By Linlin Jia, Benoit Gaüzère, Florian Yger, and Paul Honeine.
In Proceedings of the IAPR Joint International Workshops on Statistical Techniques in Pattern Recognition (SPR) and Structural and Syntactic Pattern Recognition (S+SSPR), Venice, Italy, 21 – 22 January 2021.
by Thi Phuong Thao Tran, Ahlame Douzal-Chouakria, Saeed Varasteh Yazdi, Paul Honeine, Patrick Gallinari.
Paper published in Artificial Intelligence (Volume 286, September 2020, 103342):
Abstract. Kernel methods are known to be effective to analyse complex objects by implicitly embedding them into some feature space. To interpret and analyse the obtained results, it is often required to restore in the input space the results obtained in the feature space, by using pre-image estimation methods. This work proposes a new closed-form pre-image estimation method for time series kernel analytics that consists of two steps. In the first step, a time warp function, driven by distance constraints in the feature space, is defined to embed time series in a metric space where analytics can be performed conveniently. In the second step, the time series pre-image estimation is cast as learning a linear (or a nonlinear) transformation that ensures a local isometry between the time series embedding space and the feature space. The proposed method is compared to the state of the art through three major tasks that require pre-image estimation: 1) time series averaging, 2) time series reconstruction and denoising and 3) time series representation learning. The extensive experiments conducted on 33 publicly-available datasets show the benefits of the pre-image estimation for time series kernel analytics.
By Pierre Laforgue, Alex Lambert, Luc Brogat-Motte, Florence d’Alche-Buc.
In Proceedings of the 37th International Conference on Machine Learning (ICML), Online, PMLR 119, 2020.
Abstract. Operator-Valued Kernels (OVKs) and associated vector-valued Reproducing Kernel Hilbert Spaces provide an elegant way to extend scalar kernel methods when the output space is a Hilbert space. Although primarily used in finite dimension for problems like multi-task regression, the ability of this framework to deal with infinite dimensional output spaces unlocks many more applications, such as functional regression, structured output prediction, and structured data representation. However, these sophisticated schemes crucially rely on the kernel trick in the output space, so that most of previous works have focused on the square norm loss function, completely neglecting robustness issues that may arise in such surrogate problems. To overcome this limitation, this paper develops a duality approach that allows to solve OVK machines for a wide range of loss functions. The infinite dimensional Lagrange multipliers are handled through a Double Representer Theorem, and algorithms for epsilon-insensitive losses and the Huber loss are thoroughly detailed. Robustness benefits are emphasized by a theoretical stability analysis, as well as empirical improvements on structured data applications.
By Fei Zhu, Paul Honeine, Jie Chen.
In Proc. 45th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Barcelona, Spain, 4 – 8 May 2020.
link paper doi:10.1109/ICASSP40776.2020.9053239
Abstract. Nonlinear spectral unmixing is a challenging and important task in hyperspectral image analysis. The kernel-based bi-objective non-negative matrix factorization (Bi-NMF) has shown its usefulness in nonlinear unmixing; However, it suffers several issues that prohibit its practical application. In this work, we propose an unsupervised nonlinear unmixing method that overcomes these weaknesses. Specifically, the new method introduces into each pixel a parameter that adjusts the nonlinearity therein. These parameters are jointly optimized with endmembers and abundances, using a carefully designed objective function by multiplicative update rules. Experiments on synthetic and real datasets confirm the effectiveness of the proposed method.