NumPy-compatible sparse array library that integrates with Dask and SciPy's sparse linear algebra.ĭeep learning framework that accelerates the path from research prototyping to production deployment.Īn end-to-end platform for machine learning to easily build and deploy ML powered applications.ĭeep learning framework suited for flexible research prototyping and production.Ī cross-language development platform for columnar in-memory data and analytics. Labeled, indexed multi-dimensional arrays for advanced analytics and visualization NumPy-compatible array library for GPU-accelerated computing with Python.Ĭomposable transformations of NumPy programs: differentiate, vectorize, just-in-time compilation to GPU/TPU. NumPy's API is the starting point when libraries are written to exploit innovative hardware, create specialized array types, or add capabilities beyond what NumPy provides.ĭistributed arrays and advanced parallelism for analytics, enabling performance at scale. With this power comes simplicity: a solution in NumPy is often clear and elegant. NumPy brings the computational power of languages like C and Fortran to Python, a language much easier to learn and use. Finally, we conduct several experiments to test these techniques.Nearly every scientist working in Python draws on the power of NumPy. We prove that it yields accurate reconstructions and that it is also stable to noise. Then, we propose a computationally efficient decoder to reconstruct k-bandlimited signals from their samples. This second strategy is based on a careful choice of the sampling distribution, which can be estimated quickly. Indeed, no more than O(k log(k)) measurements are sufficient to ensure an accurate and stable recovery of all k-bandlimited signals. On the contrary, the second strategy is adaptive but yields optimal results. The first strategy is non-adaptive, i.e., independent of the graph structure, and its performance depends on a parameter called the graph coherence. We propose two such sampling strategies that consist in selecting a small subset of nodes at random. Leveraging ideas from compressive sensing, it is possible to design efficient sampling strategies for low-pass signals on graphs. Sampling k-bandlimited signals on graphs. Transposed to general graph data, this leads to applications as diverse as community detection, recommender systems, or matrix completion on graphs. More generally they open the door to using the extensive toolset of sparse signal models that, in recent years, have achieved tremendous success in solving large classes of inverse problems with guaranteed performances and efficient algorithms based on convex optimization. Fourier or wavelet transforms on graphs allow the extension of notions such as the smoothness of a signal. Various wavelet transforms can also be defined on graphs, and the teams involved in this proposal have pioneered the design of wavelet transforms on graphs using spectral graph theory. Thanks to spectral graph theory, a Fourier transform can be defined on graphs from the eigen decomposition of the graph’s Laplacian operator. Among signal processing tools, transforms naturally play a key role in modelling data. This has opened the path to many exciting future research, calling to revisit most of the usual signal processing tasks (filtering, denoising, compression, etc.). As such, “signal processing on graphs” (SPG) is an emerging topic, that has already lead to pioneering theoretical and practical work to formalize foundational definitions and tools. Nowadays, more and more data natively “live” on the vertices of a graph: brain activity supported by neurons in networks, traffic on transport and energy networks, data from users of social media, complex 3D surfaces describing real objects… Although graphs have been extensively studied in mathematics and computer science, a “signal processing” viewpoint on these objects remains largely to be invented.
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