610 research outputs found
Estimating Maximally Probable Constrained Relations by Mathematical Programming
Estimating a constrained relation is a fundamental problem in machine
learning. Special cases are classification (the problem of estimating a map
from a set of to-be-classified elements to a set of labels), clustering (the
problem of estimating an equivalence relation on a set) and ranking (the
problem of estimating a linear order on a set). We contribute a family of
probability measures on the set of all relations between two finite, non-empty
sets, which offers a joint abstraction of multi-label classification,
correlation clustering and ranking by linear ordering. Estimating (learning) a
maximally probable measure, given (a training set of) related and unrelated
pairs, is a convex optimization problem. Estimating (inferring) a maximally
probable relation, given a measure, is a 01-linear program. It is solved in
linear time for maps. It is NP-hard for equivalence relations and linear
orders. Practical solutions for all three cases are shown in experiments with
real data. Finally, estimating a maximally probable measure and relation
jointly is posed as a mixed-integer nonlinear program. This formulation
suggests a mathematical programming approach to semi-supervised learning.Comment: 16 page
A Message Passing Algorithm for the Minimum Cost Multicut Problem
We propose a dual decomposition and linear program relaxation of the NP -hard
minimum cost multicut problem. Unlike other polyhedral relaxations of the
multicut polytope, it is amenable to efficient optimization by message passing.
Like other polyhedral elaxations, it can be tightened efficiently by cutting
planes. We define an algorithm that alternates between message passing and
efficient separation of cycle- and odd-wheel inequalities. This algorithm is
more efficient than state-of-the-art algorithms based on linear programming,
including algorithms written in the framework of leading commercial software,
as we show in experiments with large instances of the problem from applications
in computer vision, biomedical image analysis and data mining.Comment: Added acknowledgment
Decomposition of Trees and Paths via Correlation
We study the problem of decomposing (clustering) a tree with respect to costs
attributed to pairs of nodes, so as to minimize the sum of costs for those
pairs of nodes that are in the same component (cluster). For the general case
and for the special case of the tree being a star, we show that the problem is
NP-hard. For the special case of the tree being a path, this problem is known
to be polynomial time solvable. We characterize several classes of facets of
the combinatorial polytope associated with a formulation of this clustering
problem in terms of lifted multicuts. In particular, our results yield a
complete totally dual integral (TDI) description of the lifted multicut
polytope for paths, which establishes a connection to the combinatorial
properties of alternative formulations such as set partitioning.Comment: v2 is a complete revisio
Combinatorial persistency criteria for multicut and max-cut
In combinatorial optimization, partial variable assignments are called
persistent if they agree with some optimal solution. We propose persistency
criteria for the multicut and max-cut problem as well as fast combinatorial
routines to verify them. The criteria that we derive are based on mappings that
improve feasible multicuts, respectively cuts. Our elementary criteria can be
checked enumeratively. The more advanced ones rely on fast algorithms for upper
and lower bounds for the respective cut problems and max-flow techniques for
auxiliary min-cut problems. Our methods can be used as a preprocessing
technique for reducing problem sizes or for computing partial optimality
guarantees for solutions output by heuristic solvers. We show the efficacy of
our methods on instances of both problems from computer vision, biomedical
image analysis and statistical physics
Runtime-Flexible Multi-dimensional Arrays and Views for C++98 and C++0x
Multi-dimensional arrays are among the most fundamental and most useful data
structures of all. In C++, excellent template libraries exist for arrays whose
dimension is fixed at runtime. Arrays whose dimension can change at runtime
have been implemented in C. However, a generic object-oriented C++
implementation of runtime-flexible arrays has so far been missing. In this
article, we discuss our new implementation called Marray, a package of class
templates that fills this gap. Marray is based on views as an underlying
concept. This concept brings some of the flexibility known from script
languages such as R and MATLAB to C++. Marray is free both for commercial and
non-commercial use and is publicly available from www.andres.sc/marrayComment: Free source code availabl
How to Extract the Geometry and Topology from Very Large 3D Segmentations
Segmentation is often an essential intermediate step in image analysis. A
volume segmentation characterizes the underlying volume image in terms of
geometric information--segments, faces between segments, curves in which
several faces meet--as well as a topology on these objects. Existing algorithms
encode this information in designated data structures, but require that these
data structures fit entirely in Random Access Memory (RAM). Today, 3D images
with several billion voxels are acquired, e.g. in structural neurobiology.
Since these large volumes can no longer be processed with existing methods, we
present a new algorithm which performs geometry and topology extraction with a
runtime linear in the number of voxels and log-linear in the number of faces
and curves. The parallelizable algorithm proceeds in a block-wise fashion and
constructs a consistent representation of the entire volume image on the hard
drive, making the structure of very large volume segmentations accessible to
image analysis. The parallelized C++ source code, free command line tools and
MATLAB mex files are avilable from
http://hci.iwr.uni-heidelberg.de/software.phpComment: C++ source code, free command line tools and MATLAB mex files are
avilable from http://hci.iwr.uni-heidelberg.de/software.ph
Correlation Clustering of Bird Sounds
Bird sound classification is the task of relating any sound recording to
those species of bird that can be heard in the recording. Here, we study bird
sound clustering, the task of deciding for any pair of sound recordings whether
the same species of bird can be heard in both. We address this problem by first
learning, from a training set, probabilities of pairs of recordings being
related in this way, and then inferring a maximally probable partition of a
test set by correlation clustering. We address the following questions: How
accurate is this clustering, compared to a classification of the test set? How
do the clusters thus inferred relate to the clusters obtained by
classification? How accurate is this clustering when applied to recordings of
bird species not heard during training? How effective is this clustering in
separating, from bird sounds, environmental noise not heard during training?Comment: 13 page
DeeperCut: A Deeper, Stronger, and Faster Multi-Person Pose Estimation Model
The goal of this paper is to advance the state-of-the-art of articulated pose
estimation in scenes with multiple people. To that end we contribute on three
fronts. We propose (1) improved body part detectors that generate effective
bottom-up proposals for body parts; (2) novel image-conditioned pairwise terms
that allow to assemble the proposals into a variable number of consistent body
part configurations; and (3) an incremental optimization strategy that explores
the search space more efficiently thus leading both to better performance and
significant speed-up factors. Evaluation is done on two single-person and two
multi-person pose estimation benchmarks. The proposed approach significantly
outperforms best known multi-person pose estimation results while demonstrating
competitive performance on the task of single person pose estimation. Models
and code available at http://pose.mpi-inf.mpg.deComment: ECCV'16. High-res version at
https://www.d2.mpi-inf.mpg.de/sites/default/files/insafutdinov16arxiv.pd
The Lazy Flipper: MAP Inference in Higher-Order Graphical Models by Depth-limited Exhaustive Search
This article presents a new search algorithm for the NP-hard problem of
optimizing functions of binary variables that decompose according to a
graphical model. It can be applied to models of any order and structure. The
main novelty is a technique to constrain the search space based on the topology
of the model. When pursued to the full search depth, the algorithm is
guaranteed to converge to a global optimum, passing through a series of
monotonously improving local optima that are guaranteed to be optimal within a
given and increasing Hamming distance. For a search depth of 1, it specializes
to Iterated Conditional Modes. Between these extremes, a useful tradeoff
between approximation quality and runtime is established. Experiments on models
derived from both illustrative and real problems show that approximations found
with limited search depth match or improve those obtained by state-of-the-art
methods based on message passing and linear programming.Comment: C++ Source Code available from
http://hci.iwr.uni-heidelberg.de/software.ph
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