Related papers: A Unified Framework for Approximating and Clusteri…

This paper considers the optimization problem in the form of $\min_{X \in \mathcal{F}_v} f(x) + \lambda \|X\|_1,$ where $f$ is smooth, $\mathcal{F}_v = \{X \in \mathbb{R}^{n \times q} : X^T X = I_q, v \in \mathrm{span}(X)\}$, and $v$ is a…

We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…

Clustering is a powerful and extensively used data science tool. While clustering is generally thought of as an unsupervised learning technique, there are also supervised variations such as Spath's clusterwise regression that attempt to…

In this paper, we first propose a new iterative algorithm, called the K-sets+ algorithm for clustering data points in a semi-metric space, where the distance measure does not necessarily satisfy the triangular inequality. We show that the…

Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…

This paper proposes a novel similarity measure for clustering sequential data. We first construct a common state-space by training a single probabilistic model with all the sequences in order to get a unified representation for the dataset.…

For many machine learning problem settings, particularly with structured inputs such as sequences or sets of objects, a distance measure between inputs can be specified more naturally than a feature representation. However, most standard…

Measuring similarity between two objects is the core operation in existing clustering algorithms in grouping similar objects into clusters. This paper introduces a new similarity measure called point-set kernel which computes the similarity…

Large-scale federated learning (FL) over wireless multiple access channels (MACs) has emerged as a crucial learning paradigm with a wide range of applications. However, its widespread adoption is hindered by several major challenges,…

Similarity plays a fundamental role in many areas, including data mining, machine learning, statistics and various applied domains. Inspired by the success of ensemble methods and the flexibility of trees, we propose to learn a similarity…

We consider the $k$-Median problem on planar graphs: given an edge-weighted planar graph $G$, a set of clients $C \subseteq V(G)$, a set of facilities $F \subseteq V(G)$, and an integer parameter $k$, the task is to find a set of at most…

This paper provides a theoretical framework for interpreting acoustic neighbor embeddings, which are representations of the phonetic content of variable-width audio or text in a fixed-dimensional embedding space. A probabilistic…

We address the problem of communicating domain knowledge from a user to the designer of a clustering algorithm. We propose a protocol in which the user provides a clustering of a relatively small random sample of a data set. The algorithm…

The use of approximation is fundamental in computational science. Almost all computational methods adopt approximations in some form in order to obtain a favourable cost/accuracy trade-off and there are usually many approximations that…

With the aggressive scaling of VLSI technology, the explosion of layout patterns creates a critical bottleneck for DFM applications like OPC. Pattern clustering is essential to reduce data complexity, yet existing methods struggle with…

Subspace clustering is the unsupervised grouping of points lying near a union of low-dimensional linear subspaces. Algorithms based directly on geometric properties of such data tend to either provide poor empirical performance, lack…

We devise coresets for kernel $k$-Means with a general kernel, and use them to obtain new, more efficient, algorithms. Kernel $k$-Means has superior clustering capability compared to classical $k$-Means, particularly when clusters are…

We consider a generalization of the fundamental $k$-means clustering for data with incomplete or corrupted entries. When data objects are represented by points in $\mathbb{R}^d$, a data point is said to be incomplete when some of its…

Due to the progressive growth of the amount of data available in a wide variety of scientific fields, it has become more difficult to ma- nipulate and analyze such information. Even though datasets have grown in size, the K-means algorithm…

Dealing with massive data is a challenging task for machine learning. An important aspect of machine learning is function approximation. In the context of massive data, some of the commonly used tools for this purpose are sparsity,…