相关论文: Lower density selection schemes via small universa…

Weighted minwise hashing is a standard dimensionality reduction technique with applications to similarity search and large-scale kernel machines. We introduce a simple algorithm that takes a weighted set $x \in \mathbb{R}_{\geq 0}^{d}$ and…

Many distributed optimization algorithms achieve existentially-optimal running times, meaning that there exists some pathological worst-case topology on which no algorithm can do better. Still, most networks of interest allow for…

We introduce a novel criterion in clustering that seeks clusters with limited range of values associated with each cluster's elements. In clustering or classification the objective is to partition a set of objects into subsets, called…

Clustering is one of the most fundamental tools in data science and machine learning, and k-means clustering is one of the most common such methods. There is a variety of approximate algorithms for the k-means problem, but computing the…

A word $u=u_1\dots u_n$ is a scattered factor of a word $w$ if $u$ can be obtained from $w$ by deleting some of its letters: there exist the (potentially empty) words $v_0,v_1,..,v_n$ such that $w = v_0u_1v_1...u_nv_n$. The set of all…

A scheme for locally adaptive bandwidth selection is proposed which sensitively shrinks the bandwidth of a kernel estimator at lowest density regions such as the support boundary which are unknown to the statistician. In case of 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…

Majorization-minimization (MM) is a family of optimization methods that iteratively reduce a loss by minimizing a locally-tight upper bound, called a majorizer. Traditionally, majorizers were derived by hand, and MM was only applicable to a…

In optimization or machine learning problems we are given a set of items, usually points in some metric space, and the goal is to minimize or maximize an objective function over some space of candidate solutions. For example, in clustering…

Sequential minimum optimization is a machine-learning global search training algorithm. It is applicable when the functional dependence of the cost function on a tunable parameter given the other parameters can be cheaply determined. This…

The deletion distance between two binary words $u,v \in \{0,1\}^n$ is the smallest $k$ such that $u$ and $v$ share a common subsequence of length $n-k$. A set $C$ of binary words of length $n$ is called a $k$-deletion code if every pair of…

We describe the shrinking target problem for random iterated function systems which semi-conjugate to a random subshifts of finite type. We get the Hausdorff dimension of the set based on shrinking target problems with given targets. The…

It was recently shown that spatial coupling of individual low-density parity-check codes improves the belief-propagation threshold of the coupled ensemble essentially to the maximum a posteriori threshold of the underlying ensemble. We…

We define a novel, basic, unsupervised learning problem - learning the lowest density homogeneous hyperplane separator of an unknown probability distribution. This task is relevant to several problems in machine learning, such as…

In this paper, we propose a method for density-based clustering in high-dimensional spaces that combines Locality-Sensitive Hashing (LSH) with the Quick Shift algorithm. The Quick Shift algorithm, known for its hierarchical clustering…

Word embedding algorithms produce very reliable feature representations of words that are used by neural network models across a constantly growing multitude of NLP tasks. As such, it is imperative for NLP practitioners to understand how…

In this paper, vector optimization is considered in the framework of decision making and optimization in general spaces. Interdependencies between domination structures in decision making and domination sets in vector optimization are…

Density level sets can be estimated using plug-in methods, excess mass algorithms or a hybrid of the two previous methodologies. The plug-in algorithms are based on replacing the unknown density by some nonparametric estimator, usually the…

We consider the SUBSET SUM problem and its important variants in this paper. In the SUBSET SUM problem, a (multi-)set $X$ of $n$ positive numbers and a target number $t$ are given, and the task is to find a subset of $X$ with the maximal…

A pattern $\alpha$ is a string of variables and terminal letters. We say that $\alpha$ matches a word $w$, consisting only of terminal letters, if $w$ can be obtained by replacing the variables of $\alpha$ by terminal words. The matching…