7,778 research outputs found
A kernel for time series based on global alignments
We propose in this paper a new family of kernels to handle times series,
notably speech data, within the framework of kernel methods which includes
popular algorithms such as the Support Vector Machine. These kernels elaborate
on the well known Dynamic Time Warping (DTW) family of distances by considering
the same set of elementary operations, namely substitutions and repetitions of
tokens, to map a sequence onto another. Associating to each of these operations
a given score, DTW algorithms use dynamic programming techniques to compute an
optimal sequence of operations with high overall score. In this paper we
consider instead the score spanned by all possible alignments, take a smoothed
version of their maximum and derive a kernel out of this formulation. We prove
that this kernel is positive definite under favorable conditions and show how
it can be tuned effectively for practical applications as we report encouraging
results on a speech recognition task
Times series averaging from a probabilistic interpretation of time-elastic kernel
At the light of regularized dynamic time warping kernels, this paper
reconsider the concept of time elastic centroid (TEC) for a set of time series.
From this perspective, we show first how TEC can easily be addressed as a
preimage problem. Unfortunately this preimage problem is ill-posed, may suffer
from over-fitting especially for long time series and getting a sub-optimal
solution involves heavy computational costs. We then derive two new algorithms
based on a probabilistic interpretation of kernel alignment matrices that
expresses in terms of probabilistic distributions over sets of alignment paths.
The first algorithm is an iterative agglomerative heuristics inspired from the
state of the art DTW barycenter averaging (DBA) algorithm proposed specifically
for the Dynamic Time Warping measure. The second proposed algorithm achieves a
classical averaging of the aligned samples but also implements an averaging of
the time of occurrences of the aligned samples. It exploits a straightforward
progressive agglomerative heuristics. An experimentation that compares for 45
time series datasets classification error rates obtained by first near
neighbors classifiers exploiting a single medoid or centroid estimate to
represent each categories show that: i) centroids based approaches
significantly outperform medoids based approaches, ii) on the considered
experience, the two proposed algorithms outperform the state of the art DBA
algorithm, and iii) the second proposed algorithm that implements an averaging
jointly in the sample space and along the time axes emerges as the most
significantly robust time elastic averaging heuristic with an interesting noise
reduction capability. Index Terms-Time series averaging Time elastic kernel
Dynamic Time Warping Time series clustering and classification
MRFalign: Protein Homology Detection through Alignment of Markov Random Fields
Sequence-based protein homology detection has been extensively studied and so
far the most sensitive method is based upon comparison of protein sequence
profiles, which are derived from multiple sequence alignment (MSA) of sequence
homologs in a protein family. A sequence profile is usually represented as a
position-specific scoring matrix (PSSM) or an HMM (Hidden Markov Model) and
accordingly PSSM-PSSM or HMM-HMM comparison is used for homolog detection. This
paper presents a new homology detection method MRFalign, consisting of three
key components: 1) a Markov Random Fields (MRF) representation of a protein
family; 2) a scoring function measuring similarity of two MRFs; and 3) an
efficient ADMM (Alternating Direction Method of Multipliers) algorithm aligning
two MRFs. Compared to HMM that can only model very short-range residue
correlation, MRFs can model long-range residue interaction pattern and thus,
encode information for the global 3D structure of a protein family.
Consequently, MRF-MRF comparison for remote homology detection shall be much
more sensitive than HMM-HMM or PSSM-PSSM comparison. Experiments confirm that
MRFalign outperforms several popular HMM or PSSM-based methods in terms of both
alignment accuracy and remote homology detection and that MRFalign works
particularly well for mainly beta proteins. For example, tested on the
benchmark SCOP40 (8353 proteins) for homology detection, PSSM-PSSM and HMM-HMM
succeed on 48% and 52% of proteins, respectively, at superfamily level, and on
15% and 27% of proteins, respectively, at fold level. In contrast, MRFalign
succeeds on 57.3% and 42.5% of proteins at superfamily and fold level,
respectively. This study implies that long-range residue interaction patterns
are very helpful for sequence-based homology detection. The software is
available for download at http://raptorx.uchicago.edu/download/.Comment: Accepted by both RECOMB 2014 and PLOS Computational Biolog
Autoregressive Kernels For Time Series
We propose in this work a new family of kernels for variable-length time
series. Our work builds upon the vector autoregressive (VAR) model for
multivariate stochastic processes: given a multivariate time series x, we
consider the likelihood function p_{\theta}(x) of different parameters \theta
in the VAR model as features to describe x. To compare two time series x and
x', we form the product of their features p_{\theta}(x) p_{\theta}(x') which is
integrated out w.r.t \theta using a matrix normal-inverse Wishart prior. Among
other properties, this kernel can be easily computed when the dimension d of
the time series is much larger than the lengths of the considered time series x
and x'. It can also be generalized to time series taking values in arbitrary
state spaces, as long as the state space itself is endowed with a kernel
\kappa. In that case, the kernel between x and x' is a a function of the Gram
matrices produced by \kappa on observations and subsequences of observations
enumerated in x and x'. We describe a computationally efficient implementation
of this generalization that uses low-rank matrix factorization techniques.
These kernels are compared to other known kernels using a set of benchmark
classification tasks carried out with support vector machines
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