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 ...

The weighted k-nearest neighbors algorithm is one of the most fundamental nonparametric methods in pattern recognition and machine learning. The question of setting the optimal number of neighbors as well as the optimal weights has received much attention throughout the years, nevertheless this problem seems to have remained unsettled. In this paper we offer a simple approach to locally weighte...

Directed graphs are commonly drawn by the Sugiyama algorithm, where crossing reduction is a crucial phase. It is done by repeated one-sided 2-level crossing minimizations, which are still NP-hard. We introduce a global crossing reduction, which at any particular time captures all crossings, especially for long edges. Our approach is based on the sifting technique and improves the level-by-level...

Let k ≥ 0 be an integer. A set S of vertices of a graph G = (V (G), E(G)) is called a global offensive k-alliance if |N(v) ∩ S| ≥ |N(v) − S| + k for every v ∈ V (G) − S, where 0 ≤ k ≤ ∆ and ∆ is the maximum degree of G. The global offensive k-alliance number γ o (G) is the minimum cardinality of a global offensive k-alliance in G. We show that for every bipartite graph G and every integer k ≥ 2...

The global k-means algorithm is an incremental approach to clustering that dynamically adds one cluster center at a time through a deterministic global search procedure from suitable initial positions, and employs k-means to minimize the sum of the intra-cluster variances. However the global k-means algorithm sometimes results singleton clusters and the initial positions sometimes are bad, afte...

K-means clustering is a popular clustering algorithm based on the partition of data. However, K-means clustering algorithm suffers from some shortcomings, such as its requiring a user to give out the number of clusters at first, and its sensitiveness to initial conditions, and its being easily trapped into a local solution et cetera. The global Kmeans algorithm proposed by Likas et al is an inc...

We consider finite graphs G with vertex set V (G). For a subset S ⊆ V (G), we define by G[S] the subgraph induced by S. By n(G) = |V (G)| and δ(G) we denote the order and the minimum degree of G, respectively. Let k be a positive integer. A subset S ⊆ V (G) is a connected global offensive k-alliance of the connected graphG, ifG[S] is connected and |N(v)∩S| ≥ |N(v)−S|+k for every vertex v ∈ V (G...

Let Γ = (V,E) be a simple graph. For a nonempty set X ⊆ V , and a vertex v ∈ V , δX(v) denotes the number of neighbors v has in X. A nonempty set S ⊆ V is a defensive k-alliance in Γ = (V,E) if δS(v) ≥ δS̄(v)+k, ∀v ∈ S. A defensive k-alliance S is called global if it forms a dominating set. The global defensive k-alliance number of Γ, denoted by γ k(Γ), is the minimum cardinality of a defensive ...

We present the global k-means algorithm which is an incremental approach to clustering that dynamically adds one cluster center at a time through a deterministic global search procedure consisting of N (with N being the size of the data set) executions of the k-means algorithm from suitable initial positions. We also propose modifications of the method to reduce the computational load without s...

In [AL07] and [AL10], Arone and Lesh constructed and studied spectrum level filtrations that interpolate between connective (topological or algebraic) K-theory and the Eilenberg-MacLane spectrum for the integers. In this paper we consider (global) equivariant generalizations of these filtrations and of another closely related class of filtrations, the modified rank filtrations of the K-theory s...