Manifold Spanning Graphs
نویسندگان
چکیده
Graph construction is the essential first step for nearly all manifold learning algorithms. While many applications assume that a simple k-nearest or -close neighbors graph will accurately model the topology of the underlying manifold, these methods often require expert tuning and may not produce high quality graphs. In this paper, the hyperparameter sensitivity of existing graph construction methods is demonstrated. We then present a new algorithm for unsupervised graph construction, based on minimal assumptions about the input data and its manifold structure.
منابع مشابه
Counting the number of spanning trees of graphs
A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.
متن کاملNUMBER OF SPANNING TREES FOR DIFFERENT PRODUCT GRAPHS
In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...
متن کاملRegularity of Soap Film-like Surfaces Spanning Graphs in a Riemannian Manifold
Let M be an n-dimensional complete simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant −κ2. Using the cone total curvature TC(Γ) of a graph Γ which was introduced by Gulliver and Yamada [8], we prove that the density at any point of a soap film-like surface Σ spanning a graph Γ ⊂ M is less than or equal to 1 2π {TC(Γ)− κArea(p×Γ)}. From this den...
متن کاملManifold Learning Using Euclidean -nearest Neighbor Graphs
In the manifold learning problem one seeks to discover a smooth low dimensional surface, i.e., a manifold embedded in a higher dimensional linear vector space, based on a set of measured sample points on the surface. In this paper we consider the closely related problem of estimating the manifold’s intrinsic dimension and the intrinsic entropy of the sample points. Specifically, we view the sam...
متن کاملProximity Graphs for Clustering and Manifold Learning
Many machine learning algorithms for clustering or dimensionality reduction take as input a cloud of points in Euclidean space, and construct a graph with the input data points as vertices. This graph is then partitioned (clustering) or used to redefine metric information (dimensionality reduction). There has been much recent work on new methods for graph-based clustering and dimensionality red...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014