## REFERENCES

[1]Shuman, D.I.; Narang, S.K.; Frossard, P.; Ortega, A.; Vandergheynst, P.: The emerging field of signal processing on graphs: extending high-dimensional data analysis to networks and other irregular domains. IEEE Signal Process. Mag., 30(3) (2013), 83–98.

[2]Sandryhaila, A.; Moura, J.; M.F.: Discrete signal processing on graphs: Frequency analysis. IEEE. Trans. Signal Process., 62(12) (2014), 3042–3054.

[3]Crovella, M.; Kolaczyk, E.: Graph wavelets for spatial traffic analysis, in Proc. IEEE INFOCOM, vol. 3, March 2003, 1848–1857, San Francisco, CA, USA.

[4]Maggioni, M.; Bremer, J.C.; Coifman, R.R.; Szlam, A.D.: Biorthogonal diffusion wavelets for multiscale representations on manifolds and graphs, in Proc. SPIE Wavelet XI, vol. 914, September 2005.

[5]Szlam, A.D.; Maggioni, M.; Coifman, R.R.; Bremer, J.C. Jr.: Diffusion-driven multiscale analysis on manifolds and graphs: top-down and bottom-up constructions, in Proc. SPIE Wavelets, vol. 5914, August 2005, 445–455.

[6]Coifman, R.R.; Maggioni, M.: Diffusion wavelets. Appl. Comput. Harmon. Anal., 21(1) (2006), 53–94.

[7]Bremer, J.C.; Coifman, R.R.; Maggioni, M.; Szlam, A.D.: Diffusion wavelet packets. Appl. Comput. Harmon. Anal., 21(1) (2006), 95–112.

[8]Lafon, S.; Lee, A.B.: Diffusion maps and coarse-graining: A unified framework for dimensionality reduction, graph partitioning, and data set parameterization. IEEE Trans. Pattern Anal. Mach. Intell., 28(9) (2006), 1393–1403.

[9]Wang, W.; Ramchandran, K.: Random multiresolution representations for arbitrary sensor network graphs, in Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing vol. 4, May 2006, 161–164, Toulouse, France.

[10]Narang, S.K.; Ortega, A.: Lifting based wavelet transforms on graphs, in *Proc. APSIPA ASC*, Sapporo, Japan, October 2009, 441–444.

[11]Jansen, M.; Nason, G.P.; Silverman, B.W.: Multiscale methods for data on graphs and irregular multidimensional situations. J. R. Stat. Soc. Ser. B Stat. Methodol., 71(1) (2009), 97–125.

[12]Gavish, M.; Nadler, B.; Coifman, R.R.: Multiscale wavelets on trees, graphs and high dimensional data: Theory and applications to semi supervised learning, in *Proc. Int. Conf. Mach. Learn.*, Haifa, Israel, June 2010, 367–374.

[13]Hammond, D.K.; Vandergheynst, P.; Gribonval, R.: Wavelets on graphs via spectral graph theory. Appl. Comput. Harmon. Anal., 30(2) (2011), 129–150.

[14]Ram, I.; Elad, M.; Cohen, I.: Generalized tree-based wavelet transform. IEEE Trans. Signal Process., 59(9) (2011), 4199–4209.

[15]Narang, S.K.; Ortega, A.: Perfect reconstruction two-channel wavelet filter-banks for graph structured data. IEEE. Trans. Signal Process., 60(6) (2012), 2786–2799.

[16]Leonardi, N.; Van De Ville, D.: Tight wavelet frames on multislice graphs. IEEE Trans. Signal Process., 61(13) (2013), 3357–3367.

[17]Ekambaram, V.N.; Fanti, G.C.; Ayazifar, B.; Ramchandran, K.: Critically-sampled perfect-reconstruction spline-wavelet filter banks for graph signals, in *Proc. Global Conf. Signal and Information Processing*, Austin, TX, December 2013, 475–478.

[18]Narang, S.K.; Ortega, A.: Compact support biorthogonal wavelet filterbanks for arbitrary undirected graphs. IEEE Trans. Signal Process., 61(19) (2013), 4673–4685.

[19]Liu, P.; Wang, X.; Gu, Y.: Coarsening graph signal with spectral invariance, in *Proc. IEEE Int. Conf. Accoustics, Speech, and Signal Process.*, Florence, Italy, May 2014, 1070–1074.

[20]Sakiyama, A.; Tanaka, Y.: Oversampled graph Laplacian matrix for graph filter banks. IEEE Trans. Signal Process., 62(24) (2014), 6425–6437.

[21]Nguyen, H.Q.; Do, M.N.: Downsampling of signals on graphs via maximum spanning trees. IEEE Trans. Signal Process., 63(1) (2015), 182–191.

[22]Shuman, D.I.; Wiesmeyr, C.; Holighaus, N.; Vandergheynst, P.: Spectrum-adapted tight graph wavelet and vertex-frequency frames. IEEE Trans. Signal Process., 63(16) (2015), 4223–4235.

[23]Shuman, D.I.; Ricaud, B.; Vandergheynst, P.: Vertex-frequency analysis on graphs. Appl. Comput. Harmon. Anal., 40(2) (2016), 260–291.

[24]Shuman, D.I.; Faraji, M.; Vandergheynst, P.: A multiscale pyramid transform for graph signals. IEEE. Trans. Signal Process., vol. 64, 2016, 2119–2134.

[25]Matolcsi, T.; Szücs, J.: Intersections Des Mesures Spectrales Conjugées, vol. 277, CR Acad. Sci., Paris, 1973, 841–843.

[26]Donoho, D.L.; Stark, P.B.: Uncertainty principles and signal recovery. SIAM J. Appl. Math, 49(3) (1989), 906–931.

[27]Donoho, D.L.; Huo, X.: Uncertainty principles and ideal atomic decomposition. IEEE Trans. Inf. Theory, 47(7) (2001), 2845–2862.

[28]Elad, M.; Bruckstein, A.M.: A generalized uncertainty principle and sparse representation in pairs of bases. IEEE Trans. Inf. Theory, 48(9) (2002), 2558–2567.

[29]Gribonval, R.; Nielsen, M.: Sparse representations in unions of bases. IEEE Trans. Inf. Theory, 49(12) (2003), 3320–3325.

[30]Candes, E.J.; Romberg, J.: Quantitative robust uncertainty principles and optimally sparse decompositions. Found. Comput. Math., 6(2) (2006), 227–254.

[31]Ghobber, S.; Jaming, P.: On uncertainty principles in the finite dimensional setting. Linear Algebra Appl., 435(4) (2011), 751–768.

[32]Ricaud, B.; Torrésani, B.: Refined support and entropic uncertainty inequalities. IEEE Trans. Inf. Theory, 59(7) (2013), 4272–4279.

[33]Ricaud, B.; Shuman, D.I.; Vandergheynst, P.: n the sparsity of wavelet coefficients for signals on graphs, in *SPIE Wavelets and Sparsity*, San Diego, California, August 2013.

[34]McGraw, P.N.; Menzinger, M.: Laplacian spectra as a diagnostic tool for network structure and dynamics. Phys. Rev. E, 77(3) (2008), 031102-1–031102-14.

[35]Saito, N.; Woei, E.: On the phase transition phenomenon of graph Laplacian eigenfunctions on trees. RIMS Kokyuroku, vol. 1743 (2011), 77–90.

[36]Folland, G.; Sitaram, A.: The uncertainty principle: A mathematical survey. J. Fourier Anal. Appl., 3(3) (1997), 207–238.

[37]Mallat, S.G.: A Wavelet Tour of Signal Processing: the sparse way, 3rd ed. *Academic Press*, 2008.

[38]Agaskar, A.; Lu, Y.M.: An uncertainty principle for functions defined on graphs, in Proc. SPIE, vol. 8138, San Diego, CA, August 2011, 81380T-1–81380T-11.

[39]Agaskar, A.; Lu, Y.M.: Uncertainty principles for signals defined on graphs: bounds and characterizations, in *Proc. IEEE Int. Conf. Acc., Speech, and Signal Process.*, Kyoto, Japan, March 2012, 3493–3496.

[40]Agaskar, A.; Lu, Y.M.: A spectral graph uncertainty principle. IEEE Trans. Inf. Theory, 59(7) (2013), 4338–4356.

[41]Pasdeloup, B.; Alami, R.; Gripon, V.; Rabbat, M.: Toward an uncertainty principle for weighted graphs, in *Proc. Eur. Signal Process. Conf. (EUSIPCO)*, August 2015, 1496–1500, Nice, France.

[42]Tsitsvero, M.; Barbarossa, S.; Di Lorenzo, P.: Signals on graphs: Uncertainty principle and sampling. IEEE Trans. Signal Process., 64(18) (2016), 4845–4860.

[43]Slepian, D.; Pollak, H.O.: Prolate spheroidal wave functions, Fourier analysis and uncertainty. Bell System Tech. J., 40(1) (1961), 43–63.

[44]Pesenson, I.Z.: Sampling solutions of schrödinger equations on combinatorial graphs, in *IEEE 2015 Int. Conf. Sampling Theory and Applications (SampTA)*, 2015, 82–85, Washington, DC, USA.

[45]Maassen, H.; Uffink, J.: Generalized entropic uncertainty relations. Phys. Rev. Lett., 60(12) (1988), 1103–1106.

[46]Reed, M.; Simon, B.: Methods of Modern Mathematical Physics, Vol. 2.: Fourier Analysis, Self-Adjointness, Academic Press, 1975.

[47]Grady, L.J.; Polimeni, J.R.: Discrete Calculus, *in Applied Analysis on Graphs for Computational Science*, Springer-Verlag London, 2010.

[48]Lieb, E.H.: Integral bounds for radar ambiguity functions and Wigner distributions. J. Math. Phys., 31(3) (1990), 594.

[49]Sandryhaila, A.; Moura, J.; M.F.: Discrete signal processing on graphs. IEEE. Trans. Signal Process., 61(7) (2013), 1644–1656.

[50]Chung, F.; R.K.: Spectral Graph Theory, in Vol. 92 of the CBMS Regional Conference Series in Mathematics. *American Mathematical Society*, 1997, pp. 212.

[51]Rényi, A.: On measures of entropy and information, in *Proc. Fourth Berkeley Symp. Mathematics, Statistics and Probability*, 1961, 547–561, University of California Press.

[52]Ricaud, B.; Torrésani, B.: A survey of uncertainty principles and some signal processing applications. Adv. Comput. Math., 40(3) (2014), 629–650.

[53]Dekel, Y.; Lee, J.R.; Linial, N.: Eigenvectors of random graphs: Nodal domains. Random Structures Algorithms, 39(1) (2011), 39–58.

[54]Dumitriu, I.; Pal, S.: Sparse regular random graphs: Spectral density and eigenvectors. Ann. Probab., 40(5) (2012), 2197–2235.

[55]Tran, L.V.; Vu, V.H.; Wang, K.: Sparse random graphs: Eigenvalues and eigenvectors. Random Struct. Algo., 42(1) (2013), 110–134.

[56]Brooks, S.; Lindenstrauss, E.: Non-localization of eigenfunctions on large regular graphs. Israel J. Math., 193(1) (2013), 1–14.

[57]Nakatsukasa, Y.; Saito, N.; Woei, E.: Mysteries around the graph Laplacian eigenvalue 4. Linear Algebra Appl., 438(8) (2013), 3231–3246.

[58]Beckner, W.: Inequalities in Fourier analysis. Ann. Math., 102(1) (1975), 159–182.

[59]Gilbert, J.; Rzeszotnik, Z.: The norm of the {Fourier} transform on finite abelian groups. Ann. Inst. Fourier, 60(4) (2010), 1317–1346.

[60]Christensen, O.: Frames and Bases: An Introductory Course, *in Applied and Numerical Harmonic Analysis*, 2008, Birkhäuser Basel.

[61]Kovačević, J.; Chebira, A.: Life beyond bases: The advent of frames (part I). IEEE Signal Process. Mag., 24(4) (2007), 86–104.

[62]Kovačević, J.; Chebira, A.: Life beyond bases: The advent of frames (part II). IEEE Signal Process. Mag., 24(5) (2007), 115–125.

[63]Metzger, B.; Stollmann, P.: Heat kernel estimates on weighted graphs. Bull. London Math. Soc., 32(4) (2000), 477–483.

[64]Leonardi, N.; Van De Ville, D.: Wavelet frames on graphs defined by FMRI functional connectivity, in *Proc. IEEE Int. Symp. Biomed. Imag.*, Chicago, IL, March 2011, 2136–2139.

[65]Thanou, D.; Shuman, D.I.; Frossard, P.: Learning parametric dictionaries for signals on graphs. IEEE. Trans. Signal Process., 62(15) (2014), 3849–3862.

[66]Feichtinger, H.; Onchis-Moaca, D.; Ricaud, B.; Torrésani, B.; Wiesmeyr, C.: A method for optimizing the ambiguity function concentration, in *Proc. Eur. Signal Processing Conf. (EUSIPCO)*, August 2012, 804–808, Bucharest, Romania.

[67]Perraudin, N.; Vandergheynst, P.: Stationary signal processing on graphs. IEEE. Trans. Signal Process., 65(13) (2017), 3462–3477.

[68]Gadde, A.; Ortega, A.: A probabilistic interpretation of sampling theory of graph signals, in *Proc. IEEE Int. Conf. Acc., Speech, and Signal Processing*, April 2015, 3257–3261, Brisbane, QLD, Australia.

[69]Zhang, C.; Florêncio, D.; Chou, P.A.: Graph signal processing–a probabilistic framework. Microsoft Res., Redmond, WA, USA, Technical Report MSR-TR-2015-31, 2015.

[70]Pesenson, I.: Variational splines and Paley-Wiener spaces on combinatorial graphs. Constr. Approx., 29(1) (2009), 1–21.

[71]Perraudin, N.; Shuman, D.; Puy, G.; Vandergheynst, P.: UNLocBoX: a matlab convex optimization toolbox using proximal splitting methods, 2014. ArXiv preprint arXiv:1402.0779.

[72]Perraudin, N.; Paratte, J.; Shuman, D.; Kalofolias, V.; Vandergheynst, P.; Hammond, D.K.: GSPBOX: a toolbox for signal processing on graphs, 2014. ArXiv preprint arXiv:1408.5781.

[73]Puy, G.; Tremblay, N.; Gribonval, R.; Vandergheynst, P.: Random sampling of bandlimited signals on graphs. Appl. Comput. Harmon. Anal., vol. 44, 2018, 446–475.

[74]Chen, S.; Varma, R.; Singh, A.; Kovacević, J.: Signal recovery on graphs: Random versus experimentally designed sampling, in *IEEE Int. Conf. Sampling Theory and Applications (SampTA) 2015*, 2015, 337–341, Washington, DC, USA.

[75]Anis, A.; Gadde, A.; Ortega, A.: Efficient sampling set selection for bandlimited graph signals using graph spectral proxies. IEEE Trans. Signal Process., 64(14) (2016), 3775–3789.

[76]Chen, S.; Varma, R.; Singh, A.; Kova{č}ević, J.: Signal recovery on graphs: Fundamental limits of sampling strategies. IEEE Trans. Signal Info. Process. Networks, 2(4) (2016), 539–554.

[77]Strang, G.: The discrete cosine transform. SIAM Review, 41(1) (1999), 135–147.

[78]Pinsky, M.A.: Introduction to Fourier Analysis and Wavelets, Vol. 102 of the Graduate Studies in Mathematics, *Am. Math. Soci.*, 2002.