Recommender systems suggest to users items that they might like (e.g., news articles, songs, movies) and, in doing so, they help users deal with information overload and enjoy a personalized experience. One of the main problems of these systems is the item cold-start, i.e., when a new item is introduced in the system and no past information is available, then no effective recommendations can be produced. The item cold-start is a very common problem in practice: modern online platforms have hundreds of new items published every day. To address this problem, we propose to learn Local Collective Embeddings: a matrix factorization that exploits items' properties and past user preferences while enforcing the manifold structure exhibited by the collective embeddings. We present a learning algorithm based on multiplicative update rules that are efficient and easy to implement. The experimental results on two item cold-start use cases: news recommendation and email recipient recommendation, demonstrate the effectiveness of this approach and show that it significantly outperforms six state-of-the-art methods for item cold-start.