Practically, we are often in the dilemma that the labeled data at hand are
inadequate to train a reliable classifier, and more seriously, some of these
labeled data may be mistakenly labeled due to the various human factors.
Therefore, this paper proposes a novel semi-supervised learning paradigm that
can handle both label insufficiency and label inaccuracy. To address label
insufficiency, we use a graph to bridge the data points so that the label
information can be propagated from the scarce labeled examples to unlabeled
examples along the graph edges. To address label inaccuracy, Graph Trend
Filtering (GTF) and Smooth Eigenbase Pursuit (SEP) are adopted to filter out
the initial noisy labels. GTF penalizes the l_0 norm of label difference
between connected examples in the graph and exhibits better local adaptivity
than the traditional l_2 norm-based Laplacian smoother. SEP reconstructs the
correct labels by emphasizing the leading eigenvectors of Laplacian matrix
associated with small eigenvalues, as these eigenvectors reflect real label
smoothness and carry rich class separation cues. We term our algorithm as
`Semi-supervised learning under Inadequate and Incorrect Supervision' (SIIS).
Thorough experimental results on image classification, text categorization, and
speech recognition demonstrate that our SIIS is effective in label error
correction, leading to superior performance to the state-of-the-art methods in
the presence of label noise and label scarcity.

本文提出了一种新颖的半监督学习范式，旨在解决标签不足和标签不准确的问题，该方法使用图来连接数据点以便在图边沿将标签信息从稀少标记示例传播到未标记的示例。实验证明，该方法在图像分类、文本分类和语音识别等领域有效降低标签误差，表现优于其他现有的半监督学习方法。

不充分和不正确监督下的学习

Learning with Inadequate and Incorrect Supervision

We introduce a family of adaptive estimators on graphs, based on penalizing
the $\ell_1$ norm of discrete graph differences. This generalizes the idea of
trend filtering [Kim et al. (2009), Tibshirani (2014)], used for univariate
nonparametric regression, to graphs. Analogous to the univariate case, graph
trend filtering exhibits a level of local adaptivity unmatched by the usual
$\ell_2$-based graph smoothers. It is also defined by a convex minimization
problem that is readily solved (e.g., by fast ADMM or Newton algorithms). We
demonstrate the merits of graph trend filtering through examples and theory.

基于离散图差的 L1 范数惩罚，我们介绍了一族图上的自适应估计器。该方法将非参数回归中的趋势滤波推广到图中，相当于 univariate case，它表现出一定程度的局部适应性，也是由一个凸优化问题定义的，可以很容易地通过高效 ADMM 或 Newton 算法进行求解。通过实例和理论，我们展示了图趋势滤波的优点。