Semi–supervised clustering is an attempt to reconcile clustering (unsupervised learning) and classification (supervised learning, using prior information on the data.) These two modes of data analysis are combined in a parameterized model, the parameter θ∈ [0, 1] is the weight attributed to the prior information, θ = 0 corresponding to clustering, and θ = 1 to classification. The results (clust...

A subset A of a space X is called regular open if A = IntA, and regular closed if X\A is regular open, or equivalently, if A= IntA. A is called semiopen [16] (resp., preopen [17], semi-preopen [3], b-open [4]) ifA⊂ IntA (resp.,A⊂ IntA,A⊂ IntA ,A⊂ IntA∪ IntA). The concept of a preopen set was introduced in [6] where the term locally dense was used and the concept of a semi-preopen set was introd...

From the work of Simmons about nuclei in frames it follows that a topological space X is scattered if and only if each congruence Θ on the frame of open sets is induced by a unique subspace A so that Θ = {(U, V ) |U ∩A = V ∩A}, and that the same holds without the uniqueness requirement iff X is weakly scattered (corrupt). We prove a seemingly similar but substantially different result about qua...

The aim of this paper is to introduce various functions associated with semi*α-open sets. Here semi*αcontinuous, semi*α-irresolute, contra-semi*α-continuous and contra-semi*α-irresolute functions are defined. Characterizations for these functions are given. Further their fundamental properties are investigated. Many other functions associated with semi*α-open sets and their contra versions are ...

In this paper, we extend the notions of γ-operation introduced in [12], by using the soft ideal notions. We introduce the notions of Ĩ-open soft sets, pre-Ĩopen soft sets, α-Ĩ-open soft sets, semi-Ĩ-open soft sets and β-Ĩ-open soft sets to soft topological spaces. We study the relations between these different types of subsets of soft topological spaces with soft ideal. We also introduce the co...

The notions of pre-local function, semi-local functions and α-local functions with respect to a topology and an ideal are introduced, and several properties are investigated. Also, the concept of P -I-open sets and P -I-closed sets in ideal topological spaces are discussed. Relations between I-open sets and P -I-open sets are provided, and several properties related to P -I-open sets, pre-local...

Let {p θ , θ ∈ Θ} be a family of probability densities with respect to µ where Θ is an open subinterval (finite, infinite or semi-infinite) of the real line. The Fisher Information for this family is defined by: I(θ) := E θ ∂ ∂θ log p θ (X) 2 Note that the densities p θ can be on arbitrary spaces; the only condition for defining I(θ) is that θ is real. The function ∂ ∂θ log p θ (X) is called th...

In this paper a new generalization of semi-open maps via the concept of sg-closed sets is considered. They are called approximately semi-open maps and are used to obtain a characterization of semi-T1/2 spaces.