25,394 research outputs found
Detecting Blackholes and Volcanoes in Directed Networks
In this paper, we formulate a novel problem for finding blackhole and volcano
patterns in a large directed graph. Specifically, a blackhole pattern is a
group which is made of a set of nodes in a way such that there are only inlinks
to this group from the rest nodes in the graph. In contrast, a volcano pattern
is a group which only has outlinks to the rest nodes in the graph. Both
patterns can be observed in real world. For instance, in a trading network, a
blackhole pattern may represent a group of traders who are manipulating the
market. In the paper, we first prove that the blackhole mining problem is a
dual problem of finding volcanoes. Therefore, we focus on finding the blackhole
patterns. Along this line, we design two pruning schemes to guide the blackhole
finding process. In the first pruning scheme, we strategically prune the search
space based on a set of pattern-size-independent pruning rules and develop an
iBlackhole algorithm. The second pruning scheme follows a divide-and-conquer
strategy to further exploit the pruning results from the first pruning scheme.
Indeed, a target directed graphs can be divided into several disconnected
subgraphs by the first pruning scheme, and thus the blackhole finding can be
conducted in each disconnected subgraph rather than in a large graph. Based on
these two pruning schemes, we also develop an iBlackhole-DC algorithm. Finally,
experimental results on real-world data show that the iBlackhole-DC algorithm
can be several orders of magnitude faster than the iBlackhole algorithm, which
has a huge computational advantage over a brute-force method.Comment: 18 page
Sparse Learning over Infinite Subgraph Features
We present a supervised-learning algorithm from graph data (a set of graphs)
for arbitrary twice-differentiable loss functions and sparse linear models over
all possible subgraph features. To date, it has been shown that under all
possible subgraph features, several types of sparse learning, such as Adaboost,
LPBoost, LARS/LASSO, and sparse PLS regression, can be performed. Particularly
emphasis is placed on simultaneous learning of relevant features from an
infinite set of candidates. We first generalize techniques used in all these
preceding studies to derive an unifying bounding technique for arbitrary
separable functions. We then carefully use this bounding to make block
coordinate gradient descent feasible over infinite subgraph features, resulting
in a fast converging algorithm that can solve a wider class of sparse learning
problems over graph data. We also empirically study the differences from the
existing approaches in convergence property, selected subgraph features, and
search-space sizes. We further discuss several unnoticed issues in sparse
learning over all possible subgraph features.Comment: 42 pages, 24 figures, 4 table
GCG: Mining Maximal Complete Graph Patterns from Large Spatial Data
Recent research on pattern discovery has progressed from mining frequent
patterns and sequences to mining structured patterns, such as trees and graphs.
Graphs as general data structure can model complex relations among data with
wide applications in web exploration and social networks. However, the process
of mining large graph patterns is a challenge due to the existence of large
number of subgraphs. In this paper, we aim to mine only frequent complete graph
patterns. A graph g in a database is complete if every pair of distinct
vertices is connected by a unique edge. Grid Complete Graph (GCG) is a mining
algorithm developed to explore interesting pruning techniques to extract
maximal complete graphs from large spatial dataset existing in Sloan Digital
Sky Survey (SDSS) data. Using a divide and conquer strategy, GCG shows high
efficiency especially in the presence of large number of patterns. In this
paper, we describe GCG that can mine not only simple co-location spatial
patterns but also complex ones. To the best of our knowledge, this is the first
algorithm used to exploit the extraction of maximal complete graphs in the
process of mining complex co-location patterns in large spatial dataset.Comment: 1
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