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Quantum computing has great potential for advancing machine learning algorithms beyond classical reach. Even though full-fledged universal quantum computers do not exist yet, its expected benefits for machine learning can already be shown…
The analysis of continously larger datasets is a task of major importance in a wide variety of scientific fields. In this sense, cluster analysis algorithms are a key element of exploratory data analysis, due to their easiness in the…
The $k$-means algorithm (Lloyd's algorithm) is a widely used method for clustering unlabeled data. A key bottleneck of the $k$-means algorithm is that each iteration requires time linear in the number of data points, which can be expensive…
We give a quantum approximation scheme (i.e., $(1 + \varepsilon)$-approximation for every $\varepsilon > 0$) for the classical $k$-means clustering problem in the QRAM model with a running time that has only polylogarithmic dependence on…
k-medoids algorithm is a partitional, centroid-based clustering algorithm which uses pairwise distances of data points and tries to directly decompose the dataset with $n$ points into a set of $k$ disjoint clusters. However, k-medoids…
The Incremental K-means (IKM), an improved version of K-means (KM), was introduced to improve the clustering quality of KM significantly. However, the speed of IKM is slower than KM. My thesis proposes two algorithms to speed up IKM while…
Effectively applying the K-means algorithm to clustering tasks with incomplete features remains an important research area due to its impact on real-world applications. Recent work has shown that unifying K-means clustering and imputation…
Mining clusters from data is an important endeavor in many applications. The $k$-means method is a popular, efficient, and distribution-free approach for clustering numerical-valued data, but does not apply for categorical-valued…
We study the complexity of the classic capacitated k-median and k-means problems parameterized by the number of centers, k. These problems are notoriously difficult since the best known approximation bound for high dimensional Euclidean…
Quantum machine learning is emerging as a promising application of quantum computing due to its distinct way of encoding and processing data. It is believed that large-scale quantum machine learning demonstrates substantial advantages over…
In this paper, we study clustering with respect to the k-modes objective function, a natural formulation of clustering for categorical data. One of the main contributions of this paper is to establish the connection between k-modes and…
Clustering is a classic topic in optimization with $k$-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best known algorithm for $k$-means with a provable guarantee is a simple…
This paper presents a novel accelerated exact k-means algorithm called the Ball k-means algorithm, which uses a ball to describe a cluster, focusing on reducing the point-centroid distance computation. The Ball k-means can accurately find…
In this dissertation, we study the intersection of quantum computing and supervised machine learning algorithms, which means that we investigate quantum algorithms for supervised machine learning that operate on classical data. This area of…
Clustering with fast algorithms large samples of high dimensional data is an important challenge in computational statistics. Borrowing ideas from MacQueen (1967) who introduced a sequential version of the $k$-means algorithm, a new class…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
The k-means clustering algorithm is a popular algorithm that partitions data into k clusters. There are many improvements to accelerate the standard algorithm. Most current research employs upper and lower bounds on point-to-cluster…
Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…
K-nearest neighbor classification algorithm is one of the most basic algorithms in machine learning, which determines the sample's category by the similarity between samples. In this paper, we propose a quantum K-nearest neighbor…
In this work we introduce a quantum sorting algorithm with adaptable requirements of memory and circuit depth, and then use it to develop a new quantum version of the classical machine learning algorithm known as k-nearest neighbors (k-NN).…