10,740 research outputs found
Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs
Laplacian mixture models identify overlapping regions of influence in
unlabeled graph and network data in a scalable and computationally efficient
way, yielding useful low-dimensional representations. By combining Laplacian
eigenspace and finite mixture modeling methods, they provide probabilistic or
fuzzy dimensionality reductions or domain decompositions for a variety of input
data types, including mixture distributions, feature vectors, and graphs or
networks. Provable optimal recovery using the algorithm is analytically shown
for a nontrivial class of cluster graphs. Heuristic approximations for scalable
high-performance implementations are described and empirically tested.
Connections to PageRank and community detection in network analysis demonstrate
the wide applicability of this approach. The origins of fuzzy spectral methods,
beginning with generalized heat or diffusion equations in physics, are reviewed
and summarized. Comparisons to other dimensionality reduction and clustering
methods for challenging unsupervised machine learning problems are also
discussed.Comment: 13 figures, 35 reference
Event-Based Motion Segmentation by Motion Compensation
In contrast to traditional cameras, whose pixels have a common exposure time,
event-based cameras are novel bio-inspired sensors whose pixels work
independently and asynchronously output intensity changes (called "events"),
with microsecond resolution. Since events are caused by the apparent motion of
objects, event-based cameras sample visual information based on the scene
dynamics and are, therefore, a more natural fit than traditional cameras to
acquire motion, especially at high speeds, where traditional cameras suffer
from motion blur. However, distinguishing between events caused by different
moving objects and by the camera's ego-motion is a challenging task. We present
the first per-event segmentation method for splitting a scene into
independently moving objects. Our method jointly estimates the event-object
associations (i.e., segmentation) and the motion parameters of the objects (or
the background) by maximization of an objective function, which builds upon
recent results on event-based motion-compensation. We provide a thorough
evaluation of our method on a public dataset, outperforming the
state-of-the-art by as much as 10%. We also show the first quantitative
evaluation of a segmentation algorithm for event cameras, yielding around 90%
accuracy at 4 pixels relative displacement.Comment: When viewed in Acrobat Reader, several of the figures animate. Video:
https://youtu.be/0q6ap_OSBA
Relational visual cluster validity
The assessment of cluster validity plays a very important role in cluster analysis. Most commonly used cluster validity methods are based on statistical hypothesis testing or finding the best clustering scheme by computing a number of different cluster validity indices. A number of visual methods of cluster validity have been produced to display directly the validity of clusters by mapping data into two- or three-dimensional space. However, these methods may lose too much information to correctly estimate the results of clustering algorithms. Although the visual cluster validity (VCV) method of Hathaway and Bezdek can successfully solve this problem, it can only be applied for object data, i.e. feature measurements. There are very few validity methods that can be used to analyze the validity of data where only a similarity or dissimilarity relation exists – relational data. To tackle this problem, this paper presents a relational visual cluster validity (RVCV) method to assess the validity of clustering relational data. This is done by combining the results of the non-Euclidean relational fuzzy c-means (NERFCM) algorithm with a modification of the VCV method to produce a visual representation of cluster validity. RVCV can cluster complete and incomplete relational data and adds to the visual cluster validity theory. Numeric examples using synthetic and real data are presente
Latent class analysis for segmenting preferences of investment bonds
Market segmentation is a key component of conjoint analysis which addresses consumer
preference heterogeneity. Members in a segment are assumed to be homogenous in their
views and preferences when worthing an item but distinctly heterogenous to members of other
segments. Latent class methodology is one of the several conjoint segmentation procedures
that overcome the limitations of aggregate analysis and a-priori segmentation. The main
benefit of Latent class models is that market segment membership and regression parameters
of each derived segment are estimated simultaneously. The Latent class model presented in
this paper uses mixtures of multivariate conditional normal distributions to analyze rating
data, where the likelihood is maximized using the EM algorithm. The application focuses on
customer preferences for investment bonds described by four attributes; currency, coupon
rate, redemption term and price. A number of demographic variables are used to generate
segments that are accessible and actionable.peer-reviewe
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