A Unifying Probabilistic Framework for Partially Labeled Data Learning.

Partially labeled data learning (PLDL), including partial label learning (PLL) and partial multi-label learning (PML), has been widely used in nowadays data science. Researchers attempt to construct different specific models to deal with the different classification tasks for PLL and PML scenarios respectively. The main challenge in training classifiers for PLL and PML is how to deal with ambiguities caused by the noisy false-positive labels in the candidate label set. The state-of-the-art strategy for both scenarios is to perform disambiguation by identifying the ground-truth label(s) directly from the candidate label set, which can be summarized into two categories: 'the identifying method' and 'the embedding method'. However, both kinds of methods are constructed by hand-designed heuristic modeling under considerations like feature/label correlations with no theoretical interpretation. Instead of adopting heuristic or specific modeling, we propose a novel unifying framework called A Unifying Probabilistic Framework for Partially Labeled Data Learning (UPF-PLDL), which is derived from a clear probabilistic formulation, and brings existing research on PLL and PML under one theoretical interpretation with respect to information theory. Furthermore, the proposed UPF-PLDL also unifies 'the identifying method' and 'the embedding method' into one integrated framework, which naturally incorporates the feature and label correlation considerations. Comprehensive experiments on synthetic and real-world datasets for both PLL and PML scenarios clearly demonstrate the superiorities of the derived framework.

Discriminative Metric Learning for Partial Label Learning.

One simple strategy to deal with ambiguity in partial label learning (PLL) is to regard all candidate labels equally as the ground-truth label, and then solve the PLL problem using existing multiclass classification algorithms. However, due to the noisy false-positive labels in the candidate set, these approaches are readily mislead and do not generalize well in testing. Consequently, the method of identifying the ground-truth label straight from the candidate label set has grown popular and effective. When the labeling information in PLL is ambiguous, we ought to take advantage of the data's underlying structure, such as label and feature interdependencies, to conduct disambiguation. Furthermore, while metric learning is an excellent method for supervised learning classification that takes feature and label interdependencies into account, it cannot be used to solve the weekly supervised learning PLL problem directly due to the ambiguity of labeling information in the candidate label set. In this article, we propose an effective PLL paradigm called discriminative metric learning for partial label learning (DML-PLL), which aims to learn a Mahanalobis distance metric discriminatively while identifying the ground-truth label iteratively for PLL. We also design an efficient algorithm to alternatively optimize the metric parameter and the latent ground-truth label in an iterative way. Besides, we prove the convergence of the designed algorithms by two proposed lemmas. We additionally study the computational complexity of the proposed DML-PLL in terms of training and testing time for each iteration. Extensive experiments on both controlled UCI datasets and real-world PLL datasets from diverse domains demonstrate that the proposed DML-PLL regularly outperforms the compared approaches in terms of prediction accuracy.

Top-k Partial Label Machine.

To deal with ambiguities in partial label learning (PLL), the existing PLL methods implement disambiguations, by either identifying the ground-truth label or averaging the candidate labels. However, these methods can be easily misled by the false-positive labels in the candidate label set. We find that these ambiguities often originate from the noise caused by highly correlated or overlapping candidate labels, which leads to the difficulty in identifying the ground-truth label on the first attempt. To give the trained models more tolerance, we first propose the top-k partial loss and convex top-k partial hinge loss. Based on the losses, we present a novel top-k partial label machine (TPLM) for partial label classification. An efficient optimization algorithm is proposed based on accelerated proximal stochastic dual coordinate ascent (Prox-SDCA) and linear programming (LP). Moreover, we present a theoretical analysis of the generalization error for TPLM. Comprehensive experiments on both controlled UCI datasets and real-world partial label datasets demonstrate that the proposed method is superior to the state-of-the-art approaches.

A novel Z-scheme porous g-C3N4 nanosheet/Ag3PO4 photocatalyst decorated with N-doped CDs for high efficiency removal of antibiotics.

A number of porous g-C3N4 nanosheet/Ag3PO4/NCDs (PCNNS/AP/NCDs) with little amounts of Ag3PO4 were synthesized via an in situ sedimentation-calcination method. The PCNNS/AP/NCDs photocatalyst exhibited excellent photocatalytic performance for the photocatalytic degradation of tetracycline (TC) under visible light irradiation at a removal rate of 90.5% in 40 min. The study of the reaction kinetics of the as-prepared samples was in accordance with the pseudo-second-order kinetics, with the correlation coefficient (R2) being greater than 0.9776. Meanwhile, the photocatalyst was capable of degrading ciprofloxacin (CIP), and showed good performance even under actual water conditions with natural sunlight irradiation, indicating that the photocatalyst has wide practical applications. In addition, the photocatalytic performance and the XRD and FTIR spectra showed no obvious changes even after four photocatalytic degradation cycles, which revealed the high stability of the PCNNS/AP/NCDs photocatalyst. Furthermore, the possible degradation pathways of TC and the possible Z-scheme mechanism were proposed with ˙O2- and h+ as the main active species contributing to photocatalytic degradation. The results provide a novel insight into the fabrication of Z-scheme PCNNS/AP/NCDs and introduce them as an efficient visible-light-responsive photocatalyst for use in practical applications.

Mining Top K Spread Sources for a Specific Topic and a Given Node.

In social networks, nodes (or users) interested in specific topics are often influenced by others. The influence is usually associated with a set of nodes rather than a single one. An interesting but challenging task for any given topic and node is to find the set of nodes that represents the source or trigger for the topic and thus identify those nodes that have the greatest influence on the given node as the topic spreads. We find that it is an NP-hard problem. This paper proposes an effective framework to deal with this problem. First, the topic propagation is represented as the Bayesian network. We then construct the propagation model by a variant of the voter model. The probability transition matrix (PTM) algorithm is presented to conduct the probability inference with the complexity O(θ(3)log2θ), while θ is the number nodes in the given graph. To evaluate the PTM algorithm, we conduct extensive experiments on real datasets. The experimental results show that the PTM algorithm is both effective and efficient.