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

• • • • Introduction Label Trees Label Embeddings Experiment result Outline

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

Introduction Label Tree: Indexed nodes: Edges: Label Predictors: 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.

Classifying an example: Introduction

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

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 Replace indicator function with hinge loss and Relaxation 2

Label tree Learning label tree structure for disjoint tree Basic idea: group together labels into the same label set that are likely to be confused at test time.

Treat A as the affinity matrix and apply the steps similar to spectral clustering

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

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

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

Dataset Experiment

Experiment

Experiment