Which unsupervised learning algorithm attempts to describe observations as a mixture of distinct categories?

The chosen answer, which involves Amazon SageMaker Latent Dirichlet Allocation (LDA), is correct as it is specifically designed for topic modeling, a technique used within unsupervised learning to discover the underlying categorical structure in a set of documents. LDA operates on the principle that documents can be represented as mixtures of topics, where each topic is characterized by a distribution over words. This approach allows users to find patterns in the data by revealing the hidden thematic structure.

Unlike other algorithms mentioned, LDA effectively handles the probabilistic distribution of topics across documents and can model how a document can belong to multiple themes simultaneously. This capability to describe observations as mixtures of distinct categories makes LDA particularly suited for tasks involving natural language processing, such as determining the topics within large collections of text.

K-Means focuses on partitioning data into distinct groups rather than identifying overlapping categories. Principal Component Analysis reduces dimensionality without explicitly categorizing observations into topics. Factorization Machines are used primarily for prediction tasks and are suited for high-dimensional sparse data but do not specialize in topic modeling. Thus, LDA stands out as the most appropriate choice for the question posed.