Related papers: Simple and sharp analysis of k-means||
Dependent rounding is a useful technique for optimization problems with hard budget constraints. This framework naturally leads to \emph{negative correlation} properties. However, what if an application naturally calls for dependent…
In their seminal work on the Stable Marriage Problem, Gale and Shapley describe an algorithm which finds a stable matching in $O(n^2)$ communication rounds. Their algorithm has a natural interpretation as a distributed algorithm where each…
In recent years, data streaming has gained prominence due to advances in technologies that enable many applications to generate continuous flows of data. This increases the need to develop algorithms that are able to efficiently process…
K-Means++ and its distributed variant K-Means$\|$ have become de facto tools for selecting the initial seeds of K-means. While alternatives have been developed, the effectiveness, ease of implementation, and theoretical grounding of the…
Spherical k-Means is frequently used to cluster document collections because it performs reasonably well in many settings and is computationally efficient. However, the time complexity increases linearly with the number of clusters k, which…
We study beyond worst case analysis for the $k$-means problem where the goal is to model typical instances of $k$-means arising in practice. Existing theoretical approaches provide guarantees under certain assumptions on the optimal…
We prove the inequality $E[(X/\mu)^k] \le (\frac{k/\mu}{\log(k/\mu+1)})^k \le \exp(k^2/(2\mu))$ for sub-Poissonian random variables, such as Binomially or Poisson distributed random variables with mean $\mu$. The asymptotics $1+O(k^2/\mu)$…
Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…
Reduced k-means clustering is a method for clustering objects in a low-dimensional subspace. The advantage of this method is that both clustering of objects and low-dimensional subspace reflecting the cluster structure are simultaneously…
We consider the classic Euclidean $k$-median and $k$-means objective on data streams, where the goal is to provide a $(1+\varepsilon)$-approximation to the optimal $k$-median or $k$-means solution, while using as little memory as possible.…
Clustering is an effective technique in data mining to generate groups that are the matter of interest. Among various clustering approaches, the family of k-means algorithms and min-cut algorithms gain most popularity due to their…
We give a polynomial-time approximation algorithm for the (not necessarily metric) $k$-Median problem. The algorithm is an $\alpha$-size-approximation algorithm for $\alpha < 1 + 2 \ln(n/k)$. That is, it guarantees a solution having size at…
We study lower bounds on information dissemination in adversarial dynamic networks. Initially, k pieces of information (henceforth called tokens) are distributed among n nodes. The tokens need to be broadcast to all nodes through a…
The $k$-Means clustering problem on $n$ points is NP-Hard for any dimension $d\ge 2$, however, for the 1D case there exists exact polynomial time algorithms. Previous literature reported an $O(kn^2)$ time dynamic programming algorithm that…
In this note, we introduce a new algorithm to deal with finite dimensional clustering with errors in variables. The design of this algorithm is based on recent theoretical advances (see Loustau (2013a,b)) in statistical learning with errors…
The $k$-median and $k$-means clustering objectives are classic objectives for modeling clustering in a metric space. Given a set of points in a metric space, the goal of the $k$-median (resp. $k$-means) problem is to find $k$ representative…
Smoothed analysis of complexity bounds and condition numbers has been done, so far, on a case by case basis. In this paper we consider a reasonably large class of condition numbers for problems over the complex numbers and we obtain…
We study (Euclidean) $k$-median and $k$-means with constraints in the streaming model. There have been recent efforts to design unified algorithms to solve constrained $k$-means problems without using knowledge of the specific constraint at…
The $k$-means is one of the most important unsupervised learning techniques in statistics and computer science. The goal is to partition a data set into many clusters, such that observations within clusters are the most homogeneous and…
We present improved deterministic distributed algorithms for a number of well-studied matching problems, which are simpler, faster, more accurate, and/or more general than their known counterparts. The common denominator of these results is…