基於矩陣分解模型的多標籤排序與分級的多標籤預測

Abstract

多標籤分類在機器學習領域是一個常見的問題。此問題還可以更進一步的做延伸，我們稱作標籤排序以及多標籤預測。在這篇論文中，我們主要的問題是這兩類問題的一個特例，即多標籤為部分被觀察到的。我們提出了一個基於矩陣分解的模型來處理這類問題。最基本的想法為，利用矩陣分解模型我們可以學習標籤的分數或排名並考慮標籤之間的相關性。利用此相關性，我們的模型仍可因為考慮相關性而有較佳的效能。同時，我們也提出了一個結合基於事例和基於模型的方法。根據我們的實驗，我們可以看出矩陣分解模型表現得比線性模型還要好。結合基於事例和基於模型的方法，也可以更進一步改善方法的效能。同時我們也比較了矩陣分解模型和成列、成對和點的目標函數結合的效果，結果證實成列的目標函數是表現最好的。

Multi-label classification has attracted much attention in these days. The extension of the multi-label classification problem are the label ranking or and graded multi-label prediction problems. In this thesis, we focus on a special case of these two extension problem where only partial ranking or incomplete label are observed. We propose a matrix factorization approach to deal these problems. The merit of the matrix factorization model is that it can learn rating or ranking of labels and model the correlations between labels simultaneously. With this model, we can still learn well because our model considering the correlations between labels during training. We also propose a method to combine instance-based model into model-based approach. The experiments show that the matrix factorization model can outperform the baseline model, especially when our target is low rank matrix or training data is insufficient. Combining instance-based method can further boost the performance of our model. We also compare different loss functions combining with matrix factorization, and show that listwise loss can outperform others.