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Found 26 papers, 2 papers with code
Differentially-Private Hierarchical Clustering with Provable Approximation Guarantees
Then, we exhibit a polynomial-time approximation algorithm with $O(|V|^{2. 5}/ \epsilon)$-additive error, and an exponential-time algorithm that meets the lower bound.
Private estimation algorithms for stochastic block models and mixture models
For the latter, we design an $(\epsilon, \delta)$-differentially private algorithm that recovers the centers of the $k$-mixture when the minimum separation is at least $ O(k^{1/t}\sqrt{t})$.
Improved Coresets for Euclidean $k$-Means
the Euclidean $k$-median problem) consists of finding $k$ centers such that the sum of squared distances (resp.
Scalable Differentially Private Clustering via Hierarchically Separated Trees
We study the private $k$-median and $k$-means clustering problem in $d$ dimensional Euclidean space.
Beyond Impossibility: Balancing Sufficiency, Separation and Accuracy
Among the various aspects of algorithmic fairness studied in recent years, the tension between satisfying both \textit{sufficiency} and \textit{separation} -- e. g. the ratios of positive or negative predictive values, and false positive or false negative rates across groups -- has received much attention.
Improved Approximations for Euclidean $k$-means and $k$-median, via Nested Quasi-Independent Sets
Motivated by data analysis and machine learning applications, we consider the popular high-dimensional Euclidean $k$-median and $k$-means problems.
Near-Optimal Correlation Clustering with Privacy
Correlation clustering is a central problem in unsupervised learning, with applications spanning community detection, duplicate detection, automated labelling and many more.
Towards Optimal Lower Bounds for k-median and k-means Coresets
Given a set of points in a metric space, the $(k, z)$-clustering problem consists of finding a set of $k$ points called centers, such that the sum of distances raised to the power of $z$ of every data point to its closest center is minimized.
On Complexity of 1-Center in Various Metrics
Moreover, we extend one of our hardness results to rule out subquartic algorithms for the well-studied 1-median problem in the edit metric, where given a set of n strings each of length n, the goal is to find a string in the set that minimizes the sum of the edit distances to the rest of the strings in the set.
Improved Coresets and Sublinear Algorithms for Power Means in Euclidean Spaces
Special cases of problem include the well-known Fermat-Weber problem -- or geometric median problem -- where $z = 1$, the mean or centroid where $z=2$, and the Minimum Enclosing Ball problem, where $z = \infty$. We consider these problem in the big data regime. Here, we are interested in sampling as few points as possible such that we can accurately estimate $m$. More specifically, we consider sublinear algorithms as well as coresets for these problems. Sublinear algorithms have a random query access to the $A$ and the goal is to minimize the number of queries. Here, we show that $\tilde{O}(\varepsilon^{-z-3})$ samples are sufficient to achieve a $(1+\varepsilon)$ approximation, generalizing the results from Cohen, Lee, Miller, Pachocki, and Sidford [STOC '16] and Inaba, Katoh, and Imai [SoCG '94] to arbitrary $z$.
Parallel and Efficient Hierarchical k-Median Clustering
In this paper we introduce a new parallel algorithm for the Euclidean hierarchical $k$-median problem that, when using machines with memory $s$ (for $s\in \Omega(\log^2 (n+\Delta+d))$), outputs a hierarchical clustering such that for every fixed value of $k$ the cost of the solution is at most an $O(\min\{d, \log n\} \log \Delta)$ factor larger in expectation than that of an optimal solution.
Johnson Coverage Hypothesis: Inapproximability of k-means and k-median in L_p metrics
We then show that together with generalizations of the embedding techniques introduced by Cohen-Addad and Karthik (FOCS '19), JCH implies hardness of approximation results for k-median and k-means in $\ell_p$-metrics for factors which are close to the ones obtained for general metrics.
Correlation Clustering in Constant Many Parallel Rounds
Correlation clustering is a central topic in unsupervised learning, with many applications in ML and data mining.
Fast and Accurate $k$-means++ via Rejection Sampling
$k$-means++ \cite{arthur2007k} is a widely used clustering algorithm that is easy to implement, has nice theoretical guarantees and strong empirical performance.
On the Power of Louvain in the Stochastic Block Model
A classic problem in machine learning and data analysis is to partition the vertices of a network in such a way that vertices in the same set are densely connected and vertices in different sets are loosely connected.
On Approximability of Clustering Problems Without Candidate Centers
In practice and historically, k-means is thought of in a continuous setting, namely where the centers can be located anywhere in the metric space.
On Efficient Low Distortion Ultrametric Embedding
In this paper, we provide a new algorithm which takes as input a set of points $P$ in $\mathbb{R}^d$, and for every $c\ge 1$, runs in time $n^{1+\frac{\rho}{c^2}}$ (for some universal constant $\rho>1$) to output an ultrametric $\Delta$ such that for any two points $u, v$ in $P$, we have $\Delta(u, v)$ is within a multiplicative factor of $5c$ to the distance between $u$ and $v$ in the "best" ultrametric representation of $P$.
Fully Dynamic Consistent Facility Location
This improves over the naive algorithm which consists in recomputing a solution at each time step and that can take up to $O(n^2)$ update time, and $O(n^2)$ total recourse.
Subquadratic High-Dimensional Hierarchical Clustering
We consider the widely-used average-linkage, single-linkage, and Ward's methods for computing hierarchical clusterings of high-dimensional Euclidean inputs.
Online k-means Clustering
The specific formulation we use is the $k$-means objective: At each time step the algorithm has to maintain a set of k candidate centers and the loss incurred is the squared distance between the new point and the closest center.
Clustering Redemption–Beyond the Impossibility of Kleinberg’s Axioms
In this work, we take a different approach, based on the observation that the consistency axiom fails to be satisfied when the “correct” number of clusters changes.
Instance-Optimality in the Noisy Value-and Comparison-Model --- Accept, Accept, Strong Accept: Which Papers get in?
In this paper, we show optimal worst-case query complexity for the \textsc{max},\textsc{threshold-$v$} and \textsc{Top}-$k$ problems.
Hierarchical Clustering Beyond the Worst-Case
Hiererachical clustering, that is computing a recursive partitioning of a dataset to obtain clusters at increasingly finer granularity is a fundamental problem in data analysis.
Hierarchical Clustering: Objective Functions and Algorithms
For similarity-based hierarchical clustering, Dasgupta showed that the divisive sparsest-cut approach achieves an $O(\log^{3/2} n)$-approximation.
On the Local Structure of Stable Clustering Instances
We study the classic $k$-median and $k$-means clustering objectives in the beyond-worst-case scenario.
Online Optimization of Smoothed Piecewise Constant Functions
We study online optimization of smoothed piecewise constant functions over the domain [0, 1).
