14,403 research outputs found
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
Efficient Optimization of Echo State Networks for Time Series Datasets
Echo State Networks (ESNs) are recurrent neural networks that only train
their output layer, thereby precluding the need to backpropagate gradients
through time, which leads to significant computational gains. Nevertheless, a
common issue in ESNs is determining its hyperparameters, which are crucial in
instantiating a well performing reservoir, but are often set manually or using
heuristics. In this work we optimize the ESN hyperparameters using Bayesian
optimization which, given a limited budget of function evaluations, outperforms
a grid search strategy. In the context of large volumes of time series data,
such as light curves in the field of astronomy, we can further reduce the
optimization cost of ESNs. In particular, we wish to avoid tuning
hyperparameters per individual time series as this is costly; instead, we want
to find ESNs with hyperparameters that perform well not just on individual time
series but rather on groups of similar time series without sacrificing
predictive performance significantly. This naturally leads to a notion of
clusters, where each cluster is represented by an ESN tuned to model a group of
time series of similar temporal behavior. We demonstrate this approach both on
synthetic datasets and real world light curves from the MACHO survey. We show
that our approach results in a significant reduction in the number of ESN
models required to model a whole dataset, while retaining predictive
performance for the series in each cluster
Modeling and Recognition of Smart Grid Faults by a Combined Approach of Dissimilarity Learning and One-Class Classification
Detecting faults in electrical power grids is of paramount importance, either
from the electricity operator and consumer viewpoints. Modern electric power
grids (smart grids) are equipped with smart sensors that allow to gather
real-time information regarding the physical status of all the component
elements belonging to the whole infrastructure (e.g., cables and related
insulation, transformers, breakers and so on). In real-world smart grid
systems, usually, additional information that are related to the operational
status of the grid itself are collected such as meteorological information.
Designing a suitable recognition (discrimination) model of faults in a
real-world smart grid system is hence a challenging task. This follows from the
heterogeneity of the information that actually determine a typical fault
condition. The second point is that, for synthesizing a recognition model, in
practice only the conditions of observed faults are usually meaningful.
Therefore, a suitable recognition model should be synthesized by making use of
the observed fault conditions only. In this paper, we deal with the problem of
modeling and recognizing faults in a real-world smart grid system, which
supplies the entire city of Rome, Italy. Recognition of faults is addressed by
following a combined approach of multiple dissimilarity measures customization
and one-class classification techniques. We provide here an in-depth study
related to the available data and to the models synthesized by the proposed
one-class classifier. We offer also a comprehensive analysis of the fault
recognition results by exploiting a fuzzy set based reliability decision rule
A Two-stage Classification Method for High-dimensional Data and Point Clouds
High-dimensional data classification is a fundamental task in machine
learning and imaging science. In this paper, we propose a two-stage multiphase
semi-supervised classification method for classifying high-dimensional data and
unstructured point clouds. To begin with, a fuzzy classification method such as
the standard support vector machine is used to generate a warm initialization.
We then apply a two-stage approach named SaT (smoothing and thresholding) to
improve the classification. In the first stage, an unconstraint convex
variational model is implemented to purify and smooth the initialization,
followed by the second stage which is to project the smoothed partition
obtained at stage one to a binary partition. These two stages can be repeated,
with the latest result as a new initialization, to keep improving the
classification quality. We show that the convex model of the smoothing stage
has a unique solution and can be solved by a specifically designed primal-dual
algorithm whose convergence is guaranteed. We test our method and compare it
with the state-of-the-art methods on several benchmark data sets. The
experimental results demonstrate clearly that our method is superior in both
the classification accuracy and computation speed for high-dimensional data and
point clouds.Comment: 21 pages, 4 figure
Data granulation by the principles of uncertainty
Researches in granular modeling produced a variety of mathematical models,
such as intervals, (higher-order) fuzzy sets, rough sets, and shadowed sets,
which are all suitable to characterize the so-called information granules.
Modeling of the input data uncertainty is recognized as a crucial aspect in
information granulation. Moreover, the uncertainty is a well-studied concept in
many mathematical settings, such as those of probability theory, fuzzy set
theory, and possibility theory. This fact suggests that an appropriate
quantification of the uncertainty expressed by the information granule model
could be used to define an invariant property, to be exploited in practical
situations of information granulation. In this perspective, a procedure of
information granulation is effective if the uncertainty conveyed by the
synthesized information granule is in a monotonically increasing relation with
the uncertainty of the input data. In this paper, we present a data granulation
framework that elaborates over the principles of uncertainty introduced by
Klir. Being the uncertainty a mesoscopic descriptor of systems and data, it is
possible to apply such principles regardless of the input data type and the
specific mathematical setting adopted for the information granules. The
proposed framework is conceived (i) to offer a guideline for the synthesis of
information granules and (ii) to build a groundwork to compare and
quantitatively judge over different data granulation procedures. To provide a
suitable case study, we introduce a new data granulation technique based on the
minimum sum of distances, which is designed to generate type-2 fuzzy sets. We
analyze the procedure by performing different experiments on two distinct data
types: feature vectors and labeled graphs. Results show that the uncertainty of
the input data is suitably conveyed by the generated type-2 fuzzy set models.Comment: 16 pages, 9 figures, 52 reference
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
- …