Paper notes: Dynamic Label propagation for semi-supervised multi-class Multi-label Classification ICCV 2013

　　Dynamic Label propagation for semi-supervised multi-class multi-label classification

ICCV 2013

In the semi-supervised learning method based on graph, the accuracy of classification is highly dependent on the accuracy of the available tagged data and similarity measures. Here, this paper presents a semi-supervised multi-class and multi-label classification mechanism, dynamic label propagation (DLP), which is passed in a dynamic process, performing transductive learning. The existing semi-supervised methods are generally difficult to deal with multi-label/multi-classification problems, because of the lack of consideration of the relationship between labels, the method proposed in this paper focuses on dynamic measurement and label information Fusion.

　　

　　the supervised metric learning method often learns the Markov distance (Mahalanobis distance), trying to narrow the distance between the same tags, while keeping or pulling the distance between the different label images as much as possible. the graph-based supervised learning framework uses a small amount of tagged information to mine a large amount of information about untagged data. label Propagation specifically believes that in a graph through the information transmission, there is a greater similarity by the edge of the linked point tends to have the same label. Another type of supervised learning method, co- training (co-training), uses multi-view features to help each other, pulls in untagged data to retrain and enhance the classifier (by pulling out unlabeled data to Re-train and enhance the classifiers).

The above methods are generally used to deal with the two classification problem, for multi-classification/multi-label problem, the label transfer algorithm has a problem, need some extra action. A common approach to multi-classification and multi-label learning is to leverage the one vs all strategy. However, the disadvantage is that the relationships between different categories cannot be fully processed. With the relationship between categories, the effect of classification is significantly improved.

In this paper, we propose a new, DLP to handle multi-label/multi-classification problems at the same time. The label relationship and the example similarity (label correlations and instance similarities) are combined into a new way of performing label passing. The intuition in DLP is a dynamic update of similarity metrics by fusing multi-label/multi-classification information, which can be understood in a probabilistic framework. The KNN matrix is used to store the intrinsic structure of the input data.

　　Review:label Propagation

Given a finite weighted graph G = (V, E, W), the vertex of the graph is each sample, which is composed of X = {XI, i = 1...N}, and the set of Edge E is: V*v, nonnegative symmetric weighting function w:e->[0, 1]. W (I,J) is considered >0 if there is an edge connected between the sample XI XJ. We use the weight function w (i, j) as a similarity metric for the sample XI XJ. If the metric matrix defined on the diagram is:

where h (x) = exp(-X), two parameters in the denominator are hyper-parameters,/delta is learned by the mean distance to k-nearest neighborhoods (the average distance to K nearest neighbors?? ？ Not quite understood here ).

A very natural transition matrix for vertex v can be defined as a normalized weight matrix:　　

So Σj∈v P (i, j) = 1. The note:p becomes symmetrical after normalization.

The dataset table is X = {xl U Xu}, and XL indicates that the label data Xu represents untagged data. In the process of label delivery, it is very important that:clamping, that is, after each iteration, the label data label will be reset, this is to exclude interference, because these tagged data do not need to propagation, so as long as there is a change, it will be reset back. For the two classification of LP, the author suggested reading the relevant reference, for the multi-classification problem, 1-OF-C, so the label matrix is: y = [Y (l), Y (u)];n is the number of data points, C is the number of categories. Y (l) is a label matrix with tagged data, and y (u) is a label matrix for untagged data. Set Y (L) (i, k) = 1, or 0 if XI is labeled as Category K. During the iteration, the iteration performs two columns of two steps:

1. Labels is propagated Yt = P * Yt-1.

2. Labels of labeled Data Xl is reset.

The main flow of the algorithm is as follows:

Dynamic Label Propagation:

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Paper notes: Dynamic Label propagation for semi-supervised multi-class multi-label classification ICCV