A major assumption in many machine learning algorithms is that the training and testing data must come from the same feature space or have the same distributions. However, in real applications, this strong hypothesis does not hold. In this paper, we introduce a new framework for transfer where the source and target domains are represented by subspaces described by eigenvector matrices. To unify subspace distribution between domains, we propose to use a fast efficient approximative SVD for fast features generation. In order to make a transfer learning between domains, we firstly use a subspace learning approach to develop a domain adaption algorithm where only target knowledge is transferable. Secondly, we use subspace alignment trick to propose a novel transfer domain adaptation method. To evaluate the proposal, we use large-scale data sets. Numerical results, based on accuracy and computational time are provided with comparison with state-of-the-art methods.

International audience

Linear Discriminant Analysis (LDA) is a technique which is frequently used to extract discriminative features that preserve the class separability. LDA involves matrices eigen decomposition which can be computationally expensive in both time and memory, in particular when the number of samples and the number of features are large. This is the case for text and image data sets where the dimension can reach in order of hundreds of thousands or more. In this paper, we propose an efficient algorithm Fast-LDA to handle large scale data for discriminant analysis. The proposed approach uses a feature extraction method based on random projection to reduce the dimensionality and then perform LDA in the reduced space. By reducing data dimension, we reduce the complexity of data analysis. The accuracy and the computational time of the proposed approach are provided for a wide variety of real image and text data sets. The results show the relevance of the proposed method compared to other methods.

Linear mixture models are commonly used to represent a hyperspectral data cube as linear combinations of endmember spectra. However, determining the number of endmembers for images embedded in noise is a crucial task. This paper proposes a fully automatic approach for estimating the number of endmembers in hyperspectral images. The estimation is based on recent results of random matrix theory related to the so-called spiked population model. More precisely, we study the gap between successive eigenvalues of the sample covariance matrix constructed from high-dimensional noisy samples. The resulting estimation strategy is fully automatic and robust to correlated noise owing to the consideration of a noise-whitening step. This strategy is validated on both synthetic and real images. The experimental results are very promising and show the accuracy of this algorithm with respect to state-of-the-art algorithms.

In this article, random matrix theory is used to propose a new K-means clustering algorithm via linear PCA. Our approach is devoted to linear PCA estimation when the number of the features d and the number of samples n go to infinity at the same rate. More precisely, we deal with the problem of building a consistent estimator of the eigenvectors of the covariance data matrix. Numerical results, based on the normalized mutual information (NMI) and the final error rate (ER), are provided and support our algorithm, even for a small number of features/samples. We also compare our approach to spectral clustering, K-means and traditional PCA methods.

In the context of multidimensional signals, the linear Wiener receiver is frequently encountered in wireless communication and in array processing; it is in fact the linear receiver that achieves the lowest level of interference. In this contribution, we focus on the study of the associated Signal-to-interference plus noise ratio (SINR) at its output in the context of Ricean multiple-input multiple-output (MIMO) channels. The case of Ricean channels, which induces non-centered random variables, can be encountered in several practical environments and has not been studied so far, as it raises substantial technical issues. With the help of large random matrix theory, which has shown to be fruitful to successfully address several problems in wireless communications, we study the behaviour of the SINR, together with its fluctuations via a central limit theorem. As realistic models also involve non-Gaussian random variables, we relax the Gaussian assumption. This results in an extra term involving the fourth cumulant in the expression of the variance.

This paper is devoted to the study of the performance of the linear minimum mean-square error (LMMSE) receiver for (receive) correlated multiple-input multiple-output (MIMO) systems. By the random matrix theory, it is well known that the signal-to-noise ratio (SNR) at the output of this receiver behaves asymptotically like a Gaussian random variable as the number of receive and transmit antennas converge to+infin at the same rate. However, this approximation being inaccurate for the estimation of some performance metrics such as the bit error rate (BER) and the outage probability, especially for small system dimensions, Li proposed convincingly to assume that the SNR follows a generalized gamma distribution which parameters are tuned by computing the first three asymptotic moments of the SNR. In this paper, this technique is generalized to (receive) correlated channels, and closed-form expressions for the first three asymptotic moments of the SNR are provided. To obtain these results, a random matrix theory technique adapted to matrices with Gaussian elements is used. This technique is believed to be simple, efficient, and of broad interest in wireless communications. Simulations are provided, and show that the proposed technique yields in general a good accuracy, even for small system dimensions.

This paper is devoted to the performance study of the linear minimum mean squared error (LMMSE) estimator for multidimensional signals in the large-dimension regime. Such an estimator is frequently encountered in wireless communications and in array processing, and the signal-to-interference-plus-noise ratio (SINR) at its output is a popular performance index. The SINR can be modeled as a random quadratic form which can be studied with the help of large random matrix theory, if one assumes that the dimension of the received and transmitted signals go to infinity at the same pace. This paper considers the asymptotic behavior of the SINR for a wide class of multidimensional signal models that includes general multiple-antenna as well as spread-spectrum transmission models. The expression of the deterministic approximation of the SINR in the large-dimension regime is recalled and the SINR fluctuations around this deterministic approximation are studied. These fluctuations are shown to converge in distribution to the Gaussian law in the large-dimension regime, and their variance is shown to decrease as the inverse of the signal dimension.