Invariant feature descriptors such as SIFT and GLOH have been demonstrated to be very robust for image matching and visual recognition. However, such descriptors are generally parameterised in very high dimensional spaces e.g. 128 dimensions in the case of SIFT. This limits the performance of feature matching techniques in terms of speed and scalability. Furthermore, these descriptors have traditionally been carefully hand crafted by manually tuning many parameters. In this paper, we tackle both of these problems by formulating descriptor design as a nonparametric dimensionality reduction problem. In contrast to previous approaches that use only the global statistics of the inputs, we adopt a discriminative approach. Starting from a large training set of labelled match/non-match pairs, we pursue lower dimensional embeddings that are optimised for their discriminative power. Extensive comparative experiments demonstrate that we can exceed the performance of the current state of the art techniques such as SIFT with far fewer dimensions, and with virtually no parameters to be tuned by hand.

A generalized discriminant analysis based on a new optimization criterion is presented. The criterion extends the optimization criteria of the classical Linear Discriminant Analysis (LDA) when the scatter matrices are singular. An efficient algorithm for the new optimization problem is presented. The solutions to the proposed criterion form a family of algorithms for generalized LDA, which can be characterized in a closed form. We study two specific algorithms, namely Uncorrelated LDA (ULDA) and Orthogonal LDA (OLDA). ULDA was previously proposed for feature extraction and dimension reduction, whereas OLDA is a novel algorithm proposed in this paper. The features in the reduced space of ULDA are uncorrelated, while the discriminant vectors of OLDA are orthogonal to each other. We have conducted a comparative study on a variety of real-world data sets to evaluate ULDA and OLDA in terms of classification accuracy.

[30] V. Patrascu and V. Buzuloiu, “Image dynamic range enhancement in

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Dimensionality reduction is an important pre-processing step for many applications. Linear Discriminant Analysis (LDA) is one of the well known methods for supervised dimensionality reduction. However, the classical LDA formulation requires the nonsingularity of scatter matrices involved. For undersampled problems, where the data dimension is much larger than the sample size, all scatter matrices are singular and classical LDA fails. Many extensions, including null space based LDA (NLDA), orthogonal LDA (OLDA), etc, have been proposed in the past to overcome this problem. In this paper, we present a computational and theoretical analysis of NLDA and OLDA. Our main result shows that under a mild condition which holds in many applications involving high-dimensional data, NLDA is equivalent to OLDA. We have performed extensive experiments on various types of data and results are consistent with our theoretical analysis. The presented analysis and experimental results provide further insight into several LDA based algorithms. 1.

We report on an extensive simulation study comparing eight statistical classification methods, focusing on problems where the number of observations is less than the number of variables. Using a wide range of artificial and real data, two types of classifiers were contrasted; methods that classify using all variables, and methods that first reduce the number of dimensions to two or three. The full feature space methods include linear, quadratic and regularized discriminant analysis, and the nearest neighbour method. The four dimensionality reducing classifiers are characterized by the transform they implement. The four transforms compared are the Fisher discriminant plane, the Fisher-Fukunaga-Koonz, the Fisher-radius, and the Fisher-variance transforms. The FisherFukunaga and the Fisher-radius transform based classifiers have recently been proposed for two class classification problems. We also present an extension to these transforms such that they can be applied to classification pro...

Abstract—High-dimensional data appear in many applications of data mining, machine learning, and bioinformatics. Feature reduction is commonly applied as a preprocessing step to overcome the curse of dimensionality. Uncorrelated Linear Discriminant Analysis (ULDA) was recently proposed for feature reduction. The extracted features via ULDA were shown to be statistically uncorrelated, which is desirable for many applications. In this paper, an algorithm called ULDA/QR is proposed to simplify the previous implementation of ULDA. Then, the ULDA/GSVD algorithm is proposed, based on a novel optimization criterion, to address the singularity problem which occurs in undersampled problems, where the data dimension is larger than the sample size. The criterion used is the regularized version of the one in ULDA/QR. Surprisingly, our theoretical result shows that the solution to ULDA/GSVD is independent of the value of the regularization parameter. Experimental results on various types of data sets are reported to show the effectiveness of the proposed algorithm and to compare it with other commonly used feature reduction algorithms. Index Terms—Feature reduction, uncorrelated linear discriminant analysis, QR-decomposition, generalized singular value decomposition. 1

We describe a way to measure the diversity of consumer’s musical interests and characterize this diversity using published musical playlists. For each song in the playlist we calculate a set of features, which were optimized for genre recognition, and represent the song as a single point in a multidimensional genre-space. Given the points for a set of songs, we fit an ellipsoid to the data, and then describe the diversity of the playlist by calculating the volume of the enclosing ellipsoid. We compare 887 different playlists, representing nearly 29,000 distinct songs, to collections of different genres and to the size of our entire database. Playlists tend to be less diverse than a genre, and, by our measure, about 5 orders of magnitude smaller than the entire song set. These characteristics are important for recommendation systems, which want to present users with a set of recommendations tuned to each user’s diversity.

The paper presents an emotional speech recognition system with the analysis of manifolds of speech. Working with large volumes of high-dimensional acoustic features, the researchers confront the problem of dimensionality reduction. Unlike classical techniques, such as Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA), a new approach, named Enhanced Lipschitz Embedding (ELE) is proposed in the paper to discover the nonlinear degrees of freedom that underlie the emotional speech corpus. ELE adopts geodesic distance to preserve the intrinsic geometry at all scales of speech corpus. Based on geodesic distance estimation, ELE embeds the 64-dimensional acoustic features into a six-dimensional space in which speech data with the same emotional state are generally clustered around one plane and the data distribution feature is beneficial to emotion classification. The compressed testing data is classified into six emotional states (neutral, anger, fear, happiness, sadness and surprise) by a trained linear Support Vector Machine (SVM) system. Considering the perception

Several kernel algorithms have recently been proposed for nonlinear discriminant analysis. However, these methods mainly address the singularity problem in the high dimensional feature space. Less attention has been focused on the properties of the resulting discriminant vectors and feature vectors in the reduced dimensional space. In this paper, we present a new formulation for kernel discriminant analysis. The proposed formulation includes, as special cases, kernel uncorrelated discriminant analysis (KUDA) and kernel orthogonal discriminant analysis (KODA). The feature vectors of KUDA are uncorrelated, while the discriminant vectors of KODA are orthogonal to each other in the feature space. We present theoretical derivations of proposed KUDA and KODA algorithms. The experimental results show that both KUDA and KODA are very competitive in comparison with other nonlinear discriminant algorithms in terms of classification accuracy. 1.