The surge in interest in Artificial Intelligence (AI) over the past decade has been driven almost exclusively by advances in Artificial Neural Networks (ANNs). While ANNs set state-of-the-art performance for many previously intractable problems, the use of global gradient descent necessitates large datasets and computational resources for training, potentially limiting their scalability for real-world domains. Spiking Neural Networks (SNNs) are an alternative to ANNs that use more brain-like artificial neurons and can use local unsupervised learning to rapidly discover sparse recognizable features in the input data. SNNs, however, struggle with dynamical stability and have failed to match the accuracy of ANNs. Here we show how an SNN can overcome many of the shortcomings that have been identified in the literature, including offering a principled solution to the dynamical "vanishing spike problem", to outperform all existing shallow SNNs and equal the performance of an ANN. It accomplishes this while using unsupervised learning with unlabeled data and only 1/50th of the training epochs (labeled data is used only for a simple linear readout layer). This result makes SNNs a viable new method for fast, accurate, efficient, explainable, and re-deployable machine learning with unlabeled data.