Automatic classification methods widely used for diagnosing and analyzing COVID-19 cases. These methods assume known labels and rely on a single view of the dataset. Given the prevalence of COVID-19 cases and the extensive volume of patient records lacking labels, this communication underscores our unique approach—conducting the first study on COVID-19 case diagnosis in an unsupervised manner. Our work operates under the assumption of prior knowledge regarding the number of classes, such as COVID-19, pneumonia, and normal, in a case study. By adopting an unsupervised learning paradigm, we leverage the wealth of unlabeled data, reducing dependence on human experts for annotating numerous images. This paper introduces an enhanced version of a recent direct method where non-negative cluster indices and spectral embeddings are jointly estimated. Beyond the inherent advantages of this method, our proposed model introduces improvements through two additional types of constraints: (i) ensuring consistent smoothing of cluster labels across all views and (ii) imposing an orthogonality constraint on the matrix of cluster assignments. The efficacy of the proposed method is demonstrated using the public COVIDx dataset with three classes, showcasing promising results in categorizing radiographs. The proposed approach is tested on other public image datasets to assess its effectiveness.