1. Label Embedding Trees for Large Multi-class Tasks Samy Bengio Jason Weston David Grangier Presented by Zhengming Xing

2. Outline Introduction Label Trees Label Embeddings Experiment result

3. Introduction Main idea: propose a fast and memory saving multi-class classifier for large dataset based on trees structure method Large scale problem: the number of example Feature dimension Number of class

4. Introduction Label Tree: Label Predictors: Indexed nodes: Edges: Label sets: The root contain all classes, and each child label set is a subset of its parent K is the number of classes Disjoint tree: any two nodes at the same depth cannot share any labels.

5. Introduction Classifying an example:

6. Label Trees Tree loss I is the indicator function is the depth in the tree of the final prediction for x

7. Label tree Learning with fixed label tree: N,E,L chosen in advance Goal: minimize the tree loss over the variables F Given training data Relaxation 1 Relaxation 2 Replace indicator function with hinge loss and

8. Label tree Learning label tree structure for disjoint tree Treat A as the affinity matrix and apply the steps similar to spectral clustering Basic idea: group together labels into the same label set that are likely to be confused at test time.

9. Label embeddings is a k-dimensional vector with a 1 in the yth position and 0 otherwise Problem : how to learn W, V define solve

10. Label embeddings Method 1: The same two steps of algorithm 2 Learn V Learn W minimize

11. Label embedding Combine all the methods discussed above Method 2: join learn W and V minimize

12. Experiment Dataset

13. Experiment