7,118 research outputs found
Group Invariance, Stability to Deformations, and Complexity of Deep Convolutional Representations
The success of deep convolutional architectures is often attributed in part
to their ability to learn multiscale and invariant representations of natural
signals. However, a precise study of these properties and how they affect
learning guarantees is still missing. In this paper, we consider deep
convolutional representations of signals; we study their invariance to
translations and to more general groups of transformations, their stability to
the action of diffeomorphisms, and their ability to preserve signal
information. This analysis is carried by introducing a multilayer kernel based
on convolutional kernel networks and by studying the geometry induced by the
kernel mapping. We then characterize the corresponding reproducing kernel
Hilbert space (RKHS), showing that it contains a large class of convolutional
neural networks with homogeneous activation functions. This analysis allows us
to separate data representation from learning, and to provide a canonical
measure of model complexity, the RKHS norm, which controls both stability and
generalization of any learned model. In addition to models in the constructed
RKHS, our stability analysis also applies to convolutional networks with
generic activations such as rectified linear units, and we discuss its
relationship with recent generalization bounds based on spectral norms
Classification of Arrhythmia by Using Deep Learning with 2-D ECG Spectral Image Representation
The electrocardiogram (ECG) is one of the most extensively employed signals
used in the diagnosis and prediction of cardiovascular diseases (CVDs). The ECG
signals can capture the heart's rhythmic irregularities, commonly known as
arrhythmias. A careful study of ECG signals is crucial for precise diagnoses of
patients' acute and chronic heart conditions. In this study, we propose a
two-dimensional (2-D) convolutional neural network (CNN) model for the
classification of ECG signals into eight classes; namely, normal beat,
premature ventricular contraction beat, paced beat, right bundle branch block
beat, left bundle branch block beat, atrial premature contraction beat,
ventricular flutter wave beat, and ventricular escape beat. The one-dimensional
ECG time series signals are transformed into 2-D spectrograms through
short-time Fourier transform. The 2-D CNN model consisting of four
convolutional layers and four pooling layers is designed for extracting robust
features from the input spectrograms. Our proposed methodology is evaluated on
a publicly available MIT-BIH arrhythmia dataset. We achieved a state-of-the-art
average classification accuracy of 99.11\%, which is better than those of
recently reported results in classifying similar types of arrhythmias. The
performance is significant in other indices as well, including sensitivity and
specificity, which indicates the success of the proposed method.Comment: 14 pages, 5 figures, accepted for future publication in Remote
Sensing MDPI Journa
Robust ASR using Support Vector Machines
The improved theoretical properties of Support Vector Machines with respect to other machine learning alternatives due to their max-margin training paradigm have led us to suggest them as a good technique for robust speech recognition. However, important shortcomings have had to be circumvented, the most important being the normalisation of the time duration of different realisations of the acoustic speech units.
In this paper, we have compared two approaches in noisy environments: first, a hybrid HMM–SVM solution where a fixed number of frames is selected by means of an HMM segmentation and second, a normalisation kernel called Dynamic Time Alignment Kernel (DTAK) first introduced in Shimodaira et al. [Shimodaira, H., Noma, K., Nakai, M., Sagayama, S., 2001. Support vector machine with dynamic time-alignment kernel for speech recognition. In: Proc. Eurospeech, Aalborg, Denmark, pp. 1841–1844] and based on DTW (Dynamic Time Warping). Special attention has been paid to the adaptation of both alternatives to noisy environments, comparing two types of parameterisations and performing suitable feature normalisation operations. The results show that the DTA Kernel provides important advantages over the baseline HMM system in medium to bad noise conditions, also outperforming the results of the hybrid system.Publicad
Low-Rank Matrices on Graphs: Generalized Recovery & Applications
Many real world datasets subsume a linear or non-linear low-rank structure in
a very low-dimensional space. Unfortunately, one often has very little or no
information about the geometry of the space, resulting in a highly
under-determined recovery problem. Under certain circumstances,
state-of-the-art algorithms provide an exact recovery for linear low-rank
structures but at the expense of highly inscalable algorithms which use nuclear
norm. However, the case of non-linear structures remains unresolved. We revisit
the problem of low-rank recovery from a totally different perspective,
involving graphs which encode pairwise similarity between the data samples and
features. Surprisingly, our analysis confirms that it is possible to recover
many approximate linear and non-linear low-rank structures with recovery
guarantees with a set of highly scalable and efficient algorithms. We call such
data matrices as \textit{Low-Rank matrices on graphs} and show that many real
world datasets satisfy this assumption approximately due to underlying
stationarity. Our detailed theoretical and experimental analysis unveils the
power of the simple, yet very novel recovery framework \textit{Fast Robust PCA
on Graphs
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