GPU Parallel Implementation of Dual-Depth Sparse Probabilistic Latent Semantic Analysis for Hyperspectral Unmixing

Hyperspectral unmixing (HU) is an important task for remotely sensed hyperspectral (HS) data exploitation. It comprises the identification of pure spectral signatures (endmembers) and their corresponding fractional abundances in each pixel of the HS data cube. Several methods have been developed for (semi-) supervised and automatic identification of endmembers and abundances. Recently, the statistical dual-depth sparse probabilistic latent semantic analysis (DEpLSA) method has been developed to tackle the HU problem as a latent topic-based approach in which both endmembers and abundances can be simultaneously estimated according to the semantics encapsulated by the latent topic space. However, statistical models usually lead to computationally demanding algorithms and the computational time of the DEpLSA is often too high for practical use, in particular, when the dimensionality of the HS data cube is large. In order to mitigate this limitation, this article resorts to graphical processing units (GPUs) to provide a new parallel version of the DEpLSA, developed using the NVidia compute device unified architecture. Our experimental results, conducted using four well-known HS datasets and two different GPU architectures (GTX 1080 and Tesla P100), show that our parallel versions of the DEpLSA and the traditional pLSA approach can provide accurate HU results fast enough for practical use, accelerating the corresponding serial versions in at least 30x in the GTX 1080 and up to 147x in the Tesla P100 GPU, which are quite significant acceleration factors that increase with the image size, thus allowing for the possibility of the fast processing of massive HS data repositories

Scalable Text Mining with Sparse Generative Models

The information age has brought a deluge of data. Much of this is in text form, insurmountable in scope for humans and incomprehensible in structure for computers. Text mining is an expanding field of research that seeks to utilize the information contained in vast document collections. General data mining methods based on machine learning face challenges with the scale of text data, posing a need for scalable text mining methods. This thesis proposes a solution to scalable text mining: generative models combined with sparse computation. A unifying formalization for generative text models is defined, bringing together research traditions that have used formally equivalent models, but ignored parallel developments. This framework allows the use of methods developed in different processing tasks such as retrieval and classification, yielding effective solutions across different text mining tasks. Sparse computation using inverted indices is proposed for inference on probabilistic models. This reduces the computational complexity of the common text mining operations according to sparsity, yielding probabilistic models with the scalability of modern search engines. The proposed combination provides sparse generative models: a solution for text mining that is general, effective, and scalable. Extensive experimentation on text classification and ranked retrieval datasets are conducted, showing that the proposed solution matches or outperforms the leading task-specific methods in effectiveness, with a order of magnitude decrease in classification times for Wikipedia article categorization with a million classes. The developed methods were further applied in two 2014 Kaggle data mining prize competitions with over a hundred competing teams, earning first and second places

Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for performing low-rank matrix approximation. These techniques exploit modern computational architectures more fully than classical methods and open the possibility of dealing with truly massive data sets. This paper presents a modular framework for constructing randomized algorithms that compute partial matrix decompositions. These methods use random sampling to identify a subspace that captures most of the action of a matrix. The input matrix is then compressed—either explicitly or implicitly—to this subspace, and the reduced matrix is manipulated deterministically to obtain the desired low-rank factorization. In many cases, this approach beats its classical competitors in terms of accuracy, robustness, and/or speed. These claims are supported by extensive numerical experiments and a detailed error analysis. The specific benefits of randomized techniques depend on the computational environment. Consider the model problem of finding the k dominant components of the singular value decomposition of an m × n matrix. (i) For a dense input matrix, randomized algorithms require O(mn log(k)) floating-point operations (flops) in contrast to O(mnk) for classical algorithms. (ii) For a sparse input matrix, the flop count matches classical Krylov subspace methods, but the randomized approach is more robust and can easily be reorganized to exploit multiprocessor architectures. (iii) For a matrix that is too large to fit in fast memory, the randomized techniques require only a constant number of passes over the data, as opposed to O(k) passes for classical algorithms. In fact, it is sometimes possible to perform matrix approximation with a single pass over the data