###### Abstract  
The widespread availability of large amounts of genomic data on the SARS-CoV-2 virus, as a result of the COVID-19 pandemic, has created an opportunity for researchers to analyze the disease at a level of detail, unlike any virus before it. On the one hand, this will help biologists, policymakers, and other authorities to make timely and appropriate decisions to control the spread of the coronavirus. On the other hand, such studies will help to more effectively deal with any possible future pandemic. Since the SARS-CoV-2 virus contains different variants, each of them having different mutations, performing any analysis on such data becomes a difficult task, given the size of the data. It is well known that much of the variation in the SARS-CoV-2 genome happens disproportionately in the spike region of the genome sequence--the relatively short region which codes for the spike protein(s). In this paper, we propose a robust feature-vector representation of biological sequences that, when combined with the appropriate feature selection method, allows different downstream clustering approaches to perform well on a variety of different measures. We use such proposed approach with an array of clustering techniques to cluster spike protein sequences in order to study the behavior of different known variants that are increasing at a very high rate throughout the world. We use a \(k\)-mers based approach first to generate a fixed-length feature vector representation of the spike sequences. We then show that we can efficiently and effectively cluster the spike sequences based on the different variants with the appropriate feature selection. Using a publicly available set of SARS-CoV-2 spike sequences, we perform clustering of these sequences using both hard and soft clustering methods and show that, with our feature selection methods, we can achieve higher \(F_{1}\) scores for the clusters and also better clustering quality metrics compared to baselines. COVID-19; SARS-CoV-2; spike protein sequences; cluster analysis; feature selection; \(k\)-mers +
Footnote †: journal: Applied Topics in  
tural proteins are encoded by the S, E, M, and N genes, while the ORF region encodes nonstructural proteins [4] (see Figure 1). A key factor involved in infection is the S protein on the surface of the virus [5]. The S protein of SARS-CoV-2 is similar to other coronaviruses and arbitrates receptor recognition, fusion, and cell attachment through viral infection [6; 7; 8]. The S protein has an essential role in viral infection that makes it a potential target for vaccine development, antibody-blocking therapy, and small molecule inhibitors [9]. In addition, the spike region of the SARS-CoV-2 genome is involved in a disproportionate amount of the genomic variation, for its length [10] (see, e.g., Table 1). Therefore, mutations that affect the antigenicity of the S protein are of certain importance [11]. Generally, the genetic variations of a virus are grouped into clades, which can also be called subtypes, genotypes, or groups. To study the evolutionary dynamics of viruses, building cytogenetic trees out of sequences is common [16]. On the other hand, the number of available SARS-CoV-2 sequences is huge and still increasing [17]--building trees on the millions of SARS-CoV-2 sequences would be very expensive and seems impractical. In these cases, machine learning approaches that have flexibility and scalability could be useful [18]. Since natural clusters of the sequences are formed by the major clades, clustering methods would be useful to understand the complexity behind the spread of COVID-19 in terms of its variation. In addition, by considering the certain importance of the S protein, we focus on the amino acid (protein) sequences encoded by the spike region. In this way, we would reduce the dimensionality of data without losing too much information, reducing the time and storage space required and making visualization of the data easier [19].