6,044 research outputs found
On Recursive Edit Distance Kernels with Application to Time Series Classification
This paper proposes some extensions to the work on kernels dedicated to
string or time series global alignment based on the aggregation of scores
obtained by local alignments. The extensions we propose allow to construct,
from classical recursive definition of elastic distances, recursive edit
distance (or time-warp) kernels that are positive definite if some sufficient
conditions are satisfied. The sufficient conditions we end-up with are original
and weaker than those proposed in earlier works, although a recursive
regularizing term is required to get the proof of the positive definiteness as
a direct consequence of the Haussler's convolution theorem. The classification
experiment we conducted on three classical time warp distances (two of which
being metrics), using Support Vector Machine classifier, leads to conclude
that, when the pairwise distance matrix obtained from the training data is
\textit{far} from definiteness, the positive definite recursive elastic kernels
outperform in general the distance substituting kernels for the classical
elastic distances we have tested.Comment: 14 page
Discrete Elastic Inner Vector Spaces with Application in Time Series and Sequence Mining
This paper proposes a framework dedicated to the construction of what we call
discrete elastic inner product allowing one to embed sets of non-uniformly
sampled multivariate time series or sequences of varying lengths into inner
product space structures. This framework is based on a recursive definition
that covers the case of multiple embedded time elastic dimensions. We prove
that such inner products exist in our general framework and show how a simple
instance of this inner product class operates on some prospective applications,
while generalizing the Euclidean inner product. Classification experimentations
on time series and symbolic sequences datasets demonstrate the benefits that we
can expect by embedding time series or sequences into elastic inner spaces
rather than into classical Euclidean spaces. These experiments show good
accuracy when compared to the euclidean distance or even dynamic programming
algorithms while maintaining a linear algorithmic complexity at exploitation
stage, although a quadratic indexing phase beforehand is required.Comment: arXiv admin note: substantial text overlap with arXiv:1101.431
A review on distance based time series classification
Time series classification is an increasing research topic due to the vast amount of time series data
that is being created over a wide variety of fields. The particularity of the data makes it a challenging task
and different approaches have been taken, including the distance based approach. 1-NN has been a widely used
method within distance based time series classification due to its simplicity but still good performance. However,
its supremacy may be attributed to being able to use specific distances for time series within the classification
process and not to the classifier itself. With the aim of exploiting these distances within more complex classifiers,
new approaches have arisen in the past few years that are competitive or which outperform the 1-NN based
approaches. In some cases, these new methods use the distance measure to transform the series into feature
vectors, bridging the gap between time series and traditional classifiers. In other cases, the distances are employed
to obtain a time series kernel and enable the use of kernel methods for time series classification. One of the main
challenges is that a kernel function must be positive semi-definite, a matter that is also addressed within this
review. The presented review includes a taxonomy of all those methods that aim to classify time series using a
distance based approach, as well as a discussion of the strengths and weaknesses of each method.TIN2016-78365-
An Overview on Application of Machine Learning Techniques in Optical Networks
Today's telecommunication networks have become sources of enormous amounts of
widely heterogeneous data. This information can be retrieved from network
traffic traces, network alarms, signal quality indicators, users' behavioral
data, etc. Advanced mathematical tools are required to extract meaningful
information from these data and take decisions pertaining to the proper
functioning of the networks from the network-generated data. Among these
mathematical tools, Machine Learning (ML) is regarded as one of the most
promising methodological approaches to perform network-data analysis and enable
automated network self-configuration and fault management. The adoption of ML
techniques in the field of optical communication networks is motivated by the
unprecedented growth of network complexity faced by optical networks in the
last few years. Such complexity increase is due to the introduction of a huge
number of adjustable and interdependent system parameters (e.g., routing
configurations, modulation format, symbol rate, coding schemes, etc.) that are
enabled by the usage of coherent transmission/reception technologies, advanced
digital signal processing and compensation of nonlinear effects in optical
fiber propagation. In this paper we provide an overview of the application of
ML to optical communications and networking. We classify and survey relevant
literature dealing with the topic, and we also provide an introductory tutorial
on ML for researchers and practitioners interested in this field. Although a
good number of research papers have recently appeared, the application of ML to
optical networks is still in its infancy: to stimulate further work in this
area, we conclude the paper proposing new possible research directions
High-Dimensional Feature Selection by Feature-Wise Kernelized Lasso
The goal of supervised feature selection is to find a subset of input
features that are responsible for predicting output values. The least absolute
shrinkage and selection operator (Lasso) allows computationally efficient
feature selection based on linear dependency between input features and output
values. In this paper, we consider a feature-wise kernelized Lasso for
capturing non-linear input-output dependency. We first show that, with
particular choices of kernel functions, non-redundant features with strong
statistical dependence on output values can be found in terms of kernel-based
independence measures. We then show that the globally optimal solution can be
efficiently computed; this makes the approach scalable to high-dimensional
problems. The effectiveness of the proposed method is demonstrated through
feature selection experiments with thousands of features.Comment: 18 page
Learning to rank from medical imaging data
Medical images can be used to predict a clinical score coding for the
severity of a disease, a pain level or the complexity of a cognitive task. In
all these cases, the predicted variable has a natural order. While a standard
classifier discards this information, we would like to take it into account in
order to improve prediction performance. A standard linear regression does
model such information, however the linearity assumption is likely not be
satisfied when predicting from pixel intensities in an image. In this paper we
address these modeling challenges with a supervised learning procedure where
the model aims to order or rank images. We use a linear model for its
robustness in high dimension and its possible interpretation. We show on
simulations and two fMRI datasets that this approach is able to predict the
correct ordering on pairs of images, yielding higher prediction accuracy than
standard regression and multiclass classification techniques
Time Series Cluster Kernel for Learning Similarities between Multivariate Time Series with Missing Data
Similarity-based approaches represent a promising direction for time series
analysis. However, many such methods rely on parameter tuning, and some have
shortcomings if the time series are multivariate (MTS), due to dependencies
between attributes, or the time series contain missing data. In this paper, we
address these challenges within the powerful context of kernel methods by
proposing the robust \emph{time series cluster kernel} (TCK). The approach
taken leverages the missing data handling properties of Gaussian mixture models
(GMM) augmented with informative prior distributions. An ensemble learning
approach is exploited to ensure robustness to parameters by combining the
clustering results of many GMM to form the final kernel.
We evaluate the TCK on synthetic and real data and compare to other
state-of-the-art techniques. The experimental results demonstrate that the TCK
is robust to parameter choices, provides competitive results for MTS without
missing data and outstanding results for missing data.Comment: 23 pages, 6 figure
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