Network-aware credit scoring system for telecom subscribers using machine learning and network analysis

PurposeA good decision support system for credit scoring enables telecom operators to measure the subscribers' creditworthiness in a fine-grained manner. This paper aims to propose a robust credit scoring system by leveraging latent information embedded in the telecom subscriber relation network based on multi-source data sources, including telecom inner data, online app usage, and offline consumption footprint.Design/methodology/approachRooting from network science, the relation network model and singular value decomposition are integrated to infer different subscriber subgroups. Employing the results of network inference, the paper proposed a network-aware credit scoring system to predict the continuous credit scores by implementing several state-of-art techniques, i.e. multivariate linear regression, random forest regression, support vector regression, multilayer perceptron, and a deep learning algorithm. The authors use a data set consisting of 926 users of a Chinese major telecom operator within one month of 2018 to verify the proposed approach.FindingsThe distribution of telecom subscriber relation network follows a power-law function instead of the Gaussian function previously thought. This network-aware inference divides the subscriber population into a connected subgroup and a discrete subgroup. Besides, the findings demonstrate that the network-aware decision support system achieves better and more accurate prediction performance. In particular, the results show that our approach considering stochastic equivalence reveals that the forecasting error of the connected-subgroup model is significantly reduced by 7.89–25.64% as compared to the benchmark. Deep learning performs the best which might indicate that a non-linear relationship exists between telecom subscribers' credit scores and their multi-channel behaviours.Originality/valueThis paper contributes to the existing literature on business intelligence analytics and continuous credit scoring by incorporating latent information of the relation network and external information from multi-source data (e.g. online app usage and offline consumption footprint). Also, the authors have proposed a power-law distribution-based network-aware decision support system to reinforce the prediction performance of individual telecom subscribers' credit scoring for the telecom marketing domain.

THE SMOOTHNESS OF ORBITAL MEASURES ON NONCOMPACT SYMMETRIC SPACES

Let $G/K$ be an irreducible symmetric space, where G is a noncompact, connected Lie group and K is a compact, connected subgroup. We use decay properties of the spherical functions to show that the convolution product of any $r=r(G/K)$ continuous orbital measures has its density function in $L^{2}(G)$ and hence is an absolutely continuous measure with respect to the Haar measure. The number r is approximately the rank of $G/K$ . For the special case of the orbital measures, $\nu _{a_{i}}$ , supported on the double cosets $Ka_{i}K$ , where $a_{i}$ belongs to the dense set of regular elements, we prove the sharp result that $\nu _{a_{1}}\ast \nu _{a_{2}}\in L^{2},$ except for the symmetric space of Cartan class $AI$ when the convolution of three orbital measures is needed (even though $\nu _{a_{1}}\ast \nu _{a_{2}}$ is absolutely continuous).

Delta-invariants for Fano varieties with large automorphism groups

For a variety [Formula: see text], a big [Formula: see text]-divisor [Formula: see text] and a closed connected subgroup [Formula: see text] we define a [Formula: see text]-invariant version of the [Formula: see text]-threshold. We prove that for a Fano variety [Formula: see text] and a connected subgroup [Formula: see text] this invariant characterizes [Formula: see text]-equivariant uniform [Formula: see text]-stability. We also use this invariant to investigate [Formula: see text]-equivariant [Formula: see text]-stability of some Fano varieties with large groups of symmetries, including spherical Fano varieties. We also consider the case of [Formula: see text] being a finite group.

-TYPE SUBGROUPS CONTAINING REGULAR UNIPOTENT ELEMENTS

Let $G$ be a simple exceptional algebraic group of adjoint type over an algebraically closed field of characteristic $p>0$ and let $X=\text{PSL}_{2}(p)$ be a subgroup of $G$ containing a regular unipotent element $x$ of $G$. By a theorem of Testerman, $x$ is contained in a connected subgroup of $G$ of type $A_{1}$. In this paper we prove that with two exceptions, $X$ itself is contained in such a subgroup (the exceptions arise when $(G,p)=(E_{6},13)$ or $(E_{7},19)$). This extends earlier work of Seitz and Testerman, who established the containment under some additional conditions on $p$ and the embedding of $X$ in $G$. We discuss applications of our main result to the study of the subgroup structure of finite groups of Lie type.

An example of a non-Borel locally-connected finite-dimensional topological group

According to a classical theorem of Gleason and Montgomery, every finite-dimensional locally path-connected topological group is a Lie group. In the paper for every $n\ge 2$ we construct a locally connected subgroup $G\subset{\mathbb R}^{n+1}$ of dimension $\dim(G)=n$, which is not locally compact. This answers a question posed by S. Maillot on MathOverflow and shows that the local path-connectedness in the result of Gleason and Montgomery can not be weakened to the local connectedness.

Quantum Unique Ergodicity on Locally Symmetric Spaces: the Degenerate Lift

Given a measureon a locally symmetric spaceobtained as a weak-* limit of probability measures associated with eigenfunctions of the ring of invariant differential operators, we construct a measureon the homogeneous spaceX= Γ\Gthat liftsand is invariant by a connected subgroupA1⊂Aof positive dimension, whereG=NAKis an Iwasawa decomposition. If the functions are, in addition, eigenfunctions of the Hecke operators, thenis also the limit of measures associated with Hecke eigenfunctions on X. This generalizes results of the author with A.Venkatesh in the case where the spectral parameters stay away from the walls of the Weyl chamber.

Corwin–Greenleaf multiplicity function for compact extensions of ℝn

Let G = K ⋉ ℝn, where K is a compact connected subgroup of O(n) acting on ℝn by rotations. Let 𝔤 ⊃ 𝔨 be the respective Lie algebras of G and K, and pr : 𝔤* → 𝔨* the natural projection. For admissible coadjoint orbits [Formula: see text] and [Formula: see text], we denote by [Formula: see text] the number of K-orbits in [Formula: see text], which is called the Corwin–Greenleaf multiplicity function. Let π ∈ Ĝ and [Formula: see text] be the unitary representations corresponding, respectively, to [Formula: see text] and [Formula: see text] by the orbit method. In this paper, we investigate the relationship between [Formula: see text] and the multiplicity m(π, τ) of τ in the restriction of π to K. If π is infinite-dimensional and the associated little group is connected, we show that [Formula: see text] if and only if m(π, τ) ≠ 0. Furthermore, for K = SO(n), n ≥ 3, we give a sufficient condition on the representations π and τ in order that [Formula: see text].

Stability of discontinuous groups for reduced threadlike Lie groups

Let G be a reduced threadlike Lie group, H an arbitrary closed connected subgroup of G and Γ ⊂ G an abelian discontinuous subgroup for G/H. We study in this work some topological properties of the parameter space [Formula: see text] and the deformation space [Formula: see text], namely the stability and the rigidity. Instead of treating stability, we consider a weaker form by using an explicit covering of Hom (Γ, G) which we call layering and we show that the local rigidity holds if and only if Γ is finite.

THE FUNDAMENTAL GROUP OF G-MANIFOLDS

Let G be a connected compact Lie group, and let M be a connected Hamiltonian G-manifold with equivariant moment map ϕ. We prove that if there is a simply connected orbit G ⋅ x, then π1(M) ≅ π1(M/G); if additionally ϕ is proper, then π1(M) ≅ π1 (ϕ-1(G⋅a)), where a = ϕ(x). We also prove that if a maximal torus of G has a fixed point x, then π1(M) ≅ π1(M/K), where K is any connected subgroup of G; if additionally ϕ is proper, then π1(M) ≅ π1(ϕ-1(G⋅a)) ≅ π1(ϕ-1(a)), where a = ϕ(x). Furthermore, we prove that if ϕ is proper, then [Formula: see text] for all a ∈ ϕ(M), where [Formula: see text] is any connected subgroup of G which contains the identity component of each stabilizer group; in particular, π1(M/G) ≅ π1(ϕ-1(G⋅a)/G) for all a ∈ ϕ(M).

ON CENTRALISERS AND NORMALISERS FOR GROUPS

Let 𝕂 be a field, char(𝕂)≠2, and G a subgroup of GL(n,𝕂). Suppose g↦g♯ is a 𝕂-linear antiautomorphism of G, and then define G1={g∈G∣g♯g=I}. For C being the centraliser 𝒞G (G1) , or any subgroup of the centre 𝒵(G) , define G(C) ={g∈G∣g♯g∈C}. We show that G(C) is a subgroup of G, and study its structure. When C=𝒞G (G1) , we have that G(C) =𝒩G (G1) , the normaliser of G1 in G. Suppose 𝕂 is algebraically closed, 𝒞G (G1) consists of scalar matrices and G1 is a connected subgroup of an affine group G. Under the latter assumptions, 𝒩G (G1) is a self-normalising subgroup of G. This holds for a number of interesting pairs (G,G1); in particular, for those that we call parabolic pairs. As well, for a certain specific setting we generalise a standard result about centres of Borel subgroups.