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Low-rank Dictionary Learning for Unsupervised Feature Selection

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 Publication date 2021
and research's language is English




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There exist many high-dimensional data in real-world applications such as biology, computer vision, and social networks. Feature selection approaches are devised to confront with high-dimensional data challenges with the aim of efficient learning technologies as well as reduction of models complexity. Due to the hardship of labeling on these datasets, there are a variety of approaches on feature selection process in an unsupervised setting by considering some important characteristics of data. In this paper, we introduce a novel unsupervised feature selection approach by applying dictionary learning ideas in a low-rank representation. Dictionary learning in a low-rank representation not only enables us to provide a new representation, but it also maintains feature correlation. Then, spectral analysis is employed to preserve sample similarities. Finally, a unified objective function for unsupervised feature selection is proposed in a sparse way by an $ell_{2,1}$-norm regularization. Furthermore, an efficient numerical algorithm is designed to solve the corresponding optimization problem. We demonstrate the performance of the proposed method based on a variety of standard datasets from different applied domains. Our experimental findings reveal that the proposed method outperforms the state-of-the-art algorithm.



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Feature selection is a prevalent data preprocessing paradigm for various learning tasks. Due to the expensive cost of acquiring supervision information, unsupervised feature selection sparks great interests recently. However, existing unsupervised feature selection algorithms do not have fairness considerations and suffer from a high risk of amplifying discrimination by selecting features that are over associated with protected attributes such as gender, race, and ethnicity. In this paper, we make an initial investigation of the fairness-aware unsupervised feature selection problem and develop a principled framework, which leverages kernel alignment to find a subset of high-quality features that can best preserve the information in the original feature space while being minimally correlated with protected attributes. Specifically, different from the mainstream in-processing debiasing methods, our proposed framework can be regarded as a model-agnostic debiasing strategy that eliminates biases and discrimination before downstream learning algorithms are involved. Experimental results on multiple real-world datasets demonstrate that our framework achieves a good trade-off between utility maximization and fairness promotion.
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In medical diagnosis, physicians predict the state of a patient by checking measurements (features) obtained from a sequence of tests, e.g., blood test, urine test, followed by invasive tests. As tests are often costly, one would like to obtain only those features (tests) that can establish the presence or absence of the state conclusively. Another aspect of medical diagnosis is that we are often faced with unsupervised prediction tasks as the true state of the patients may not be known. Motivated by such medical diagnosis problems, we consider a {it Cost-Sensitive Medical Diagnosis} (CSMD) problem, where the true state of patients is unknown. We formulate the CSMD problem as a feature selection problem where each test gives a feature that can be used in a prediction model. Our objective is to learn strategies for selecting the features that give the best trade-off between accuracy and costs. We exploit the `Weak Dominance property of problem to develop online algorithms that identify a set of features which provides an `optimal trade-off between cost and accuracy of prediction without requiring to know the true state of the medical condition. Our empirical results validate the performance of our algorithms on problem instances generated from real-world datasets.
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