Developing an effective automatic classifier to separate genuine sources from artifacts is essential for transient follow-ups in wide-field optical surveys. The identification of transient detections from the subtraction artifacts after the image differencing process is a key step in such classifiers, known as real-bogus classification problem. We apply a self-supervised machine learning model, the deep-embedded self-organizing map (DESOM) to this 'real-bogus' classification problem. DESOM combines an autoencoder and a self-organizing map to perform clustering in order to distinguish between real and bogus detections, based on their dimensionality-reduced representations. We use 32 x 32 normalized detection thumbnails as the input of DESOM. We demonstrate different model training approaches, and find that our best DESOM classifier shows a missed detection rate of 6.6 per cent with a false-positive rate of 1.5 per cent. DESOM offers a more nuanced way to fine-tune the decision boundary identifying likely real detections when used in combination with other types of classifiers, e.g. built on neural networks or decision trees. We also discuss other potential usages of DESOM and its limitations.