We propose a knowledge-informed variant for learning covariance-dependent data representations using unsupervised vector quantization. In particular, we consider linear data mappings included in vector quantization models, such as c-means++, neural gas, or self-organizing maps, to achieve representations in a lower-dimensional data space. To this end, we show how additional data knowledge can be integrated into the models. The additional data structure information is used to generate an appropriate data mapping depending on the corresponding structured data covariances.
We introduce SOUMAP (Self-Organizing Uniform Manifold Approximation and Projection) as an alternative to regular Self-Organizing Map (SOM) learning intended to improve clustering of the resulting output space. Improvement is achieved by abandoning the SOM's rigid lattice structure in favor of a more expressive output topology afforded by Uniform Manifold Approximation and Projection (UMAP), which is incrementally learned in conjunction with SOUMAP prototypes. As in regular SOM learning, the Hebbian connection formed between input and output spaces results in a topologically trustworthy low-dimensional embedding amenable to clustering. Through controlled experiments we show that SOUMAP's more expressive "lattice" improves the quality of clusterings obtained from it.
While high dimensionality and the selection of meaningful features is usually a burden in machine learning, it is even more so in the case of unsupervised learning and particularly in clustering. The presence of uninformative features may bias significantly the results of distance-based methods such as K-means for instance. For tackling this issue, different versions of sparse K-means have been introduced, building on the idea of adding some penalty terms in the loss function and resulting into automatic feature selection and/or weighting. This paper investigates the connections between some of these methods, and particularly the differences induced by the choices of the penalty terms. It also illustrates the algorithms and model selection tools made available through a recently implemented R package, vimpclust.
Data quality control is fundamental in data-driven analysis with machine learning (ML) models. In the domain of drug research, there is an increasing interest in the prediction of relevant biocompounds physicochemical properties with ML. In order to build predictive models of good quality, it is important to adequately select representative datasets. In this work, we combine ML prediction and Self-Organizing Maps-based exploration to build an interpretable machine learning model and to characterize those data that are most difficult to predict in the validation stage.
In this paper we propose the application of min-max-neurons for the use in generalized learning vector quantization (GLVQ) models, which correspond to min-max-prototypes. These prototypes can be identified with hyperboxes in the data space. Keeping the general GLVQ cost function, we redefine the Hebb-responsibilities for min-max-prototypes and derive consistent learning rules for stochastic gradient descent learning. We demonstrate that the resulting hyperbox-based GLVQ is capable to solve two illustrating toy classification tasks in robust manner, which can be dedicated to the use of robust min-max-prototypes. Finally, we give suggestions for future research for GLVQ based on min-max-prototypes.
