Quantum-inspired learning vector quantizers for prototype-based classification

Prototype-based models like the Generalized Learning Vector Quantization (GLVQ) belong to the class of interpretable classifiers. Moreover, quantum-inspired methods get more and more into focus in machine learning due to its potential efficient computing. Further, its interesting mathematical perspectives offer new ideas for alternative learning scenarios. This paper proposes a quantum computing-inspired variant of the prototype-based GLVQ for classification learning. We start considering kernelized GLVQ with real- and complex-valued kernels and their respective feature mapping. Thereafter, we explain how quantum space ideas could be integrated into a GLVQ using quantum bit vector space in the quantum state space $${\mathcal {H}}^{n}$$ H n and show the relations to kernelized GLVQ. In particular, we explain the related feature mapping of data into the quantum state space $${\mathcal {H}}^{n}$$ H n . A key feature for this approach is that $${\mathcal {H}}^{n}$$ H n is an Hilbert space with particular inner product properties, which finally restrict the prototype adaptations to be unitary transformations. The resulting approach is denoted as Qu-GLVQ. We provide the mathematical framework and give exemplary numerical results.

Analysis of SARS-CoV-2 RNA-Sequences by Interpretable Machine Learning Models

We present an approach to investigate SARS-CoV-2 virus sequences based on alignment-free methods for RNA sequence comparison. In particular, we verify a given clustering result for the GISAID data set, which was obtained analyzing the molecular differences in coronavirus populations by phylogenetic trees. For this purpose, we use alignment-free dissimilarity measures for sequences and combine them with learning vector quantization classifiers for virus type discriminant analysis and classification. Those vector quantizers belong to the class of interpretable machine learning methods, which, on the one hand side provide additional knowledge about the classification decisions like discriminant feature correlations, and on the other hand can be equipped with a reject option. This option gives the model the property of self controlled evidence if applied to new data, i.e. the models refuses to make a classification decision, if the model evidence for the presented data is not given. After training such a classifier for the GISAID data set, we apply the obtained classifier model to another but unlabeled SARS-CoV-2 virus data set. On the one hand side, this allows us to assign new sequences to already known virus types and, on the other hand, the rejected sequences allow speculations about new virus types with respect to nucleotide base mutations in the viral sequences.Author summaryThe currently emerging global disease COVID-19 caused by novel SARS-CoV-2 viruses requires all scientific effort to investigate the development of the viral epidemy, the properties of the virus and its types. Investigations of the virus sequence are of special interest. Frequently, those are based on mathematical/statistical analysis. However, machine learning methods represent a promising alternative, if one focuses on interpretable models, i.e. those that do not act as black-boxes. Doing so, we apply variants of Learning Vector Quantizers to analyze the SARS-CoV-2 sequences. We encoded the sequences and compared them in their numerical representations to avoid the computationally costly comparison based on sequence alignments. Our resulting model is interpretable, robust, efficient, and has a self-controlling mechanism regarding the applicability to data. This framework was applied to two data sets concerning SARS-CoV-2. We were able to verify previously published virus type findings for one of the data sets by training our model to accurately identify the virus type of sequences. For sequences without virus type information (second data set), our trained model can predict them. Thereby, we observe a new scattered spreading of the sequences in the data space which probably is caused by mutations in the viral sequences.