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  • 1.
    Sundin, Martin
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Venkitaraman, Arun
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Jansson, Magnus
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    A Connectedness Constraint for Learning Sparse Graphs2017In: 2017 25TH EUROPEAN SIGNAL PROCESSING CONFERENCE (EUSIPCO), IEEE , 2017, p. 151-155Conference paper (Refereed)
    Abstract [en]

    Graphs are naturally sparse objects that are used to study many problems involving networks, for example, distributed learning and graph signal processing. In some cases, the graph is not given, but must be learned from the problem and available data. Often it is desirable to learn sparse graphs. However, making a graph highly sparse can split the graph into several disconnected components, leading to several separate networks. The main difficulty is that connectedness is often treated as a combinatorial property, making it hard to enforce in e.g. convex optimization problems. In this article, we show how connectedness of undirected graphs can be formulated as an analytical property and can be enforced as a convex constraint. We especially show how the constraint relates to the distributed consensus problem and graph Laplacian learning. Using simulated and real data, we perform experiments to learn sparse and connected graphs from data.

  • 2.
    Venkitaraman, Arun
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
    Graph Signal Processing Meets Machine Learning2018Doctoral thesis, monograph (Other academic)
    Abstract [en]

    Graph signal processing is an emerging paradigm in signal processing which took birth in the search for a set of consistent mathematical tools to analyze signals which occur over networks or graphs. The viewpoint of signals through graphs is universal and applicable to a large variety of diverse real-world problems. In this thesis, we make contributions to graph signal processing in two different settings: graph signal processing theory and graph signal processing with machine learning. In the first setting, we derive a novel Hilbert transform framework for graph signals in answering the question of whether amplitude and frequency modulations be defined for graph signals. We generalize Gabor’s analytic signal and define amplitude and phase modulations for graph signals via a Hilbert transform which is shown to demonstrate ability to highlight anomalies or singularities over graphs.

    In the second setting, we bring together some of the popular machine learning approaches to graph signal processing, demonstrating how the two thought pro- cesses can be mutually coupled meaningfully for significant benefits. Specifically, we deal with the problem of predicting vector target signals which are graph signals over an associated graph. The input is taken to be a general quantity associated to the graph signal, but not necessarily the same physical quantity as that of the graph signal. In this way, we make graph signal output predictions with inputs which are agnostic to a graph structure. We apply this line of thought to extend some of the popular and powerful techniques in machine learning to graph signal setting: kernel regression, multi-kernel regression, Gaussian processes, and extreme learning machines. We show that our approach outperforms the conventional versions when the training samples are scarce and noisy: application to many real-world graph signal applications show that similar prediction performance as that of non-graph- aware versions is achieved with much less training data, and that too corrupted with noise. This also includes the extreme cases where data is partly missing or corrupted with large perturbations. This observation in turn points to the efficiency of our approach in terms of both availability of resources and computational complexity, which usually increases as datasize increases. Our approach stands out uniquely in being able to handle cases where the input and output are different physical quantities. It is also interesting to note that our approach performs reasonably well even in cases where the graph exists but is not known to the user.

    We conclude by addressing the general problem of learning graphs from graph signals in two ways. First, we show that learning of connected graphs can be trans- formed into a convex optimization constraint which can be easily augmented to any of the existing graph learning techniques. Second, we propose a sparsity based approach to learn graphs in a hyperparameter-free manner which is computation- ally efficient. In our first contribution in the context of learning graphs, we are concerned with learning connected graphs which describe the data, whereas in the second part, we focus on learning graphs that are effective in making predictions for the signal value at the different nodes.

  • 3.
    Venkitaraman, Arun
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
    Händel, Peter
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
    Extreme learning machine for graph signal processing2018In: 2018 26th European Signal Processing Conference (EUSIPCO), European Signal Processing Conference, EUSIPCO , 2018, p. 136-140, article id 8553088Conference paper (Refereed)
    Abstract [en]

    In this article, we improve extreme learning machines for regression tasks using a graph signal processing based regularization. We assume that the target signal for prediction or regression is a graph signal. With this assumption, we use the regularization to enforce that the output of an extreme learning machine is smooth over a given graph. Simulation results with real data confirm that such regularization helps significantly when the available training data is limited in size and corrupted by noise.

  • 4.
    Venkitaraman, Arun
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Signal Processing.
    Händel, Peter
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Graph linear prediction results in smaller error than standard linear prediction2015In: 2015 23rd European Signal Processing Conference, EUSIPCO 2015, Institute of Electrical and Electronics Engineers (IEEE), 2015, p. 220-224Conference paper (Refereed)
    Abstract [en]

    Linear prediction is a popular strategy employed in the analysis and representation of signals. In this paper, we propose a new linear prediction approach by considering the standard linear prediction in the context of graph signal processing, which has gained significant attention recently. We view the signal to be defined on the nodes of a graph with an adjacency matrix constructed using the coefficients of the standard linear predictor (SLP). We prove theoretically that the graph based linear prediction approach results in an equal or better performance compared with the SLP in terms of the prediction gain. We illustrate the proposed concepts by application to real speech signals.

  • 5.
    Venkitaraman, Arun
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
    Händel, Peter
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
    MULTI-KERNEL REGRESSION FOR GRAPH SIGNAL PROCESSING2018In: 2018 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), IEEE, 2018, p. 4644-4648Conference paper (Refereed)
    Abstract [en]

    We develop a multi-kernel based regression method for graph signal processing where the target signal is assumed to be smooth over a graph. In multi-kernel regression, an effective kernel function is expressed as a linear combination of many basis kernel functions. We estimate the linear weights to learn the effective kernel function by appropriate regularization based on graph smoothness. We show that the resulting optimization problem is shown to be convex and propose an accelerated projected gradient descent based solution. Simulation results using real-world graph signals show efficiency of the multi-kernel based approach over a standard kernel based approach.

  • 6.
    Venkitaraman, Arun
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Händel, Peter
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
    On Hilbert transform, analytic signal, and modulation analysis for signals over graphs2019In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 156, p. 106-115Article in journal (Refereed)
    Abstract [en]

    We propose Hilbert transform and analytic signal construction for signals over graphs. This is motivated by the popularity of Hilbert transform, analytic signal, and modulation analysis in conventional signal processing, and the observation that complementary insight is often obtained by viewing conventional signals in the graph setting. Our definitions of Hilbert transform and analytic signal use a conjugate symmetry-like property exhibited by the graph Fourier transform (GFT), resulting in a 'one-sided' spectrum for the graph analytic signal. The resulting graph Hilbert transform is shown to possess many interesting mathematical properties and also exhibit the ability to highlight anomalies/discontinuities in the graph signal and the nodes across which signal discontinuities occur. Using the graph analytic signal, we further define amplitude, phase, and frequency modulations for a graph signal. We illustrate the proposed concepts by showing applications to synthesized and real-world signals. For example, we show that the graph Hilbert transform can indicate presence of anomalies and that graph analytic signal, and associated amplitude and frequency modulations reveal complementary information in speech signals.

  • 7.
    Venkitaraman, Arun
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
    Frossard, Pascal
    Ecole Polytech Fed Lausanne, Signal Proc Lab LTS4, Lausanne, Switzerland..
    Chatterjee, Saikat
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
    KERNEL REGRESSION FOR GRAPH SIGNAL PREDICTION IN PRESENCE OF SPARSE NOISE2019In: 2019 IEEE INTERNATIONAL CONFERENCE ON ACOUSTICS, SPEECH AND SIGNAL PROCESSING (ICASSP), IEEE , 2019, p. 5426-5430Conference paper (Refereed)
    Abstract [en]

    In presence of sparse noise we propose kernel regression for predicting output vectors which are smooth over a given graph. Sparse noise models the training outputs being corrupted either with missing samples or large perturbations. The presence of sparse noise is handled using appropriate use of l(1)-norm along-with use of l(2)-norm in a convex cost function. For optimization of the cost function, we propose an iteratively reweighted least-squares (IRLS) approach that is suitable for kernel substitution or kernel trick due to availability of a closed form solution. Simulations using real-world temperature data show efficacy of our proposed method, mainly for limited-size training datasets.

  • 8.
    Venkitaraman, Arun
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Jansson, Magnus
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On Estimation of Covariance Matrices Modeled as a Sum of Kronecker Products2014Conference paper (Refereed)
  • 9.
    Venkitaraman, Arun
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Makkapati, V. V.
    Motion-based segmentation of chest and abdomen region of neonates from videos2015In: ICAPR 2015 - 2015 8th International Conference on Advances in Pattern Recognition, 2015Conference paper (Refereed)
    Abstract [en]

    Respiration rate (RR) is one of the important vital signs used for clinical monitoring of neonates in intensive care units. Due to the fragile skin of the neonates, it is preferable to have monitoring systems with minimal contact with the neonate. Recently, several methods have been proposed for contact-free monitoring of vital signs using a video camera. Detection of the chest-and-abdomen region of the neonate is crucial to determining the respiration rate accurately. We propose a technique for automatic selection of the region of interest (ROI) in neonates using motion. Our approach is based on the observation that points on the chest-and-abdomen region, and hence, the corresponding optic flow vectors, exhibit coherency in the motion caused by breathing. The motion induced due to the movement of the neonate (e.g., hands and legs) is not coherent and hence does not exhibit the characteristics of respiratory motion. We evaluate the proposed technique using several videos of neonates and demonstrate that it picks up the ROI accurately in spite of the movement of the neonate. We compare its performance with that of the standard motion history image (MHI) framework, using different metrics. Results indicate that our method can be profitably employed in RR studies.

  • 10.
    Venkitaraman, Arun
    et al.
    Department of Electrical Engineering, Indian Institute of Science, Bangalore-560012, India .
    Seelamantula, Chandra Sekhar
    Department of Electrical Engineering, Indian Institute of Science, Bangalore-560012, India .
    A Technique to Compute Smooth Amplitude, Phase, and Frequency Modulations From the Analytic Signal2012In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 19, no 10, p. 623-626Article in journal (Refereed)
    Abstract [en]

    Gabor’s analytic signal (AS) is a unique complexsignal corresponding to a real signal, but in general, it admitsinfinitely-many combinations of amplitude and frequency modu-lations (AM and FM, respectively). The standard approach is toenforce a non-negativity constraint on the AM, but this results indiscontinuities in the corresponding phase modulation (PM), andhence, an FM with discontinuities particularly when the under-lying AM-FM signal is over-modulated. In this letter, we analyzethe phase discontinuities and propose a technique to computesmooth AM and FM from the AS, by relaxing the non-negativityconstraint on the AM. The proposed technique iseffective athandling over-modulated signals. We present simulation results tosupport the theoretical calculations.

  • 11.
    Venkitaraman, Arun
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Seelamantula, Chandra Sekhar
    Binaural Signal Processing Motivated Generalized Analytic Signal Construction and AM-FM Demodulation2014In: IEEE-ACM TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE PROCESSING, ISSN 2329-9290, Vol. 22, no 6, p. 1023-1036Article in journal (Refereed)
    Abstract [en]

    Binaural hearing studies show that the auditory system uses the phase-difference information in the auditory stimuli for localization of a sound source. Motivated by this finding, we present a method for demodulation of amplitude-modulated-frequency-modulated (AM-FM) signals using a signal and its arbitrary phase-shifted version. The demodulation is achieved using two allpass filters, whose impulse responses are related through the fractional Hilbert transform (FrHT). The allpass filters are obtained by cosine-modulation of a zero-phase flat-top prototype halfband lowpass filter. The outputs of the filters are combined to construct an analytic signal (AS) from which the AM and FM are estimated. We show that, under certain assumptions on the signal and the filter structures, the AM and FM can be obtained exactly. The AM-FM calculations are based on the quasi-eigenfunction approximation. We then extend the concept to the demodulation of multicomponent signals using uniform and non-uniform cosine-modulated filterbank (FB) structures consisting of flat bandpass filters, including the uniform cosine-modulated, equivalent rectangular bandwidth (ERB), and constant-Q filterbanks. We validate the theoretical calculations by considering application on synthesized AM-FM signals and compare the performance in presence of noise with three other multiband demodulation techniques, namely, the Teager-energy-based approach, the Gabor's AS approach, and the linear transduction filter approach. We also show demodulation results for real signals.

  • 12.
    Venkitaraman, Arun
    et al.
    Department of Electrical Engineering, Indian Institute of Science, Bangalore 560012, India .
    Seelamantula, Chandra Sekhar
    Indian Institute of Science Bangalore.
    Fractional Hilbert transform extensions and associated analytic signal construction2014In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 94, p. 359-372Article in journal (Refereed)
    Abstract [en]

    The analytic signal (AS) was proposed by Gabor as a complex signal corresponding to a given real signal. The AS has a one-sided spectrum and gives rise to meaningful spectral averages. The Hilbert transform (HT) is a key component in Gabor's AS construction. We generalize the construction methodology by employing the fractional Hilbert transform (FrHT), without going through the standard fractional Fourier transform (FrFT) route. We discuss some properties of the fractional Hilbert operator and show how decomposition of the operator in terms of the identity and the standard Hilbert operators enables the construction of a family of analytic signals. We show that these analytic signals also satisfy Bedrosian-type properties and that their time-frequency localization properties are unaltered. We also propose a generalized-phase AS (GPAS) using a generalized-phase Hilbert transform (GPHT). We show that the GPHT shares many properties of the FrHT, in particular, selective highlighting of singularities, and a connection with Lie groups. We also investigate the duality between analyticity and causality concepts to arrive at a representation of causal signals in terms of the FrHT and GPHT. On the application front, we develop a secure multi-key single-sideband (SSB) modulation scheme and analyze its performance in noise and sensitivity to security key perturbations.

  • 13.
    Venkitaraman, Arun
    et al.
    Indian Institute of Science Bangalore.
    Seelamantula, Chandra Sekhar
    Indian Institute of Science Bangalore, department of Electrical Engineering.
    On Computing Amplitude, Phase, and Frequency Modulations Using a Vector Interpretation of the Analytic Signal2013In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 20, no 12, p. 1187-1190Article in journal (Refereed)
    Abstract [en]

    The amplitude-modulation (AM) and phase-modulation (PM) of an amplitude-modulated frequency-modulated (AM-FM) signal are defined as the modulus and phase angle, respectively, of the analytic signal (AS). The FM is defined as the derivative of the PM. However, this standard definition results in a PM with jump discontinuities in cases when the AM index exceeds unity, resulting in an FM that contains impulses. We propose a new approach to define smooth AM, PM, and FM for the AS, where the PM is computed as the solution to an optimization problem based on a vector interpretation of the AS. Our approach is directly linked to the fractional Hilbert transform (FrHT) and leads to an eigenvalue problem. The resulting PM and AM are shown to be smooth, and in particular, the AM turns out to be bipolar. We show an equivalence of the eigenvalue formulation to the square of the AS, and arrive at a simple method to compute the smooth PM. Some examples on synthesized and real signals are provided to validate the theoretical calculations.

  • 14.
    Venkitaraman, Arun
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. Department of Electrical Engineering, Indian Institute of Science, Bangalore 560012, India .
    Seelamantula, Chandra Sekhar
    Indian Institute of Science Bangalore.
    Temporal Envelope Fit of Transient Audio Signals2013In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 20, no 12, p. 1191-1194Article in journal (Refereed)
    Abstract [en]

    We address the problem of temporal envelope modeling for transient audio signals. We propose the Gamma distribution function (GDF) as a suitable candidate for modeling the envelope keeping in view some of its interesting properties such as asymmetry, causality, near-optimal time-bandwidth product, controllability of rise and decay, etc. The problem of finding the parameters of the GDF becomes a nonlinear regression problem. We overcome the hurdle by using a logarithmic envelope fit, which reduces the problem to one of linear regression. The logarithmic transformation also has the feature of dynamic range compression. Since temporal envelopes of audio signals are not uniformly distributed, in order to compute the amplitude, we investigate the importance of various loss functions for regression. Based on synthesized data experiments, wherein we have a ground truth, and real-world signals, we observe that the least-squares technique gives reasonably accurate amplitude estimates compared with other loss functions.

  • 15.
    Venkitaraman, Arun
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
    Zachariah, Dave
    Uppsala Univ, Div Syst & Control, Dept Informat Technol, S-75237 Uppsala, Sweden..
    Learning Sparse Graphs for Prediction of Multivariate Data Processes2019In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 26, no 3, p. 495-499Article in journal (Refereed)
    Abstract [en]

    We address the problem of prediction of multivariate data process using an underlying graph model. We develop a method that learns a sparse partial correlation graph in a tuning-free and computationally efficient manner. Specifically, the graph structure is learned recursively without the need for cross validation or parameter tuning by building upon a hyperparameter-free framework. Our approach does not require the graph to be undirected and also accommodates varying noise levels across different nodes. Experiments using real-world datasets show that the proposed method offers significant performance gains in prediction, in comparison with the graphs frequently associated with these datasets.

  • 16.
    Venkitarman, Arun
    et al.
    Department of Electrical Engineering, Indian Institute of Science, Bangalore 560012, India.
    Adiga, Aniruddha
    Indian Institute of Science Bangalore.
    Seelamantula, Chandra Sekhar
    Indian Institute of Science Bangalore.
    Auditory-motivated Gammatone wavelet transform2014In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 94, p. 608-619Article in journal (Refereed)
    Abstract [en]

    The ability of the continuous wavelet transform (CWT) to provide good time and frequency localization has made it a popular tool in time-frequency analysis of signals. Wavelets exhibit constant-Q property, which is also possessed by the basilar membrane filters in the peripheral auditory system. The basilar membrane filters or auditory filters are often modeled by a Gammatone function, which provides a good approximation to experimentally determined responses. The filterbank derived from these filters is referred to as a Gammatone filterbank. In general, wavelet analysis can be likened to a filterbank analysis and hence the interesting link between standard wavelet analysis and Gammatone filterbank. However, the Gammatone function does not exactly qualify as a wavelet because its time average is not zero. We show how bona fide wavelets can be constructed out of Gammatone functions. We analyze properties such as admissibility, time-bandwidth product, vanishing moments, which are particularly relevant in the context of wavelets. We also show how the proposed auditory wavelets are produced as the impulse response of a linear, shift-invariant system governed by a linear differential equation with constant coefficients. We propose analog circuit implementations of the proposed CWT. We also show how the Gammatone-derived wavelets can be used for singularity detection and time-frequency analysis of transient signals.

  • 17.
    Zaki, Ahmed
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Venkitaraman, Arun
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Rasmussen, Lars Kildehoj
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Greedy Sparse Learning Over Network2018In: IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS, ISSN 2373-776X, Vol. 4, no 3, p. 424-435Article in journal (Refereed)
    Abstract [en]

    In this paper, we develop a greedy algorithm for solving the problem of sparse learning over a right stochastic network in a distributed manner. The nodes iteratively estimate the sparse signal by exchanging a weighted version of their individual intermediate estimates over the network. We provide a restricted-isometry-property (RIP)-based theoretical performance guarantee in the presence of additive noise. In the absence of noise, we show that under certain conditions on the RIP-constant of measurement matrix at each node of the network, the individual node estimates collectively converge to the true sparse signal. Furthermore, we provide an upper bound on the number of iterations required by the greedy algorithm to converge. Through simulations, we also show that the practical performance of the proposed algorithm is better than other state-of-the-art distributed greedy algorithms found in the literature.

  • 18.
    Zaki, Ahmed
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Venkitaraman, Arun
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Rasmussen, Lars Kildehöj
    Distributed Greedy Sparse Learning over Doubly Stochastic Networks2017In: 2017 25TH EUROPEAN SIGNAL PROCESSING CONFERENCE (EUSIPCO), IEEE , 2017, p. 361-364Conference paper (Refereed)
    Abstract [en]

    In this paper, we develop a greedy algorithm for sparse learning over a doubly stochastic network. In the proposed algorithm, nodes of the network perform sparse learning by exchanging their individual intermediate variables. The algorithm is iterative in nature. We provide a restricted isometry property (RIP)-based theoretical guarantee both on the performance of the algorithm and the number of iterations required for convergence. Using simulations, we show that the proposed algorithm provides good performance.

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