In many computer vision applications, such as face recognition and hand pose estimation, we need systems that can recognize a very large number of classes. Large margin classification methods, such as AdaBoost and SVMs, often provide competitive accuracy rates, but at the cost of evaluating a large number of binary classifiers. We propose an embedding-based method for efficient multiclass recognition. In our method, patterns and classes are mapped to vectors in such a way that patterns and their associated classes tend to get mapped close to each other. This way, given a test pattern, a small set of candidate classes can be identified efficiently using simple vector comparisons. In experiments with 3D hand pose recognition (2430 classes) and face recognition (535 classes), our method is between 3 and 28 times faster compared to evaluating all binary classifiers, with negligible or no loss in classification accuracy.