Dual Query: Practical Private Query Release for High Dimensional Data

We present a practical, differentially private algorithm for answering a large number of queries on high dimensional datasets. Like all algorithms for this task, ours necessarily has worst-case complexity exponential in the dimension of the data. However, our algorithm packages the computationally hard step into a concisely defined integer program, which can be solved non-privately using standard solvers. We prove accuracy and privacy theorems for our algorithm, and then demonstrate experimentally that our algorithm performs well in practice. For example, our algorithm can efficiently and accurately answer millions of queries on the Netflix dataset, which has over 17,000 attributes; this is an improvement on the state of the art by multiple orders of magnitude.

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Subspace Clustering for High-Dimensional Data Using Cluster Structure Similarity

International Journal of Intelligent Information Technologies ◽

10.4018/ijiit.2018070103 ◽

2018 ◽

Vol 14 (3) ◽

pp. 38-55 ◽

Cited By ~ 2

Author(s):

Kavan Fatehi ◽

Mohsen Rezvani ◽

Mansoor Fateh ◽

Mohammad-Reza Pajoohan

Keyword(s):

Similarity Measure ◽

State Of The Art ◽

Clustering Algorithms ◽

Cluster Structure ◽

High Dimensional Data ◽

Subspace Clustering ◽

The State ◽

High Dimensional ◽

Running Time ◽

Structure Similarity

This article describes how recently, because of the curse of dimensionality in high dimensional data, a significant amount of research has been conducted on subspace clustering aiming at discovering clusters embedded in any possible attributes combination. The main goal of subspace clustering algorithms is to find all clusters in all subspaces. Previous studies have mostly been generating redundant subspace clusters, leading to clustering accuracy loss and also increasing the running time of the algorithms. A bottom-up density-based approach is suggested in this article, in which the cluster structure serves as a similarity measure to generate the optimal subspaces which result in raising the accuracy of the subspace clustering. Based on this idea, the algorithm discovers similar subspaces by considering similarity in their cluster structure, then combines them and the data in the new subspaces would be clustered again. Finally, the algorithm determines all the subspaces and also finds all clusters within them. Experiments on various synthetic and real datasets show that the results of the proposed approach are significantly better in quality and runtime than the state-of-the-art on clustering high-dimensional data.

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Utility metric for unsupervised feature selection

PeerJ Computer Science ◽

10.7717/peerj-cs.477 ◽

2021 ◽

Vol 7 ◽

pp. e477

Author(s):

Amalia Villa ◽

Abhijith Mundanad Narayanan ◽

Sabine Van Huffel ◽

Alexander Bertrand ◽

Carolina Varon

Keyword(s):

Feature Selection ◽

Manifold Learning ◽

State Of The Art ◽

High Dimensional Data ◽

Subset Selection ◽

The State ◽

Computational Time ◽

High Dimensional ◽

Learning Stage ◽

Unsupervised Feature Selection

Feature selection techniques are very useful approaches for dimensionality reduction in data analysis. They provide interpretable results by reducing the dimensions of the data to a subset of the original set of features. When the data lack annotations, unsupervised feature selectors are required for their analysis. Several algorithms for this aim exist in the literature, but despite their large applicability, they can be very inaccessible or cumbersome to use, mainly due to the need for tuning non-intuitive parameters and the high computational demands. In this work, a publicly available ready-to-use unsupervised feature selector is proposed, with comparable results to the state-of-the-art at a much lower computational cost. The suggested approach belongs to the methods known as spectral feature selectors. These methods generally consist of two stages: manifold learning and subset selection. In the first stage, the underlying structures in the high-dimensional data are extracted, while in the second stage a subset of the features is selected to replicate these structures. This paper suggests two contributions to this field, related to each of the stages involved. In the manifold learning stage, the effect of non-linearities in the data is explored, making use of a radial basis function (RBF) kernel, for which an alternative solution for the estimation of the kernel parameter is presented for cases with high-dimensional data. Additionally, the use of a backwards greedy approach based on the least-squares utility metric for the subset selection stage is proposed. The combination of these new ingredients results in the utility metric for unsupervised feature selection U2FS algorithm. The proposed U2FS algorithm succeeds in selecting the correct features in a simulation environment. In addition, the performance of the method on benchmark datasets is comparable to the state-of-the-art, while requiring less computational time. Moreover, unlike the state-of-the-art, U2FS does not require any tuning of parameters.

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