Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Critical data detection for dynamically adjustable product quality in IIoT-enabled manufacturing

The IIoT technologies, due to the widespread use of sensors, generate massive data that are key in providing innovative and efficient industrial management, operation, and product quality control processes. The significance of data has prompted relevant research communities and application developers how to harness the values of these data in secure manufacturing. Critical data analysis, identification of critical factors to improve the manufacturing process and critical data associated with product quality have been investigated in the current literature. However, the current works on product quality control are mainly based on static data analysis, where data may change, but there is no way to adjust them dynamically. Thus, they are not applicable for product quality control, at which point their adjustment is instantly required. However, many manufacturing systems exist, like beverages and food, where ingredients must be adjusted instantaneously to maintain product quality. To address this research gap, we introduce a method that identifies the critical data based on their ranking by exploiting three criticality assessment criteria that capture the instantaneous product quality change during manufacturing. These three criteria are - (1) correlation, (2) percentage quality change and (3) sensitivity for the assessment of data criticality. The product quality is estimated using polynomial regression (POLY), SVM, and DNN. The proposed method is validated using wine manufacturing data. Our proposed method accurately identifies critical data, where SVM produces the lowest average production quality prediction error (10.40%) compared with that of POLY (11%) and DNN (14.40%). © 2013 IEEE

On Triangular Splines:CAD and Quadrature

The standard representation of CAD (computer aided design) models is based on the boundary representation (B-reps) with trimmed and (topologically) stitched tensor-product NURBS patches. Due to trimming, this leads to gaps and overlaps in the models. While these can be made arbitrarily small for visualisation and manufacturing purposes, they still pose problems in downstream applications such as (isogeometric) analysis and 3D printing. It is therefore worthwhile to investigate conversion methods which (necessarily approximately) convert these models into water-tight or even smooth representations. After briefly surveying existing conversion methods, we will focus on techniques that convert CAD models into triangular spline surfaces of various levels of continuity. In the second part, we will investigate efficient quadrature rules for triangular spline space

Prediksi Tinggi Muka Air (TMA) Untuk Deteksi Dini Bencana Banjir Menggunakan SVR-TVIWPSO

Abstrak Banjir merupakan salah satu jenis bencana alam yang tidak dapat diprediksi kedatangannya, salah satu penyebabnya adalah adanya hujan yang terus – menerus(dari peristiwa alam). Faktor penyebab banjir dari segi meteorologi yaitu curah hujan yang tinggi dan air laut yang sedang pasang sehingga mengakibatkan tinggi permukaan air meningkat. Analisis terhadap data curah hujan serta tinggi permukaan air setiap periodenya dirasa masih belum dapat menyelesaikan permasalahan yang ada. Oleh karena itu, pada penelitian ini diusulkan teknik integrasi metode Time Variant Inertia Weight Particle Swarm Optimization(TVIWPSO) dan Support Vector Regression(SVR). Implementasi memadukan metode Regresi yaitu SVR untuk forecasting TMA, sedangkan TVIWPSO digunakan untuk mengoptimalisasi parameter – parameter yang digunakan di dalam SVR untuk memperoleh kinerja yang maksimal dan hasil yang akurat. Harapannya sistem ini akan dapat membantu mengatasi permasalahan untuk pendeteksian dini bencana banjir karena faktor cuaca yang tidak menentu. Hasil pengujian yang didapat dari 10 data bulanan yang berbeda menunjukkan bahwa didapatkan nilai error terkecil sebesar 0.00755 dengan menggunakan Mean Absolute Error untuk data Juni 2007 dengan menggunakan integrasi metode SVR-TVIWPSO. Kata Kunci : Support Vector Regression, Tinggi Muka Air, Time Variant Inertia Weight Particle Swarm Optimization. Abstract Flood is one type of natural disaster that can not be predicted its arrival, one reason is the rain that constantly occurs (from natural events). Factors that cause flooding in terms of meteorology are high rainfall and sea water was high, resulting in high water level increases. Analysis of rainfall data and water level in each period it is still not able to solve existing problems. Therefore, in this study the method proposed integration techniques Time Variant Inertia Weight Particle Swarm Optimization (TVIWPSO) and Support Vector Regression (SVR). Implementation combines regression method for forecasting TMA is SVR, while TVIWPSO used to optimize parameters that used in the SVR to obtain maximum performance and accurate results. Hope this system will be able to help solve the problems for the early detection of floods due to erratic weather. The result of forecasting experiment in water level forecasting from 10 monthly different data show that the smallest error rate is amount to 0.00755 using Mean Absolute Error for June 2007 with the integration method SVR-TVIWPSO. Keywords: Support Vector Regression, water level, Time Variant Inertia Weight Particle Swarm Optimization