SlideShare a Scribd company logo
1 of 14
Download to read offline
QUANTIZATION FOR
CLASSIFICATION ACCURACY IN
HIGH-RATE QUANTIZERS
Behzad M. Dogahe
Manohar N. Murthi
Department of Electrical and Computer
Engineering
IEEE DSP Workshop, January 2011
Outline
• Motivation
• Background
• Problem Statement and Solution
• Simulations
• Concluding Remarks
Motivation
• Quantization of signals is required for many applications
• The original signal is quantized at the encoder and at the
decoder side a replica that should resemble the original signal
in some sense is recovered
• Present quantizers make an effort to reduce the distortion of
the signal in the sense of reproduction fidelity
• Consider scenarios in which signals are generated from
multiple classes. The encoder focuses on the task of
quantization without any regards to the class of the signal
• The quantized signal reaches the decoder where not only the
recovery of the signal should take place but also a decision is
to be made on the class of the signal based on the quantized
version of the signal only
Motivation
• Goal: Design of a quantizer that is optimized for the task of
classification at the decoder
• Application Scenarios:
 Want to have good sound fidelity (good voice/audio
quality) but also want to be able to perform speaker
recognition
 Sensor network where the sensors have low complexity,
simple quantizers, but the decoder/sensor sink node does
more sophisticated processing (so the raw signal value is
needed, but we also want to be able to classify the sensed
signal)
Background
Quantizerx )(ˆ xQx 
x
xˆ
x
)(xp
x
)(x
x
xˆ
x
)(xp
x
)(x
In high-rate theory point density function represents the density of codebook
points in any region for a quantizer. The design of a quantizer is equivalent to design
of the optimal point density function.
)(xp : Probability Density Function
Background
• Design of Quantizer involves minimizing:
where is Distortion Measure
• Examples of Distortion Measure:
 MSE
 Log Spectral Distortion
• High-Rate Theory:
2
ˆ)ˆ,( xxxxd 
Optimization Problem
Background
• Following the steps in [Gardner and Rao] point density function
will be derived as
(n is the dimension of x)
W.R. Gardner and B.D. Rao, “Theoretical analysis of the high-rate vector quantization of lpc
parameters,” Speech and Audio Processing, IEEE Transactions on, vol. 3, no. 5, pp. 367 –381,
sep 1995.
Problem Statement
• We are looking for a point density function that is representative of a
quantizer that performs well in the classification task
• We have to select a distortion measure that is well defined for
classification purposes
• We chose the symmetric Kullback-Leibler divergence measure
between probability of class given the signal before and after
quantization
Problem Statement & Solution
We assume a generative
model for classifier. Hence
and are known
a priori.
Trade-off Distortion Measure:
Simulations
• Signal is from two
classes with known
conditional PDFs
• Dashed lines represent
the decision boundaries
• Point density
function dedicates
codebook points to the
boundaries
Simulations
• only dedicates
codebook points where
the signal is concentrated
• By introducing tradeoff
between MSE and
classification, codebook
points move to the
classification boundaries
Simulations
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
KL Tradeoff (a = 0.2)Tradeoff (a = 0.8) MSE
10 Bits
8 Bits
6 Bits
Classification
Error (%)
• The higher the bit
rate of quantizer the
better classification
accuracy
• As we move from
MSE to KL, the
classification
accuracy improves
Simulations
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
KL Tradeoff (a = 0.2) Tradeoff (a = 0.8) MSE
10 Bits
8 Bits
6 Bits
Distortion
(dB)
• Pure KL performs
poorly as far as the
distortion of the signal
• However, introducing
the slightest tradeoff
with MSE improves
distortion significantly
Concluding Remarks
• A solution for quantization of signals for the purpose of obtaining
a more accurate classification at the decoder was proposed
• High-rate theory for quantizer design was employed
• An optimal point density function was derived
• The performance of this method on synthetically generated data
was examined and observed to be superior in the task of
classification of signals at the decoder
• The tradeoff between the reproduction fidelity and classification
accuracy was studied as well
• In our future work, we will study the practical vector quantizer
design based on the high-rate theory

More Related Content

What's hot

2021 03-02-transformer interpretability
2021 03-02-transformer interpretability2021 03-02-transformer interpretability
2021 03-02-transformer interpretabilityJAEMINJEONG5
 
Ml10 dimensionality reduction-and_advanced_topics
Ml10 dimensionality reduction-and_advanced_topicsMl10 dimensionality reduction-and_advanced_topics
Ml10 dimensionality reduction-and_advanced_topicsankit_ppt
 
Handwritten Digit Recognition and performance of various modelsation[autosaved]
Handwritten Digit Recognition and performance of various modelsation[autosaved]Handwritten Digit Recognition and performance of various modelsation[autosaved]
Handwritten Digit Recognition and performance of various modelsation[autosaved]SubhradeepMaji
 
Convolutional Neural Network - CNN | How CNN Works | Deep Learning Course | S...
Convolutional Neural Network - CNN | How CNN Works | Deep Learning Course | S...Convolutional Neural Network - CNN | How CNN Works | Deep Learning Course | S...
Convolutional Neural Network - CNN | How CNN Works | Deep Learning Course | S...Simplilearn
 
2021 01-04-learning filter-basis
2021 01-04-learning filter-basis2021 01-04-learning filter-basis
2021 01-04-learning filter-basisJAEMINJEONG5
 
Convolutional neural network
Convolutional neural networkConvolutional neural network
Convolutional neural networkFerdous ahmed
 
03 image transformations_i
03 image transformations_i03 image transformations_i
03 image transformations_iankit_ppt
 
PR-317: MLP-Mixer: An all-MLP Architecture for Vision
PR-317: MLP-Mixer: An all-MLP Architecture for VisionPR-317: MLP-Mixer: An all-MLP Architecture for Vision
PR-317: MLP-Mixer: An all-MLP Architecture for VisionJinwon Lee
 
05 contours seg_matching
05 contours seg_matching05 contours seg_matching
05 contours seg_matchingankit_ppt
 
IRJET- Contrast Enhancement of Grey Level and Color Image using DWT and SVD
IRJET-  	  Contrast Enhancement of Grey Level and Color Image using DWT and SVDIRJET-  	  Contrast Enhancement of Grey Level and Color Image using DWT and SVD
IRJET- Contrast Enhancement of Grey Level and Color Image using DWT and SVDIRJET Journal
 
MobileNet - PR044
MobileNet - PR044MobileNet - PR044
MobileNet - PR044Jinwon Lee
 
08 neural networks
08 neural networks08 neural networks
08 neural networksankit_ppt
 
Attention Is All You Need
Attention Is All You NeedAttention Is All You Need
Attention Is All You NeedSEMINARGROOT
 
Unsupervised visual representation learning overview: Toward Self-Supervision
Unsupervised visual representation learning overview: Toward Self-SupervisionUnsupervised visual representation learning overview: Toward Self-Supervision
Unsupervised visual representation learning overview: Toward Self-SupervisionLEE HOSEONG
 
Convolutional Neural Network (CNN) presentation from theory to code in Theano
Convolutional Neural Network (CNN) presentation from theory to code in TheanoConvolutional Neural Network (CNN) presentation from theory to code in Theano
Convolutional Neural Network (CNN) presentation from theory to code in TheanoSeongwon Hwang
 
2021 03-01-on the relationship between self-attention and convolutional layers
2021 03-01-on the relationship between self-attention and convolutional layers2021 03-01-on the relationship between self-attention and convolutional layers
2021 03-01-on the relationship between self-attention and convolutional layersJAEMINJEONG5
 
Tutorial on convolutional neural networks
Tutorial on convolutional neural networksTutorial on convolutional neural networks
Tutorial on convolutional neural networksHojin Yang
 
04 image transformations_ii
04 image transformations_ii04 image transformations_ii
04 image transformations_iiankit_ppt
 

What's hot (19)

2021 03-02-transformer interpretability
2021 03-02-transformer interpretability2021 03-02-transformer interpretability
2021 03-02-transformer interpretability
 
Ml10 dimensionality reduction-and_advanced_topics
Ml10 dimensionality reduction-and_advanced_topicsMl10 dimensionality reduction-and_advanced_topics
Ml10 dimensionality reduction-and_advanced_topics
 
Handwritten Digit Recognition and performance of various modelsation[autosaved]
Handwritten Digit Recognition and performance of various modelsation[autosaved]Handwritten Digit Recognition and performance of various modelsation[autosaved]
Handwritten Digit Recognition and performance of various modelsation[autosaved]
 
Convolutional Neural Network - CNN | How CNN Works | Deep Learning Course | S...
Convolutional Neural Network - CNN | How CNN Works | Deep Learning Course | S...Convolutional Neural Network - CNN | How CNN Works | Deep Learning Course | S...
Convolutional Neural Network - CNN | How CNN Works | Deep Learning Course | S...
 
2021 01-04-learning filter-basis
2021 01-04-learning filter-basis2021 01-04-learning filter-basis
2021 01-04-learning filter-basis
 
Convolutional neural network
Convolutional neural networkConvolutional neural network
Convolutional neural network
 
Cnn method
Cnn methodCnn method
Cnn method
 
03 image transformations_i
03 image transformations_i03 image transformations_i
03 image transformations_i
 
PR-317: MLP-Mixer: An all-MLP Architecture for Vision
PR-317: MLP-Mixer: An all-MLP Architecture for VisionPR-317: MLP-Mixer: An all-MLP Architecture for Vision
PR-317: MLP-Mixer: An all-MLP Architecture for Vision
 
05 contours seg_matching
05 contours seg_matching05 contours seg_matching
05 contours seg_matching
 
IRJET- Contrast Enhancement of Grey Level and Color Image using DWT and SVD
IRJET-  	  Contrast Enhancement of Grey Level and Color Image using DWT and SVDIRJET-  	  Contrast Enhancement of Grey Level and Color Image using DWT and SVD
IRJET- Contrast Enhancement of Grey Level and Color Image using DWT and SVD
 
MobileNet - PR044
MobileNet - PR044MobileNet - PR044
MobileNet - PR044
 
08 neural networks
08 neural networks08 neural networks
08 neural networks
 
Attention Is All You Need
Attention Is All You NeedAttention Is All You Need
Attention Is All You Need
 
Unsupervised visual representation learning overview: Toward Self-Supervision
Unsupervised visual representation learning overview: Toward Self-SupervisionUnsupervised visual representation learning overview: Toward Self-Supervision
Unsupervised visual representation learning overview: Toward Self-Supervision
 
Convolutional Neural Network (CNN) presentation from theory to code in Theano
Convolutional Neural Network (CNN) presentation from theory to code in TheanoConvolutional Neural Network (CNN) presentation from theory to code in Theano
Convolutional Neural Network (CNN) presentation from theory to code in Theano
 
2021 03-01-on the relationship between self-attention and convolutional layers
2021 03-01-on the relationship between self-attention and convolutional layers2021 03-01-on the relationship between self-attention and convolutional layers
2021 03-01-on the relationship between self-attention and convolutional layers
 
Tutorial on convolutional neural networks
Tutorial on convolutional neural networksTutorial on convolutional neural networks
Tutorial on convolutional neural networks
 
04 image transformations_ii
04 image transformations_ii04 image transformations_ii
04 image transformations_ii
 

Similar to IEEE DSP Workshop 2011

Machine learning for IoT - unpacking the blackbox
Machine learning for IoT - unpacking the blackboxMachine learning for IoT - unpacking the blackbox
Machine learning for IoT - unpacking the blackboxIvo Andreev
 
Wits presentation 6_28072015
Wits presentation 6_28072015Wits presentation 6_28072015
Wits presentation 6_28072015Beatrice van Eden
 
DC04 Image Compression Standards.pdf
DC04 Image Compression Standards.pdfDC04 Image Compression Standards.pdf
DC04 Image Compression Standards.pdfssuser1bd081
 
PR-284: End-to-End Object Detection with Transformers(DETR)
PR-284: End-to-End Object Detection with Transformers(DETR)PR-284: End-to-End Object Detection with Transformers(DETR)
PR-284: End-to-End Object Detection with Transformers(DETR)Jinwon Lee
 
Oxford 05-oct-2012
Oxford 05-oct-2012Oxford 05-oct-2012
Oxford 05-oct-2012Ted Dunning
 
Neural Networks for Machine Learning and Deep Learning
Neural Networks for Machine Learning and Deep LearningNeural Networks for Machine Learning and Deep Learning
Neural Networks for Machine Learning and Deep Learningcomifa7406
 
PR243: Designing Network Design Spaces
PR243: Designing Network Design SpacesPR243: Designing Network Design Spaces
PR243: Designing Network Design SpacesJinwon Lee
 
Speech Compression using LPC
Speech Compression using LPCSpeech Compression using LPC
Speech Compression using LPCDisha Modi
 
Multimedia lossy compression algorithms
Multimedia lossy compression algorithmsMultimedia lossy compression algorithms
Multimedia lossy compression algorithmsMazin Alwaaly
 
Enterprise Scale Topological Data Analysis Using Spark
Enterprise Scale Topological Data Analysis Using SparkEnterprise Scale Topological Data Analysis Using Spark
Enterprise Scale Topological Data Analysis Using SparkAlpine Data
 
Enterprise Scale Topological Data Analysis Using Spark
Enterprise Scale Topological Data Analysis Using SparkEnterprise Scale Topological Data Analysis Using Spark
Enterprise Scale Topological Data Analysis Using SparkSpark Summit
 
Fast Single-pass K-means Clusterting at Oxford
Fast Single-pass K-means Clusterting at Oxford Fast Single-pass K-means Clusterting at Oxford
Fast Single-pass K-means Clusterting at Oxford MapR Technologies
 
Disparity Estimation Using A Color Segmentation V3
Disparity Estimation Using A Color Segmentation V3Disparity Estimation Using A Color Segmentation V3
Disparity Estimation Using A Color Segmentation V3thomaswangxin
 
Object detection - RCNNs vs Retinanet
Object detection - RCNNs vs RetinanetObject detection - RCNNs vs Retinanet
Object detection - RCNNs vs RetinanetRishabh Indoria
 
Cahall Final Intern Presentation
Cahall Final Intern PresentationCahall Final Intern Presentation
Cahall Final Intern PresentationDaniel Cahall
 

Similar to IEEE DSP Workshop 2011 (20)

Machine learning for IoT - unpacking the blackbox
Machine learning for IoT - unpacking the blackboxMachine learning for IoT - unpacking the blackbox
Machine learning for IoT - unpacking the blackbox
 
Wits presentation 6_28072015
Wits presentation 6_28072015Wits presentation 6_28072015
Wits presentation 6_28072015
 
DC04 Image Compression Standards.pdf
DC04 Image Compression Standards.pdfDC04 Image Compression Standards.pdf
DC04 Image Compression Standards.pdf
 
PR-284: End-to-End Object Detection with Transformers(DETR)
PR-284: End-to-End Object Detection with Transformers(DETR)PR-284: End-to-End Object Detection with Transformers(DETR)
PR-284: End-to-End Object Detection with Transformers(DETR)
 
Oxford 05-oct-2012
Oxford 05-oct-2012Oxford 05-oct-2012
Oxford 05-oct-2012
 
Neural Networks for Machine Learning and Deep Learning
Neural Networks for Machine Learning and Deep LearningNeural Networks for Machine Learning and Deep Learning
Neural Networks for Machine Learning and Deep Learning
 
PR243: Designing Network Design Spaces
PR243: Designing Network Design SpacesPR243: Designing Network Design Spaces
PR243: Designing Network Design Spaces
 
Speech Compression using LPC
Speech Compression using LPCSpeech Compression using LPC
Speech Compression using LPC
 
vector QUANTIZATION
vector QUANTIZATIONvector QUANTIZATION
vector QUANTIZATION
 
vector QUANTIZATION
vector QUANTIZATIONvector QUANTIZATION
vector QUANTIZATION
 
vector QUANTIZATION
vector QUANTIZATIONvector QUANTIZATION
vector QUANTIZATION
 
Multimedia lossy compression algorithms
Multimedia lossy compression algorithmsMultimedia lossy compression algorithms
Multimedia lossy compression algorithms
 
Enterprise Scale Topological Data Analysis Using Spark
Enterprise Scale Topological Data Analysis Using SparkEnterprise Scale Topological Data Analysis Using Spark
Enterprise Scale Topological Data Analysis Using Spark
 
Enterprise Scale Topological Data Analysis Using Spark
Enterprise Scale Topological Data Analysis Using SparkEnterprise Scale Topological Data Analysis Using Spark
Enterprise Scale Topological Data Analysis Using Spark
 
Fast Single-pass K-means Clusterting at Oxford
Fast Single-pass K-means Clusterting at Oxford Fast Single-pass K-means Clusterting at Oxford
Fast Single-pass K-means Clusterting at Oxford
 
Sparksummitny2016
Sparksummitny2016Sparksummitny2016
Sparksummitny2016
 
add9.5.ppt
add9.5.pptadd9.5.ppt
add9.5.ppt
 
Disparity Estimation Using A Color Segmentation V3
Disparity Estimation Using A Color Segmentation V3Disparity Estimation Using A Color Segmentation V3
Disparity Estimation Using A Color Segmentation V3
 
Object detection - RCNNs vs Retinanet
Object detection - RCNNs vs RetinanetObject detection - RCNNs vs Retinanet
Object detection - RCNNs vs Retinanet
 
Cahall Final Intern Presentation
Cahall Final Intern PresentationCahall Final Intern Presentation
Cahall Final Intern Presentation
 

Recently uploaded

Which standard is best for your content?
Which standard is best for your content?Which standard is best for your content?
Which standard is best for your content?Rustici Software
 
The work to make the piecework work: An ethnographic study of food delivery w...
The work to make the piecework work: An ethnographic study of food delivery w...The work to make the piecework work: An ethnographic study of food delivery w...
The work to make the piecework work: An ethnographic study of food delivery w...stockholm university
 
React JS; all concepts. Contains React Features, JSX, functional & Class comp...
React JS; all concepts. Contains React Features, JSX, functional & Class comp...React JS; all concepts. Contains React Features, JSX, functional & Class comp...
React JS; all concepts. Contains React Features, JSX, functional & Class comp...Karmanjay Verma
 
Email Marketing Automation for Bonterra Impact Management (fka Social Solutio...
Email Marketing Automation for Bonterra Impact Management (fka Social Solutio...Email Marketing Automation for Bonterra Impact Management (fka Social Solutio...
Email Marketing Automation for Bonterra Impact Management (fka Social Solutio...Jeffrey Haguewood
 
THE STATE OF STARTUP ECOSYSTEM - INDIA x JAPAN 2023
THE STATE OF STARTUP ECOSYSTEM - INDIA x JAPAN 2023THE STATE OF STARTUP ECOSYSTEM - INDIA x JAPAN 2023
THE STATE OF STARTUP ECOSYSTEM - INDIA x JAPAN 2023Joshua Flannery
 
Transport in Open Pits______SM_MI10415MI
Transport in Open Pits______SM_MI10415MITransport in Open Pits______SM_MI10415MI
Transport in Open Pits______SM_MI10415MIRomil Mishra
 
Bitdefender-CSG-Report-creat7534-interactive
Bitdefender-CSG-Report-creat7534-interactiveBitdefender-CSG-Report-creat7534-interactive
Bitdefender-CSG-Report-creat7534-interactivestartupro
 
HCI Lesson 1 - Introduction to Human-Computer Interaction.pdf
HCI Lesson 1 - Introduction to Human-Computer Interaction.pdfHCI Lesson 1 - Introduction to Human-Computer Interaction.pdf
HCI Lesson 1 - Introduction to Human-Computer Interaction.pdfROWELL MARQUINA
 
QMMS Lesson 2 - Using MS Excel Formula.pdf
QMMS Lesson 2 - Using MS Excel Formula.pdfQMMS Lesson 2 - Using MS Excel Formula.pdf
QMMS Lesson 2 - Using MS Excel Formula.pdfROWELL MARQUINA
 
Digital Tools & AI in Career Development
Digital Tools & AI in Career DevelopmentDigital Tools & AI in Career Development
Digital Tools & AI in Career DevelopmentMahmoud Rabie
 
Generative Artificial Intelligence: How generative AI works.pdf
Generative Artificial Intelligence: How generative AI works.pdfGenerative Artificial Intelligence: How generative AI works.pdf
Generative Artificial Intelligence: How generative AI works.pdfIngrid Airi González
 
Accelerating Enterprise Software Engineering with Platformless
Accelerating Enterprise Software Engineering with PlatformlessAccelerating Enterprise Software Engineering with Platformless
Accelerating Enterprise Software Engineering with PlatformlessWSO2
 
Transcript: New from BookNet Canada for 2024: BNC SalesData and LibraryData -...
Transcript: New from BookNet Canada for 2024: BNC SalesData and LibraryData -...Transcript: New from BookNet Canada for 2024: BNC SalesData and LibraryData -...
Transcript: New from BookNet Canada for 2024: BNC SalesData and LibraryData -...BookNet Canada
 
MuleSoft Online Meetup Group - B2B Crash Course: Release SparkNotes
MuleSoft Online Meetup Group - B2B Crash Course: Release SparkNotesMuleSoft Online Meetup Group - B2B Crash Course: Release SparkNotes
MuleSoft Online Meetup Group - B2B Crash Course: Release SparkNotesManik S Magar
 
WomenInAutomation2024: AI and Automation for eveyone
WomenInAutomation2024: AI and Automation for eveyoneWomenInAutomation2024: AI and Automation for eveyone
WomenInAutomation2024: AI and Automation for eveyoneUiPathCommunity
 
React Native vs Ionic - The Best Mobile App Framework
React Native vs Ionic - The Best Mobile App FrameworkReact Native vs Ionic - The Best Mobile App Framework
React Native vs Ionic - The Best Mobile App FrameworkPixlogix Infotech
 
Dynamical Context introduction word sensibility orientation
Dynamical Context introduction word sensibility orientationDynamical Context introduction word sensibility orientation
Dynamical Context introduction word sensibility orientationBuild Intuit
 
Tetracrom printing process for packaging with CMYK+
Tetracrom printing process for packaging with CMYK+Tetracrom printing process for packaging with CMYK+
Tetracrom printing process for packaging with CMYK+Antonio de Llamas
 
Infrared simulation and processing on Nvidia platforms
Infrared simulation and processing on Nvidia platformsInfrared simulation and processing on Nvidia platforms
Infrared simulation and processing on Nvidia platformsYoss Cohen
 
Automation Ops Series: Session 3 - Solutions management
Automation Ops Series: Session 3 - Solutions managementAutomation Ops Series: Session 3 - Solutions management
Automation Ops Series: Session 3 - Solutions managementDianaGray10
 

Recently uploaded (20)

Which standard is best for your content?
Which standard is best for your content?Which standard is best for your content?
Which standard is best for your content?
 
The work to make the piecework work: An ethnographic study of food delivery w...
The work to make the piecework work: An ethnographic study of food delivery w...The work to make the piecework work: An ethnographic study of food delivery w...
The work to make the piecework work: An ethnographic study of food delivery w...
 
React JS; all concepts. Contains React Features, JSX, functional & Class comp...
React JS; all concepts. Contains React Features, JSX, functional & Class comp...React JS; all concepts. Contains React Features, JSX, functional & Class comp...
React JS; all concepts. Contains React Features, JSX, functional & Class comp...
 
Email Marketing Automation for Bonterra Impact Management (fka Social Solutio...
Email Marketing Automation for Bonterra Impact Management (fka Social Solutio...Email Marketing Automation for Bonterra Impact Management (fka Social Solutio...
Email Marketing Automation for Bonterra Impact Management (fka Social Solutio...
 
THE STATE OF STARTUP ECOSYSTEM - INDIA x JAPAN 2023
THE STATE OF STARTUP ECOSYSTEM - INDIA x JAPAN 2023THE STATE OF STARTUP ECOSYSTEM - INDIA x JAPAN 2023
THE STATE OF STARTUP ECOSYSTEM - INDIA x JAPAN 2023
 
Transport in Open Pits______SM_MI10415MI
Transport in Open Pits______SM_MI10415MITransport in Open Pits______SM_MI10415MI
Transport in Open Pits______SM_MI10415MI
 
Bitdefender-CSG-Report-creat7534-interactive
Bitdefender-CSG-Report-creat7534-interactiveBitdefender-CSG-Report-creat7534-interactive
Bitdefender-CSG-Report-creat7534-interactive
 
HCI Lesson 1 - Introduction to Human-Computer Interaction.pdf
HCI Lesson 1 - Introduction to Human-Computer Interaction.pdfHCI Lesson 1 - Introduction to Human-Computer Interaction.pdf
HCI Lesson 1 - Introduction to Human-Computer Interaction.pdf
 
QMMS Lesson 2 - Using MS Excel Formula.pdf
QMMS Lesson 2 - Using MS Excel Formula.pdfQMMS Lesson 2 - Using MS Excel Formula.pdf
QMMS Lesson 2 - Using MS Excel Formula.pdf
 
Digital Tools & AI in Career Development
Digital Tools & AI in Career DevelopmentDigital Tools & AI in Career Development
Digital Tools & AI in Career Development
 
Generative Artificial Intelligence: How generative AI works.pdf
Generative Artificial Intelligence: How generative AI works.pdfGenerative Artificial Intelligence: How generative AI works.pdf
Generative Artificial Intelligence: How generative AI works.pdf
 
Accelerating Enterprise Software Engineering with Platformless
Accelerating Enterprise Software Engineering with PlatformlessAccelerating Enterprise Software Engineering with Platformless
Accelerating Enterprise Software Engineering with Platformless
 
Transcript: New from BookNet Canada for 2024: BNC SalesData and LibraryData -...
Transcript: New from BookNet Canada for 2024: BNC SalesData and LibraryData -...Transcript: New from BookNet Canada for 2024: BNC SalesData and LibraryData -...
Transcript: New from BookNet Canada for 2024: BNC SalesData and LibraryData -...
 
MuleSoft Online Meetup Group - B2B Crash Course: Release SparkNotes
MuleSoft Online Meetup Group - B2B Crash Course: Release SparkNotesMuleSoft Online Meetup Group - B2B Crash Course: Release SparkNotes
MuleSoft Online Meetup Group - B2B Crash Course: Release SparkNotes
 
WomenInAutomation2024: AI and Automation for eveyone
WomenInAutomation2024: AI and Automation for eveyoneWomenInAutomation2024: AI and Automation for eveyone
WomenInAutomation2024: AI and Automation for eveyone
 
React Native vs Ionic - The Best Mobile App Framework
React Native vs Ionic - The Best Mobile App FrameworkReact Native vs Ionic - The Best Mobile App Framework
React Native vs Ionic - The Best Mobile App Framework
 
Dynamical Context introduction word sensibility orientation
Dynamical Context introduction word sensibility orientationDynamical Context introduction word sensibility orientation
Dynamical Context introduction word sensibility orientation
 
Tetracrom printing process for packaging with CMYK+
Tetracrom printing process for packaging with CMYK+Tetracrom printing process for packaging with CMYK+
Tetracrom printing process for packaging with CMYK+
 
Infrared simulation and processing on Nvidia platforms
Infrared simulation and processing on Nvidia platformsInfrared simulation and processing on Nvidia platforms
Infrared simulation and processing on Nvidia platforms
 
Automation Ops Series: Session 3 - Solutions management
Automation Ops Series: Session 3 - Solutions managementAutomation Ops Series: Session 3 - Solutions management
Automation Ops Series: Session 3 - Solutions management
 

IEEE DSP Workshop 2011

  • 1. QUANTIZATION FOR CLASSIFICATION ACCURACY IN HIGH-RATE QUANTIZERS Behzad M. Dogahe Manohar N. Murthi Department of Electrical and Computer Engineering IEEE DSP Workshop, January 2011
  • 2. Outline • Motivation • Background • Problem Statement and Solution • Simulations • Concluding Remarks
  • 3. Motivation • Quantization of signals is required for many applications • The original signal is quantized at the encoder and at the decoder side a replica that should resemble the original signal in some sense is recovered • Present quantizers make an effort to reduce the distortion of the signal in the sense of reproduction fidelity • Consider scenarios in which signals are generated from multiple classes. The encoder focuses on the task of quantization without any regards to the class of the signal • The quantized signal reaches the decoder where not only the recovery of the signal should take place but also a decision is to be made on the class of the signal based on the quantized version of the signal only
  • 4. Motivation • Goal: Design of a quantizer that is optimized for the task of classification at the decoder • Application Scenarios:  Want to have good sound fidelity (good voice/audio quality) but also want to be able to perform speaker recognition  Sensor network where the sensors have low complexity, simple quantizers, but the decoder/sensor sink node does more sophisticated processing (so the raw signal value is needed, but we also want to be able to classify the sensed signal)
  • 5. Background Quantizerx )(ˆ xQx  x xˆ x )(xp x )(x x xˆ x )(xp x )(x In high-rate theory point density function represents the density of codebook points in any region for a quantizer. The design of a quantizer is equivalent to design of the optimal point density function. )(xp : Probability Density Function
  • 6. Background • Design of Quantizer involves minimizing: where is Distortion Measure • Examples of Distortion Measure:  MSE  Log Spectral Distortion • High-Rate Theory: 2 ˆ)ˆ,( xxxxd  Optimization Problem
  • 7. Background • Following the steps in [Gardner and Rao] point density function will be derived as (n is the dimension of x) W.R. Gardner and B.D. Rao, “Theoretical analysis of the high-rate vector quantization of lpc parameters,” Speech and Audio Processing, IEEE Transactions on, vol. 3, no. 5, pp. 367 –381, sep 1995.
  • 8. Problem Statement • We are looking for a point density function that is representative of a quantizer that performs well in the classification task • We have to select a distortion measure that is well defined for classification purposes • We chose the symmetric Kullback-Leibler divergence measure between probability of class given the signal before and after quantization
  • 9. Problem Statement & Solution We assume a generative model for classifier. Hence and are known a priori. Trade-off Distortion Measure:
  • 10. Simulations • Signal is from two classes with known conditional PDFs • Dashed lines represent the decision boundaries • Point density function dedicates codebook points to the boundaries
  • 11. Simulations • only dedicates codebook points where the signal is concentrated • By introducing tradeoff between MSE and classification, codebook points move to the classification boundaries
  • 12. Simulations 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 KL Tradeoff (a = 0.2)Tradeoff (a = 0.8) MSE 10 Bits 8 Bits 6 Bits Classification Error (%) • The higher the bit rate of quantizer the better classification accuracy • As we move from MSE to KL, the classification accuracy improves
  • 13. Simulations -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 KL Tradeoff (a = 0.2) Tradeoff (a = 0.8) MSE 10 Bits 8 Bits 6 Bits Distortion (dB) • Pure KL performs poorly as far as the distortion of the signal • However, introducing the slightest tradeoff with MSE improves distortion significantly
  • 14. Concluding Remarks • A solution for quantization of signals for the purpose of obtaining a more accurate classification at the decoder was proposed • High-rate theory for quantizer design was employed • An optimal point density function was derived • The performance of this method on synthetically generated data was examined and observed to be superior in the task of classification of signals at the decoder • The tradeoff between the reproduction fidelity and classification accuracy was studied as well • In our future work, we will study the practical vector quantizer design based on the high-rate theory