As with almost all data, museum collection catalogues are largely unstructured, variable in consistency and overwhelmingly composed of thin records. The form of these catalogues means that the potential for new forms of research, access and scholarly enquiry that range across multiple collections and related datasets remains dormant. In the project Heritage Connector: Transforming text into data to extract meaning and make connections, we are applying a battery of digital techniques to connect similar, identical and related items within and across collections and other publications. In this paper we describe a framework to create a Linked Open Data knowledge graph (KG) from digital museum catalogues, connect entities within this graph to Wikidata, and create new connections in this graph from text. We focus on the use of machine learning to create these links at scale with a small amount of labelled data, on a mid-range laptop or a small cloud virtual machine. We publish open-source software providing tools to perform the tasks of KG creation, entity matching and named entity recognition under these constraints.