The Complexity of the k-means Method
نویسندگان
چکیده
The k-means method is a widely used technique for clustering points in Euclidean space. While it is extremely fast in practice, its worst-case running time is exponential in the number of data points. We prove that the k-means method can implicitly solve PSPACE-complete problems, providing a complexity-theoretic explanation for its worst-case running time. Our result parallels recent work on the complexity of the simplex method for linear programming. 1998 ACM Subject Classification I.5.3 Clustering
منابع مشابه
3D Scene and Object Classification Based on Information Complexity of Depth Data
In this paper the problem of 3D scene and object classification from depth data is addressed. In contrast to high-dimensional feature-based representation, the depth data is described in a low dimensional space. In order to remedy the curse of dimensionality problem, the depth data is described by a sparse model over a learned dictionary. Exploiting the algorithmic information theory, a new def...
متن کاملImproved COA with Chaotic Initialization and Intelligent Migration for Data Clustering
A well-known clustering algorithm is K-means. This algorithm, besides advantages such as high speed and ease of employment, suffers from the problem of local optima. In order to overcome this problem, a lot of studies have been done in clustering. This paper presents a hybrid Extended Cuckoo Optimization Algorithm (ECOA) and K-means (K), which is called ECOA-K. The COA algorithm has advantages ...
متن کاملPersistent K-Means: Stable Data Clustering Algorithm Based on K-Means Algorithm
Identifying clusters or clustering is an important aspect of data analysis. It is the task of grouping a set of objects in such a way those objects in the same group/cluster are more similar in some sense or another. It is a main task of exploratory data mining, and a common technique for statistical data analysis This paper proposed an improved version of K-Means algorithm, namely Persistent K...
متن کاملModification of the Fast Global K-means Using a Fuzzy Relation with Application in Microarray Data Analysis
Recognizing genes with distinctive expression levels can help in prevention, diagnosis and treatment of the diseases at the genomic level. In this paper, fast Global k-means (fast GKM) is developed for clustering the gene expression datasets. Fast GKM is a significant improvement of the k-means clustering method. It is an incremental clustering method which starts with one cluster. Iteratively ...
متن کاملA Hybrid Data Clustering Algorithm Using Modified Krill Herd Algorithm and K-MEANS
Data clustering is the process of partitioning a set of data objects into meaning clusters or groups. Due to the vast usage of clustering algorithms in many fields, a lot of research is still going on to find the best and efficient clustering algorithm. K-means is simple and easy to implement, but it suffers from initialization of cluster center and hence trapped in local optimum. In this paper...
متن کاملApplication of the Schwarz-Christoffel Transformation in Solving Two-Dimensional Turbulent Flows in Complex Geometries
In this paper, two-dimensional turbulent flows in different and complex geometries are simulated by using an accurate grid generation method. In order to analyze the fluid flow, numerical solution of the continuity and Navier-Stokes equations are solved using CFD techniques. Considering the complexity of the physical geometry, conformal mapping is used to generate an orthogonal grid by means of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016