Sparse PDF Volumes for Consistent Multi-resolution Volume Rendering
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http://wwx.silexlabs.org/2014/
Text classification using Text kernels
This document summarizes a presentation on using string kernels for text classification. It introduces text classification and the challenge of representing text documents as feature vectors. It then discusses how kernel methods can be used as an alternative, by mapping documents into a feature space without explicitly extracting features. Different string kernel algorithms are described that measure similarity between documents based on common subsequences of characters. The document evaluates the performance of these kernels on a text dataset and explores ways to improve efficiency, such as through kernel approximation.
Word representations in vector space
- The document discusses neural word embeddings, which represent words as dense real-valued vectors in a continuous vector space. This allows words with similar meanings to have similar vector representations.
- It describes how neural network language models like skip-gram and CBOW can be used to efficiently learn these word embeddings from unlabeled text data in an unsupervised manner. Techniques like hierarchical softmax and negative sampling help reduce computational complexity.
- The learned word embeddings show meaningful syntactic and semantic relationships between words and allow performing analogy and similarity tasks without any supervision during training.
1404.1503
This document proposes a construction for quantum hash functions based on classical universal hashing. It defines the concept of a quantum hash generator as a family of functions that maps elements to quantum states. The construction combines the robustness of classical error-correcting codes with the compact representation of quantum systems. It presents two examples of quantum hash functions: one based on binary error-correcting codes and one based on a field of elements. The construction is proved to be optimal in terms of the number of qubits needed to represent the quantum states.
Fassold-MMAsia2023-Tutorial-GeometricDL-Part1.pptx
Slides for my tutorial about "Geometric Deep Learning and its applications for Multimedia" at MMAsia 2023 Conference
CSC446: Pattern Recognition (LN7)
This document discusses nonparametric pattern recognition techniques, including density estimation methods like Parzen windows and the k-nearest neighbors algorithm. It covers density estimation, using Parzen windows to estimate densities without assuming a known form, and provides examples of applying Parzen windows to both classification and estimating mixtures of unknown densities from sample data. Probabilistic neural networks are also introduced as a parallel implementation of Parzen window density estimation.
Db Scan
DBSCAN is a density-based clustering algorithm that groups together densely populated areas of points. It requires two parameters: epsilon, which defines the neighborhood distance, and MinPts, the minimum number of points required to form a cluster. DBSCAN iteratively retrieves all points density-reachable from each point and forms clusters from core points with sufficient neighbors within epsilon distance. It can find clusters of arbitrary shape and handle noise without requiring the number of clusters to be specified.
Chap4 slides
This document discusses various group communication operations that are commonly used in parallel programs. It begins with an overview of operations like one-to-all broadcast, all-to-one reduction, all-to-all broadcast, all-reduce, scatter, gather, and all-to-all personalized communication. It then provides details on efficient algorithms for implementing each of these operations on different network topologies like rings, meshes, hypercubes, and trees. It analyzes the time complexity of the algorithms and discusses how to optimize the implementations.
Chap4 slides
This document discusses various group communication operations that are commonly used in parallel programs. It begins with an introduction and overview of operations like one-to-all broadcast, all-to-one reduction, all-to-all broadcast, all-reduce, scatter, gather, and all-to-all personalized communication. It then provides detailed descriptions and algorithms for how to implement each of these operations on different network topologies like rings, meshes, hypercubes, and trees. It analyzes the time complexity of each algorithm and compares different approaches. The goal is to provide efficient implementations of these fundamental communication patterns.
Chap4 slides
This document provides an overview and analysis of common group communication operations that are frequently used in parallel programs. It discusses efficient algorithms for one-to-all broadcast, all-to-one reduction, all-to-all broadcast, all-reduce, scatter, gather, and all-to-all personalized communication on different network topologies like rings, meshes, and hypercubes. It analyzes the time complexity of each algorithm and compares different approaches for each operation. The goal is to illustrate how to design efficient algorithms for these operations by leveraging the underlying network architecture.
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Machine Learning Foundations for Professional Managers
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Lecture 17 - Grouping and Segmentation - Vision_Spring2017.pptx
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WWX14 speech : Justin Donaldson "Promhx : Cross-platform Promises and Reactiv...
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More from Subhashis Hazarika
DNN Model Interpretability
This document discusses various techniques for interpreting and explaining deep neural network models. It begins by motivating the need for interpretability and distinguishing between interpretation and explanation. It then covers several techniques for interpreting models, including activation maximization, sensitivity analysis, and simple Taylor decomposition. For explaining individual predictions, it discusses gradient-based and decomposition-based approaches like layer-wise relevance propagation and guided backpropagation. It also evaluates explanation quality based on continuity and selectivity. Finally, it discusses applications like model validation and analyzing scientific data domains.
Deep_Learning_Frameworks_CNTK_PyTorch
This document summarizes and compares two deep learning frameworks: Microsoft Cognitive Toolkit (CNTK) and PyTorch. CNTK is an open-source toolkit created by Microsoft for deep learning. It is production-ready and optimized for performance and scalability. It uses symbolic computational graphs and supports distributed training techniques like 1-bit SGD. PyTorch is a Python-based framework developed by Facebook for rapid prototyping. It uses dynamic computational graphs and supports automatic differentiation via its autograd package. Both frameworks express neural networks as compositions of basic building blocks and allow defining and training custom models.
Word2Vec Network Structure Explained
This document provides an overview of Word2Vec network structure for generating word embeddings. It discusses how Word2Vec uses a neural network model like CBOW or Skip-gram to represent words as dense vectors based on their surrounding context words in a corpus. The Word2Vec neural network is trained to learn vector representations that are useful for performing analogy-style questions like "King - Man + Woman = Queen". The document also briefly outlines techniques like hierarchical softmax and negative sampling that allow Word2Vec training to scale to large corpora.
Probabilistic Graph Layout for Uncertain Network Visualization
This document summarizes a technique for visualizing probabilistic graphs called probabilistic graph layout. It models probabilistic graphs as graphs where edge weights are probability distributions. It samples weighted graphs from the probabilistic graph and computes force-directed layouts for each sample. It then splats the node positions across samples to approximate their distributions. It also bundles edges hierarchically and colors nodes distinctly while avoiding overlap to show connections and clusters amid the uncertainty. The method was demonstrated on synthetic and protein interaction data and its limitations in stability, ambiguity and scalability were discussed.
An analysis of_machine_and_human_analytics_in_classification
1) An analysis of machine learning and human-analytics classification models that found human-guided models performed better due to incorporating "soft knowledge" unavailable to machine models.
2) Two case studies were conducted comparing decision trees from visual analytics with human guidance to those from standard machine learning algorithms.
3) Humans were able to leverage soft knowledge like imagining outliers, looking ahead to future decisions, and incorporating domain expertise to construct superior classification models.
Uncertainty aware multidimensional ensemble data visualization and exploration
This document summarizes an approach for uncertainty-aware multidimensional projection of ensemble data. The key contributions are a new dissimilarity measure between ensemble data objects based on both mean distance and distribution distance, and an enhanced Laplacian-based projection scheme. The approach first estimates probability distributions for each ensemble data object using kernel density estimation. It then projects a subset of control points using MDS and interpolates the remaining points based on nearest neighbors. Visualization widgets allow exploration of projection results and uncertainty quantification. The approach is demonstrated on synthetic, NBA player statistic, and weather simulation datasets.
CSE5559::Visualizing the Life and Anatomy of Cosmic Particles
This document discusses visualizing the evolution and internal structure of cosmic particle halos over time through three main tasks:
1) Visualizing the evolution of halos and the highest mass halo over time and its internal structure.
2) Providing a grid-based representation of dark matter particles and a particle-based volume rendering framework to visualize the particle layout.
3) Analyzing the mass accrual pattern of the highest mass halo using a virial mass estimation theorem and plotting the contribution of dark matter particles to the halo's mass over time.
Visualizing the variability of gradient in uncertain 2d scalarfield
This document summarizes a research paper that presents techniques for visualizing uncertainty in 2D scalar fields. It derives parameters to quantify gradient uncertainty based on data variability. It describes analytical expressions for the probability distributions of gradient magnitude and orientation. A color diffusion technique indicates slope stability, and colored glyphs depict iso-contour uncertainty. The methods are demonstrated on synthetic and seismic ensemble data.
Visualization of uncertainty_without_a_mean
Talk about the use of entropy from information theoretic sense as a viable measure visualizing uncertainty
Semi automatic vortex extraction in 4 d pc-mri cardiac blood flow data using ...
This document summarizes a study that uses line predicates to semi-automatically extract vortices from 4D phase-contrast MRI cardiac blood flow data. It presents a workflow involving data acquisition, pre-processing, vortex extraction using local criteria and line predicates, and post-processing. Different line predicates are described, including geometry, flow field, mesh, stream, and smoothing predicates. Pathline integration is performed using vector interpolation and Jacobian matrix estimation. Three line predicates are applied for vortex detection, refinement of vortex shapes, and postprocessing. Finally, local vortex criteria are compared based on quality criteria to determine the best for representing vortical and helical flow.
Graph cluster randomization
Graph Cluster Randomization is a technique proposed to estimate the average treatment effect of exposures in a social network. It forms clusters by partitioning the graph and then randomizes treatment between clusters rather than individuals. This addresses limitations of A/B testing in accounting for network interference effects. The approach models different levels of neighborhood and core exposure conditions. It derives an unbiased Horvitz-Thompson estimator for the average treatment effect and proves an upper bound on the variance that is linear in maximum degree, ensuring quality estimates even for high-degree networks. Graph clustering is introduced to restrict network growth and degree, maintaining low variance estimates.
Linear programming in computational geometry
This document discusses linear programming approaches for solving casting problems in computational geometry. It first introduces the problem of determining if a polyhedron can be cast based on the angles between facets. This leads to representing the problem as finding the intersection of half-planes, which can be solved using linear programming. The document then provides algorithms for intersecting half-planes and using incremental linear programming to find a solution in linear expected time by randomly ordering the half-plane constraints.
CERN summer presentation
This document summarizes the design of a control system for the ALICE EMCal readout electronics. It involves:
1. Programming an intermediate C server between the EMCal hardware and the SCADA control software to continuously read registry values and execute commands.
2. Developing high-level control interfaces in the PVSS SCADA environment using JCOP to link objects to the intermediate server's DIM commands and services.
3. Creating PVSS data points and panels with intuitive interfaces to hierarchically display status and allow monitoring/control of hardware elements like super modules, RCUs, TRUs, and FEEs.
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The Python for beginners. This is an advance computer language.
Python language is very important language at this time. we can easily understand this language by these notes.
A review on techniques and modelling methodologies used for checking electrom...
The proper function of the integrated circuit (IC) in an inhibiting electromagnetic environment has always been a serious concern throughout the decades of revolution in the world of electronics, from disjunct devices to today’s integrated circuit technology, where billions of transistors are combined on a single chip. The automotive industry and smart vehicles in particular, are confronting design issues such as being prone to electromagnetic interference (EMI). Electronic control devices calculate incorrect outputs because of EMI and sensors give misleading values which can prove fatal in case of automotives. In this paper, the authors have non exhaustively tried to review research work concerned with the investigation of EMI in ICs and prediction of this EMI using various modelling methodologies and measurement setups.
学校原版美国波士顿大学毕业证学历学位证书原版一模一样
原版一模一样【微信：741003700 】【美国波士顿大学毕业证学历学位证书】【微信：741003700 】学位证，留信认证（真实可查，永久存档）offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原海外各大学 Bachelor Diploma degree, Master Degree Diploma
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
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Electric vehicle and photovoltaic advanced roles in enhancing the financial p...
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
TIME DIVISION MULTIPLEXING TECHNIQUE FOR COMMUNICATION SYSTEM
Time Division Multiplexing (TDM) is a method of transmitting multiple signals over a single communication channel by dividing the signal into many segments, each having a very short duration of time. These time slots are then allocated to different data streams, allowing multiple signals to share the same transmission medium efficiently. TDM is widely used in telecommunications and data communication systems.
### How TDM Works
1. **Time Slots Allocation**: The core principle of TDM is to assign distinct time slots to each signal. During each time slot, the respective signal is transmitted, and then the process repeats cyclically. For example, if there are four signals to be transmitted, the TDM cycle will divide time into four slots, each assigned to one signal.
2. **Synchronization**: Synchronization is crucial in TDM systems to ensure that the signals are correctly aligned with their respective time slots. Both the transmitter and receiver must be synchronized to avoid any overlap or loss of data. This synchronization is typically maintained by a clock signal that ensures time slots are accurately aligned.
3. **Frame Structure**: TDM data is organized into frames, where each frame consists of a set of time slots. Each frame is repeated at regular intervals, ensuring continuous transmission of data streams. The frame structure helps in managing the data streams and maintaining the synchronization between the transmitter and receiver.
4. **Multiplexer and Demultiplexer**: At the transmitting end, a multiplexer combines multiple input signals into a single composite signal by assigning each signal to a specific time slot. At the receiving end, a demultiplexer separates the composite signal back into individual signals based on their respective time slots.
### Types of TDM
1. **Synchronous TDM**: In synchronous TDM, time slots are pre-assigned to each signal, regardless of whether the signal has data to transmit or not. This can lead to inefficiencies if some time slots remain empty due to the absence of data.
2. **Asynchronous TDM (or Statistical TDM)**: Asynchronous TDM addresses the inefficiencies of synchronous TDM by allocating time slots dynamically based on the presence of data. Time slots are assigned only when there is data to transmit, which optimizes the use of the communication channel.
### Applications of TDM
- **Telecommunications**: TDM is extensively used in telecommunication systems, such as in T1 and E1 lines, where multiple telephone calls are transmitted over a single line by assigning each call to a specific time slot.
- **Digital Audio and Video Broadcasting**: TDM is used in broadcasting systems to transmit multiple audio or video streams over a single channel, ensuring efficient use of bandwidth.
- **Computer Networks**: TDM is used in network protocols and systems to manage the transmission of data from multiple sources over a single network medium.
### Advantages of TDM
- **Efficient Use of Bandwidth**: TDM all
International Conference on NLP, Artificial Intelligence, Machine Learning an...
International Conference on NLP, Artificial Intelligence, Machine Learning and Applications (NLAIM 2024) offers a premier global platform for exchanging insights and findings in the theory, methodology, and applications of NLP, Artificial Intelligence, Machine Learning, and their applications. The conference seeks substantial contributions across all key domains of NLP, Artificial Intelligence, Machine Learning, and their practical applications, aiming to foster both theoretical advancements and real-world implementations. With a focus on facilitating collaboration between researchers and practitioners from academia and industry, the conference serves as a nexus for sharing the latest developments in the field.
Literature Review Basics and Understanding Reference Management.pptx
Three-day training on academic research focuses on analytical tools at United Technical College, supported by the University Grant Commission, Nepal. 24-26 May 2024
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DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODEL
As digital technology becomes more deeply embedded in power systems, protecting the communication
networks of Smart Grids (SG) has emerged as a critical concern. Distributed Network Protocol 3 (DNP3)
represents a multi-tiered application layer protocol extensively utilized in Supervisory Control and Data
Acquisition (SCADA)-based smart grids to facilitate real-time data gathering and control functionalities.
Robust Intrusion Detection Systems (IDS) are necessary for early threat detection and mitigation because
of the interconnection of these networks, which makes them vulnerable to a variety of cyberattacks. To
solve this issue, this paper develops a hybrid Deep Learning (DL) model specifically designed for intrusion
detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
train and test our model. The results of our experiments show that our CNN-LSTM method is much better
at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
accuracy rate of 99.50%.
Recycled Concrete Aggregate in Construction Part II
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样
原版一模一样【微信：741003700 】【(csu毕业证书)查尔斯特大学毕业证硕士学历】【微信：741003700 】学位证，留信认证（真实可查，永久存档）offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原海外各大学 Bachelor Diploma degree, Master Degree Diploma
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
Modelagem de um CSTR com reação endotermica.pdf
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Unit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
Batteries -Introduction – Types of Batteries – discharging and charging of battery - characteristics of battery –battery rating- various tests on battery- – Primary battery: silver button cell- Secondary battery :Ni-Cd battery-modern battery: lithium ion battery-maintenance of batteries-choices of batteries for electric vehicle applications.
Fuel Cells: Introduction- importance and classification of fuel cells - description, principle, components, applications of fuel cells: H2-O2 fuel cell, alkaline fuel cell, molten carbonate fuel cell and direct methanol fuel cells.
Eric Nizeyimana's document 2006 from gicumbi to ttc nyamata handball play
this notes have been created
by Eric36 at nyamata ttc
after readings
pe book for y2sme .
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECT
The rivalry between prominent international actors for dominance over Central Asia's hydrocarbon
reserves and the ancient silk trade route, along with China's diplomatic endeavours in the area, has been
referred to as the "New Great Game." This research centres on the power struggle, considering
geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
Using Mackinder's Heartland, Spykman Rimland, and Hegemonic Stability theories, examines China's role
in Central Asia. This study adheres to the empirical epistemological method and has taken care of
objectivity. This study analyze primary and secondary research documents critically to elaborate role of
china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
China is seeing significant success in commerce, pipeline politics, and gaining influence on other
governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
Understanding Inductive Bias in Machine Learning
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
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Eric Nizeyimana's document 2006 from gicumbi to ttc nyamata handball play
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CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECT
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Sparse PDF Volumes for Consistent Multi-resolution Volume Rendering
- 1. Sparse PDF Volumes for Consistent Multi- Resolution Volume Rendering Authors: Ronell Sicat, KAUST Jens Kruger, University of Duisburg-Essen Torsten Moller, University of Vienna Markus Hadwiger, KAUST Presented by: Subhashis Hazarika, Ohio State University
- 2. 9/11/2014 2
- 3. Challenges •Substitutes each voxel by a weighted average of its neighbourhood, this changes the distribution values in the volume. Standard approaches use a single value (mean) to represent the voxel footprint distribution. •Application of transfer functions becomes incompatible and results in inconsistent image across resolution levels. (inconsistency artifacts). •Ideally an accurate representation of voxel footprint would provide a consistent multi-resolution volume rendering. –Histogram storage overhead. –Application of transfer function becomes expensive. 3 9/11/2014
- 4. Proposed Idea •A compact sparse pdf representation for voxels in 4D (joint space X range domain of the volume). •Optimize the sparse pdf volume data structure for parallel rendering in GPU. •A novel approach for computing a sparse 4D pdf approximation via a greedy pursuit algorithm. •An out-of-core framework for efficient parallel computation of sparse pdf volumes for large scalar volume data. 4 9/11/2014
- 6. Basic Model •Xp random variable for voxels associated with position p across different resolution levels. •fp(r) pdf at position p, r is the intensity range of the volume data. •t(r) transfer function in the domain of the range of the volume, r. •Goal of the paper is to: –Store fp(r) effectively and apply t(r) –Challenge : •Storage overhead •How to evaluate eq 1. 6 9/11/2014
- 7. Joint 4D space x range domain 7 9/11/2014
- 8. Hierarchy of 4D Gaussian Mixtures •All the Gaussians at level m have the same standard deviation. –Easy of using convolutions –Don’t have to store s.d for all Gaussians. •d 8 9/11/2014
- 9. Hierarchy Computation •Initial Gaussian Mixture: –Start at level l0 and Gaussian Mixture vo –Standard deviation: –Weight: •Subsequent computation: –Compute m from preceding level m. –Low pass filter vm to avoid artifacts •By updating spatial s.d and the coefficient ci. –Our goal is to represent m with fewer Gaussians than vm –km=km.. –This is done by sparse approximation to m. 9 9/11/2014
- 10. Sparse PDF Volume Computation •Sparse Approximation Theory: –H dictionary of atoms (basis functions) –c is the coefficient vector that determines the linear combination that should best approximate v, given H. –H in our case consists of translates of Gaussians. –Target signal v to approximate is a chosen vm after low-pass filter. –Inorder to obtain sparse representation, c should have as few non-zero elements as possible. •An NP-hard problem. •Pursuit Algorithm: greedy iterative method of finding sparse c. –In each iteration the atom from H that best approximates the target function g(x) is picked by projecting the g(x) into the dictionary. 10 9/11/2014
- 11. Dictionary Projection as Convolution •Consider 1D function g(x) that we want to approximate. •h() dictionary of atoms, where u selects the atom •We will project g(x) onto h(x) (i.e finding inner product of the two functions) •All dictionary atoms are translates of the same kernel h(x), where h is symmetric around zero. Therefore in terms of kernels h(x). •This converts the eq.9 to convolution form: 11 9/11/2014
- 12. Dictionary Projection as Convolution •In order to determine the atom that best approximates g(x) we have to determine which atom results in the largest inner product. •In terms of convolution: •Observation: in order to find the dictionary element that best approximates g(x) we simply have to find the max of the function 12 9/11/2014
- 13. Gaussian Dictionaries & Mixtures •Gaussian Dictionaries: •Gaussian Mixture: the g(x) function that we approximate is given by k Gaussians with identical s.d. 13 9/11/2014
- 14. Pursuit Algorithm 14 9/11/2014
- 15. Projection in 4D using mode finding 15 9/11/2014
- 16. Sparse PDF Volume Data Structure •Original volume is subdivided into bricks. •At l0, stored in usual way, with one scalar per voxel. •For the other levels, lm, m>0: –1st sort the set of mixture component …………… based on spatial position p. –For each voxel with position p we count how many tuples have the same p(p=pi) –This count is stored in a coefficient count block. –The pi value is dropped from the tuple and the r and c values are stored in coefficient info array. 16 9/11/2014
- 17. Sparse PDF Volume Data Structure 17 9/11/2014
- 18. Run Time Classification •Applying the transfer function to the Gaussian mixture.: 18 9/11/2014
- 19. Performance & Scalability 19 9/11/2014
- 21. Thank You 21 9/11/2014