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Found 22 papers, 6 papers with code
Approximate Algorithms For $k$-Sparse Wasserstein Barycenter With Outliers
First, we investigate the relation between $k$-sparse WB with outliers and the clustering (with outliers) problems.
A Novel Skip Orthogonal List for Dynamic Optimal Transport Problem
Optimal transport is a fundamental topic that has attracted a great amount of attention from the optimization community in the past decades.
Randomized Greedy Algorithms and Composable Coreset for k-Center Clustering with Outliers
Though a number of methods have been developed in the past decades, it is still quite challenging to design quality guaranteed algorithm with low complexity for this problem.
Sublinear Time Algorithms for Several Geometric Optimization (With Outliers) Problems In Machine Learning
Under the stability assumption, we present two sampling algorithms for computing radius-approximate MEB with sample complexities independent of the number of input points $n$.
Coresets for Wasserstein Distributionally Robust Optimization Problems
Though it is challenging to obtain a conventional coreset for \textsf{WDRO} due to the uncertainty issue of ambiguous data, we show that we can compute a ``dual coreset'' by using the strong duality property of \textsf{WDRO}.
Coresets for Relational Data and The Applications
A coreset is a small set that can approximately preserve the structure of the original input data set.
A Data-dependent Approach for High Dimensional (Robust) Wasserstein Alignment
Our framework is a ``data-dependent'' approach that has the complexity depending on the intrinsic dimension of the input data.
A Novel Sequential Coreset Method for Gradient Descent Algorithms
A wide range of optimization problems arising in machine learning can be solved by gradient descent algorithms, and a central question in this area is how to efficiently compress a large-scale dataset so as to reduce the computational complexity.
Solving Soft Clustering Ensemble via $k$-Sparse Discrete Wasserstein Barycenter
Clustering ensemble is one of the most important problems in ensemble learning.
Robust and Fully-Dynamic Coreset for Continuous-and-Bounded Learning (With Outliers) Problems
In this paper, we propose a novel robust coreset method for the {\em continuous-and-bounded learning} problems (with outliers) which includes a broad range of popular optimization objectives in machine learning, {\em e. g.,} logistic regression and $ k $-means clustering.
Is Simple Uniform Sampling Effective for Center-Based Clustering with Outliers: When and Why?
Real-world datasets often contain outliers, and the presence of outliers can make the clustering problems to be much more challenging.
Gradient Episodic Memory with a Soft Constraint for Continual Learning
Catastrophic forgetting in continual learning is a common destructive phenomenon in gradient-based neural networks that learn sequential tasks, and it is much different from forgetting in humans, who can learn and accumulate knowledge throughout their whole lives.
Defending SVMs against Poisoning Attacks: the Hardness and DBSCAN Approach
For the data sanitization defense, we link it to the intrinsic dimensionality of data; in particular, we provide a sampling theorem in doubling metrics for explaining the effectiveness of DBSCAN (as a density-based outlier removal method) for defending against poisoning attacks.
The Effectiveness of Johnson-Lindenstrauss Transform for High Dimensional Optimization With Adversarial Outliers, and the Recovery
We focus on two fundamental optimization problems: {\em SVM with outliers} and {\em $k$-center clustering with outliers}.
The Effectiveness of Uniform Sampling for Center-Based Clustering with Outliers
The experiments suggest that the uniform sampling method can achieve comparable clustering results with other existing methods, but greatly reduce the running times.
Minimum Enclosing Ball Revisited: Stability and Sub-linear Time Algorithms
Though the problem has been extensively studied before, most of the existing algorithms need at least linear time (in the number of input points $n$ and the dimensionality $d$) to achieve a $(1+\epsilon)$-approximation.
Greedy Strategy Works for $k$-Center Clustering with Outliers and Coreset Construction
Our idea is inspired by the greedy method, Gonzalez's algorithm, for solving the problem of ordinary $k$-center clustering.
On Geometric Alignment in Low Doubling Dimension
In real-world, many problems can be formulated as the alignment between two geometric patterns.
A Unified Framework for Clustering Constrained Data without Locality Property
To overcome the difficulty caused by the loss of locality, we present in this paper a unified framework, called {\em Peeling-and-Enclosing (PnE)}, to iteratively solve two variants of the constrained clustering problems, {\em constrained $k$-means clustering} ($k$-CMeans) and {\em constrained $k$-median clustering} ($k$-CMedian).
Faster Balanced Clusterings in High Dimension
For the balanced $k$-center clustering, we provide a $4$-approximation algorithm that improves the existing approximation factors; for the balanced $k$-median and $k$-means clusterings, our algorithms yield constant and $(1+\epsilon)$-approximation factors with any $\epsilon>0$.
k-Prototype Learning for 3D Rigid Structures
In this paper, we study the following new variant of prototype learning, called {\em $k$-prototype learning problem for 3D rigid structures}: Given a set of 3D rigid structures, find a set of $k$ rigid structures so that each of them is a prototype for a cluster of the given rigid structures and the total cost (or dissimilarity) is minimized.
Gauging Association Patterns of Chromosome Territories via Chromatic Median
In this paper, we introduce a novel algorithmic tool for investigating association patterns of chromosome territories in a population of cells.
