in this study, we investigate the further properties of quasi irresolute topological groupsdened in [20]. we show that if a group homomorphism f between quasi irresolute topologicalgroups is irresolute at eg, then f is irresolute on g. later we prove that in a semi-connectedquasi irresolute topological group (g; ; ), if v is any symmetric semi-open neighborhood ofeg, then g is generated by v...

For classification of time series, the simple 1-nearest neighbor (1NN) classifier in combination with an elastic distance measure such as Dynamic Time Warping (DTW) distance is considered superior in terms of classification accuracy to many other more elaborate methods, including k-nearest neighbor (kNN) with neighborhood size k > 1. In this paper we revisit this apparently peculiar relationshi...

based on a complete heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a cartesian-closed category, calledthe category of $l-$ordered fuzzifying convergence spaces, in whichthe category of $l-$fuzzifying topological spaces can be embedded.in addition, two new categories are introduced, which are called the...

Most nonlinear dimensionality reduction approaches such as Isomap heavily depend on the neighborhood structure of manifold. They determine the neighborhood graph using Euclidean distance so that they often fail to nicely deal with sparsely sampled or noise contaminated data. This paper applies the graph algebra to optimize the neighborhood structure for Isomap. The improved Isomap outperforms t...

In this paper, we address the approximate nearest neighbor (ANN) search problem over large scale visual descriptors. We investigate a simple but very effective approach, neighborhood graph (NG) search, which conducts the local search by expanding neighborhoods with a best-first manner. Expanding neighborhood makes it efficient to locate the descriptors with high probability being true NNs. Howe...

The Self-Organizing Map (SOM) is a powerful tool in the exploratory phase of data mining. It is capable of projecting high-dimensional data onto a regular, usually 2dimensional grid of neurons with good neighborhood preservation between two spaces. However, due to the dimensional conflict, the neighborhood preservation cannot always lead to perfect topology preservation. In this paper, we estab...

We propose a new approach for outlier detection, based on a new ranking measure that focuses on the question of whether a point is “important” for its nearest neighbors; using our notations low cumulative rank implies the point is central. For instance, a point centrally located in a cluster has relatively low cumulative sum of ranks because it is among the nearest neighbors of its own nearest ...

A common way of classifying network connectivity is the association of the nodal degree distribution to specific probability distribution models. During the last decades, researchers classified many networks using the Poisson or Pareto distributions. Urban infrastructures – like transportation (railways, roads, etc.) and distribution (gas, water, energy, etc.) systems – are peculiar networks st...