper, we propose improving LDA in this area, and we present a new approach which uses a generalization of the Moore–Penrose pseudoinverse to remove this weakness. Our new approach, in addition to managing the problem of inverting the covariance matrix, significantly improves the quality of classification, also on data sets where we can invert the covariance matrix. Experimental results on various data sets demonstrate that our improvements to LDA are efficient and our approach outperforms LDA.

2

Recognition of occluded traffic signs based on two-dimensional linear discriminant analysis

Forczmański P.

Archives of Transport System Telematics

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2013

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Vol. 6, iss. 3

10--13

EN

Traffic signs recognition involving digital image analysis is getting more and more popular. The main problem associated with visual recognition of traffic signs is associated with difficult conditions of image acquisition. In the paper we present a solution to the problem of signs occlusion. Presented method belongs to the group of appearance-based approaches, employing template matching working in the reduced feature space obtained by Linear Discriminant Analysis. The method deals with all types of signs, regarding their shape and color in contrast to commercial systems, installed in higher-class cars, that only detect the round speed limit signs and overtaking restrictions. Finally, we present some experiments performed on a benchmark databases with different kinds of occlusion.

3

Analysis of correlation based dimension reduction methods

Shin Y. J., Park C. H.

International Journal of Applied Mathematics and Computer Science

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2011

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Vol. 21, no 3

549-558

EN

Dimension reduction is an important topic in data mining and machine learning. Especially dimension reduction combined with feature fusion is an effective preprocessing step when the data are described by multiple feature sets. Canonical Correlation Analysis (CCA) and Discriminative Canonical Correlation Analysis (DCCA) are feature fusion methods based on correlation. However, they are different in that DCCA is a supervised method utilizing class label information, while CCA is an unsupervised method. It has been shown that the classification performance of DCCA is superior to that of CCA due to the discriminative power using class label information. On the other hand, Linear Discriminant Analysis (LDA) is a supervised dimension reduction method and it is known as a special case of CCA. In this paper, we analyze the relationship between DCCA and LDA, showing that the projective directions by DCCA are equal to the ones obtained from LDA with respect to an orthogonal transformation. Using the relation with LDA, we propose a new method that can enhance the performance of DCCA. The experimental results show that the proposed method exhibits better classification performance than the original DCCA.

4

Two-dimensional LDA approach to image compression and recognition

Kukharev G., Forczmański P.

Computing, Multimedia and Intelligent Techniques

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2006

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Vol. 2, nr 1

45-53

EN

The paper presents a novel method of reducing the dimensionality of large datasets (e.g. human faces databases). It does not incorporate any usual pre-processing stage (like down-scaling or filtering). Its main advantage is associated with efficient representation of images leading to the accurate recognition. The reduction is realized by modified Linear Discriminant Analysis. In the paper, the authors present its mathematical principles together with some results of practical recognition experiments on popular facial databases (ORL, BioID).