Denis C. Ilie-Ablachim

Denis C. Ilie-Ablachim, Bogdan Dumitrescu, Cristian Rusu

This paper presents a kernelized version of the t-SNE algorithm, capable of mapping high-dimensional data to a low-dimensional space while preserving the pairwise distances between the data points in a non-Euclidean metric. This can be achieved using a kernel trick only in the high dimensional space or in both spaces, leading to an end-to-end kernelized version. The proposed kernelized version of the t-SNE algorithm can offer new views on the relationships between data points, which can improve performance and accuracy in particular applications, such as classification problems involving kernel methods. The differences between t-SNE and its kernelized version are illustrated for several datasets, showing a neater clustering of points belonging to different classes.

Denis C. Ilie-Ablachim, Bogdan Dumitrescu

In this paper we present a new classification method based on Dictionary Learning (DL). The main contribution consists of a kernel version of incoherent DL, derived from its standard linear counterpart. We also propose an improvement of the AK-SVD algorithm concerning the representation update. Our algorithms are tested on several popular databases of classification problems.

Denis C. Ilie-Ablachim, Bogdan Dumitrescu

In this paper we present new algorithms for training reduced-size nonlinear representations in the Kernel Dictionary Learning (KDL) problem. Standard KDL has the drawback of a large size of the kernel matrix when the data set is large. There are several ways of reducing the kernel size, notably Nyström sampling. We propose here a method more in the spirit of dictionary learning, where the kernel vectors are obtained with a trained sparse representation of the input signals. Moreover, we optimize directly the kernel vectors in the KDL process, using gradient descent steps. We show with three data sets that our algorithms are able to provide better representations, despite using a small number of kernel vectors, and also decrease the execution time with respect to KDL.

Denis C. Ilie-Ablachim, Bogdan Dumitrescu

In this paper we present new methods of anomaly detection based on Dictionary Learning (DL) and Kernel Dictionary Learning (KDL). The main contribution consists in the adaption of known DL and KDL algorithms in the form of unsupervised methods, used for outlier detection. We propose a reduced kernel version (RKDL), which is useful for problems with large data sets, due to the large kernel matrix. We also improve the DL and RKDL methods by the use of a random selection of signals, which aims to eliminate the outliers from the training procedure. All our algorithms are introduced in an anomaly detection toolbox and are compared to standard benchmark results.

Andra Băltoiu, Denis C. Ilie-Ablachim, Bogdan Dumitrescu

Recent work on dictionary learning with set-atoms has shown benefits in anomaly detection. Instead of viewing an atom as a single vector, these methods allow building sparse representations with atoms taken from a set around a central vector; the set can be a cone or may have a probability distribution associated to it. We propose a method for adaptively adjusting the size of set-atoms in Gaussian and cone dictionary learning. The purpose of the algorithm is to match the atom sizes with their contribution in representing the signals. The proposed algorithm not only decreases the representation error, but also improves anomaly detection, for a class of anomalies called `dependency'. We obtain better detection performance than state-of-the-art methods.