12,817 research outputs found
Clustering of Data with Missing Entries
The analysis of large datasets is often complicated by the presence of
missing entries, mainly because most of the current machine learning algorithms
are designed to work with full data. The main focus of this work is to
introduce a clustering algorithm, that will provide good clustering even in the
presence of missing data. The proposed technique solves an fusion
penalty based optimization problem to recover the clusters. We theoretically
analyze the conditions needed for the successful recovery of the clusters. We
also propose an algorithm to solve a relaxation of this problem using
saturating non-convex fusion penalties. The method is demonstrated on simulated
and real datasets, and is observed to perform well in the presence of large
fractions of missing entries.Comment: arXiv admin note: substantial text overlap with arXiv:1709.0187
The Bane of Low-Dimensionality Clustering
In this paper, we give a conditional lower bound of on
running time for the classic k-median and k-means clustering objectives (where
n is the size of the input), even in low-dimensional Euclidean space of
dimension four, assuming the Exponential Time Hypothesis (ETH). We also
consider k-median (and k-means) with penalties where each point need not be
assigned to a center, in which case it must pay a penalty, and extend our lower
bound to at least three-dimensional Euclidean space.
This stands in stark contrast to many other geometric problems such as the
traveling salesman problem, or computing an independent set of unit spheres.
While these problems benefit from the so-called (limited) blessing of
dimensionality, as they can be solved in time or
in d dimensions, our work shows that widely-used clustering
objectives have a lower bound of , even in dimension four.
We complete the picture by considering the two-dimensional case: we show that
there is no algorithm that solves the penalized version in time less than
, and provide a matching upper bound of .
The main tool we use to establish these lower bounds is the placement of
points on the moment curve, which takes its inspiration from constructions of
point sets yielding Delaunay complexes of high complexity
Uncovering Group Level Insights with Accordant Clustering
Clustering is a widely-used data mining tool, which aims to discover
partitions of similar items in data. We introduce a new clustering paradigm,
\emph{accordant clustering}, which enables the discovery of (predefined) group
level insights. Unlike previous clustering paradigms that aim to understand
relationships amongst the individual members, the goal of accordant clustering
is to uncover insights at the group level through the analysis of their
members. Group level insight can often support a call to action that cannot be
informed through previous clustering techniques. We propose the first accordant
clustering algorithm, and prove that it finds near-optimal solutions when data
possesses inherent cluster structure. The insights revealed by accordant
clusterings enabled experts in the field of medicine to isolate successful
treatments for a neurodegenerative disease, and those in finance to discover
patterns of unnecessary spending.Comment: accepted to SDM 2017 (oral
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