Related papers: Axioms for Distanceless Graph Partitioning

Kleinberg introduced three natural clustering properties, or axioms, and showed they cannot be simultaneously satisfied by any clustering algorithm. We present a new clustering property, Monotonic Consistency, which avoids the well-known…

Development of new algorithms in the area of machine learning, especially clustering, comparative studies of such algorithms as well as testing according to software engineering principles requires availability of labeled data sets. While…

Kleinberg's axioms for distance based clustering proved to be contradictory. Various efforts have been made to overcome this problem. Here we make an attempt to handle the issue by embedding in high-dimensional space and granting wide gaps…

We investigate properties that intuitively ought to be satisfied by graph clustering quality functions, that is, functions that assign a score to a clustering of a graph. Graph clustering, also known as network community detection, is often…

This paper investigates the validity of Kleinberg's axioms for clustering functions with respect to the quite popular clustering algorithm called $k$-means. While Kleinberg's axioms have been discussed heavily in the past, we concentrate…

Network-valued data are encountered in a wide range of applications and pose challenges in learning due to their complex structure and absence of vertex correspondence. Typical examples of such problems include classification or grouping of…

The widely applied k-means algorithm produces clusterings that violate our expectations with respect to high/low similarity/density and is in conflict with Kleinberg's axiomatic system for distance based clustering algorithms that…

Despite the widespread use of Clustering, there is distressingly little general theory of clustering available. Questions like "What distinguishes a clustering of data from other data partitioning?", "Are there any principles governing all…

Graph clustering is an unsupervised machine learning method that partitions the nodes in a graph into different groups. Despite achieving significant progress in exploiting both attributed and structured data information, graph clustering…

Graph-based subspace clustering methods have exhibited promising performance. However, they still suffer some of these drawbacks: encounter the expensive time overhead, fail in exploring the explicit clusters, and cannot generalize to…

We develop new methods based on graph motifs for graph clustering, allowing more efficient detection of communities within networks. We focus on triangles within graphs, but our techniques extend to other clique motifs as well. Our…

The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…

Cluster analysis has attracted more and more attention in the field of machine learning and data mining. Numerous clustering algorithms have been proposed and are being developed due to diverse theories and various requirements of emerging…

Graph based clustering is one of the major clustering methods. Most of it work in three separate steps: similarity graph construction, clustering label relaxing and label discretization with k-means. Such common practice has three…

Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…

Graph-based clustering methods have demonstrated the effectiveness in various applications. Generally, existing graph-based clustering methods first construct a graph to represent the input data and then partition it to generate the…

Connected clustering denotes a family of constrained clustering problems in which we are given a distance metric and an undirected connectivity graph $G$ that can be completely unrelated to the metric. The aim is to partition the $n$…

Spectral clustering has become one of the most widely used clustering techniques when the structure of the individual clusters is non-convex or highly anisotropic. Yet, despite its immense popularity, there exists fairly little theory about…

We initiate the study of coresets for clustering in graph metrics, i.e., the shortest-path metric of edge-weighted graphs. Such clustering problems are essential to data analysis and used for example in road networks and data visualization.…

Conductance-based graph clustering has been recognized as a fundamental operator in numerous graph analysis applications. Despite the significant success of conductance-based graph clustering, existing algorithms are either hard to obtain…