DTSC - GPM - Artículos de Revistas
http://hdl.handle.net/10016/2315
Tue, 26 Mar 2019 13:39:30 GMT2019-03-26T13:39:30ZThe Case for Shifting the Rényi Entropy
http://hdl.handle.net/10016/28157
The Case for Shifting the Rényi Entropy
Valverde Albacete, Francisco Jose; Peláez Moreno, Carmen
We introduce a variant of the Rényi entropy definition that aligns it with the well-known Hölder mean: in the new formulation, the r-th order Rényi Entropy is the logarithm of the inverse of the r-th order Hölder mean. This brings about new insights into the relationship of the Rényi
entropy to quantities close to it, like the information potential and the partition function of statistical
mechanics. We also provide expressions that allow us to calculate the Rényi entropies from the
Shannon cross-entropy and the escort probabilities. Finally, we discuss why shifting the Rényi
entropy is fruitful in some applications.
Wed, 09 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10016/281572019-01-09T00:00:00ZAssessing Information Transmission in Data Transformations with the Channel Multivariate Entropy Triangle
http://hdl.handle.net/10016/28121
Assessing Information Transmission in Data Transformations with the Channel Multivariate Entropy Triangle
Valverde Albacete, Francisco Jose; Peláez Moreno, Carmen
Data transformation, e.g., feature transformation and selection, is an integral part of any machine learning procedure. In this paper, we introduce an information-theoretic model and tools to assess the quality of data transformations in machine learning tasks. In an unsupervised fashion, we analyze the transformation of a discrete, multivariate source of information (X) over bar into a discrete, multivariate sink of information (Y) over bar related by a distribution P-(XY) over bar. The first contribution is a decomposition of the maximal potential entropy of ((X) over bar, (Y) over bar), which we call a balance equation, into its (a) non-transferable, (b) transferable, but not transferred, and (c) transferred parts. Such balance equations can be represented in (de Finetti) entropy diagrams, our second set of contributions. The most important of these, the aggregate channel multivariate entropy triangle, is a visual exploratory tool to assess the effectiveness of multivariate data transformations in transferring information from input to output variables. We also show how these decomposition and balance equations also apply to the entropies of (X) over bar and (Y) over bar, respectively, and generate entropy triangles for them. As an example, we present the application of these tools to the assessment of information transfer efficiency for Principal Component Analysis and Independent Component Analysis as unsupervised feature transformation and selection procedures in supervised classification tasks.
Wed, 27 Jun 2018 00:00:00 GMThttp://hdl.handle.net/10016/281212018-06-27T00:00:00ZOptimized Update/Prediction Assignment for Lifting Transforms on Graphs
http://hdl.handle.net/10016/26244
Optimized Update/Prediction Assignment for Lifting Transforms on Graphs
Martínez Enríquez, Eduardo; Cid Sueiro, Jesús; Díaz de María, Fernando; Ortega, Antonio
Transformations on graphs can provide compact representations of signals with many applications in denoising, feature extraction or compression. In particular, lifting transforms have the advantage of being critically sampled and invertible by construction, but the efficiency of the transform depends on the choice of a good bipartition of the graph into update (U) and prediction (P) nodes. This is the update/prediction (U=P) assignment problem, which is the focus of this paper. We analyze this problem theoretically and derive an optimal U=P assignment under assumptions about signal model and filters. Furthermore, we prove that the best U=P partition is related to the correlation between nodes on the graph and is not the one that minimizes the number of conflicts (connections between nodes of same label) or maximizes the weight of the cut. We also provide experimental results in randomly generated graph signals and real data from image and video signals that validate our theoretical conclusions, demonstrating improved performance over state of the art solutions for this problem.
Mon, 05 Feb 2018 00:00:00 GMThttp://hdl.handle.net/10016/262442018-02-05T00:00:00ZDirectional Transforms for Video Coding Based on Lifting on Graphs
http://hdl.handle.net/10016/26235
Directional Transforms for Video Coding Based on Lifting on Graphs
Martínez Enríquez, Eduardo; Cid Sueiro, Jesús; Díaz de María, Fernando; Ortega, Antonio
In this work we describe and optimize a general scheme based on lifting transforms on graphs for video coding. A graph is constructed to represent the video signal. Each pixel becomes a node in the graph and links between nodes represent similarity between them. Therefore, spatial neighbors and temporal motion-related pixels can be linked, while nonsimilar pixels (e.g., pixels across an edge) may not be. Then, a lifting-based transform, in which filterin operations are performed using linked nodes, is applied to this graph, leading to a 3-dimensional (spatio-temporal) directional transform which can be viewed as an extension of wavelet transforms for video. The design of the proposed scheme requires four main steps: (i) graph construction, (ii) graph splitting, (iii) filte design, and (iv) extension of the transform to different levels of decomposition. We focus on the optimization of these steps in order to obtain an effective transform for video coding. Furthermore, based on this scheme, we propose a coefficien reordering method and an entropy coder leading to a complete video encoder that achieves better coding performance than a motion compensated temporal filterin wavelet-based encoder and a simple encoder derived from H.264/AVC that makes use of similar tools as our proposed encoder (reference software JM15.1 configu ed to use 1 reference frame, no subpixel motion estimation, 16 × 16 inter and 4 × 4 intra modes).
Tue, 29 Nov 2016 00:00:00 GMThttp://hdl.handle.net/10016/262352016-11-29T00:00:00Z