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Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction Wissam A. Albukhanajer, Yaochu Jin and Johann A. Briffa Wissam A. Albukhanajer (student) E: w.albukhanajer@surrey.ac.uk T: +44(0)1483 68 6051 CEC

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Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction

Wissam A. Albukhanajer, Yaochu Jin and Johann A. Briffa Wissam A. Albukhanajer (student) E: w.albukhanajer@surrey.ac.uk T: +44(0)1483 68 6051

CEC 2015, Sendai, Japan SS37: Evolutionary Feature Selection and Construction & SS13: Evolutionary Computer Vision

Nature Inspired Computing and Engineering Department of Computing Faculty of Engineering and Physical Sciences University of Surrey United Kingdom GU2 7XH

May 28 Thursday, 2015

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In this Talk

  • Introduction

– Traditional Trace Transform. – Triple Features. – Evolutionary Trace Transform. 2

  • Computational Complexity of the Trace

Transform

  • Multi-Objective Parameters Tuning

– Two-Objective Optimisation – Three-Objective Optimisation

  • Experimental Results

– Selection of Knee Point Solutions – Performance Analysis – Complexity Analysis

  • Summary and Conclusion
  • W. A. Albukhanajer et. al. “Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction,” CEC2015, Sendai, Japan.
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[15] A. Kadyrov and M. Petrou, "The Trace transform and its applications," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 23, pp. 811-828, 2001.

Introduction

  • Traditional Trace Transform (TT):

– Inspired by Radon transform, proposed by Kadyrov and Petrou[15] – Trace Transform is a generalisation of Radon Transform. The functional calculated on the image pixels is not necessary the integral. – Different Trace Transforms can be produced Using different Trace functionals T.

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  • W. A. Albukhanajer et. al. “Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction,” CEC2015, Sendai, Japan.

The Trace matrix An image

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Introduction

  • Traditional Trace Transform (TT) (cont.)

– Triple feature construction : by applying another two functionals:

  • Diametric functional D applied to the Trace Matrix to produce a vector of

length (𝜄).

  • Circus functional C is applied to the diametric vector to produce a real

number to describe the image called Triple Feature.

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Schematic diagram of Triple feature construction .

  • W. A. Albukhanajer et. al. “Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction,” CEC2015, Sendai, Japan.
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Introduction

  • Evolutionary Trace Transform:

– Using NSGA-II[17] based Multi-objective optimisation (MOO) to search the best combinations of Triple features functionals – The two objectives are: 1. Minimize the within-class feature variance (Sw) 2. Maximize the between-class feature scatter (Sb) – NSGA-II is implemented using SHARK Machine Learning Library[16] 5 where K is the number of classes, 𝐷𝑙 is the number of samples in class 𝑙, 𝜈𝑙 is the mean of class 𝑙 of Ξ Triple features, Ξ𝑘𝑙 is the jth Triple features of class 𝑙, and 𝜈Ξ is mean of all classes of Ξ Triple features.

[16] Christian Igel, Verena Heidrich-Meisner, and Tobias Glasmachers. Shark. Journal of Machine Learning Research 9, pp. 993-996, 2008. http://image.diku.dk/shark [17] K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, "A fast and elitist multiobjective genetic algorithm: NSGA-II," Evolutionary Computation, IEEE Transactions on, vol. 6, pp. 182-197, 2002.

  • W. A. Albukhanajer et. al. “Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction,” CEC2015, Sendai, Japan.
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  • Evolutionary Trace Transform in the Presence of Noise (ETTN)

– In the evolutionary set up, sample images include three different classes, each containing five different types of changes. The major difference here is that Gaussian noise is added to the sample images apart from RST deformations:

  • Sample 1 : A low-resolution image from (64 × 64) generated from a randomly chosen original image (256 ×

256);

  • Sample 2 : Random rotation, scale and translation of Sample 1 with Gaussian noise (standard deviation=4);
  • Sample 3 : Random rotation, scale and translation of Sample 1 with Gaussian noise (standard deviation=6);
  • Sample 4 : Random rotation of Sample 1;
  • Sample 5 : Random scale of Sample 1.

– Therefore, there are 15 images in ETTN (20 sample images in ETT).

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Introduction

[145] L. Fei-Fei, R. Fergus, and P. Perona, \One-shot learning of object categories," IEEE Transactions

  • n Pattern Analysis and Machine Intelligence, vol. 28, no. 4, pp. 594-611, April 2006.
  • W. A. Albukhanajer et. al. “Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction,” CEC2015, Sendai, Japan.
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Computational Complexity

  • Tuneable Parameters

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The Trace matrix of size 𝑜𝜄 × 𝑜𝜍

  • W. A. Albukhanajer et. al. “Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction,” CEC2015, Sendai, Japan.
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Computational Complexity

  • Traditional Trace Transform uses a thousand[87] (not optimised) features:

𝑜𝑢 = 𝑜𝜍 = 𝑜𝜄 = 100, 0 ≤ 𝜄 ≤ 2𝜌, and 𝑂𝑈 = 𝑂𝐸 = 𝑂𝐷 = 10

  • The largest number of sampling lines per rotation angle equals the number
  • f pixels on the image diagonal, i.e., the maximum value of 𝑜𝜍 is equal

to 𝑂2 + 𝑂2 = 2𝑂 with Δ𝜍 = 1.

  • Randon Complexity (Big O): 𝑃(𝑂2𝑜𝜄)
  • The number of operations (in Big Theta notation) required to calculate a

Triple feature is equal to: Θ(𝑂𝑈𝑜𝑢𝑜𝜍𝑜𝜄) for 0 ≤ 𝜄 ≤ 𝜌

  • For 𝑜𝜄 = 180, ∆𝜄 = 1: complexity equals to Θ(𝑂2)
  • When considering Δ𝜄, Δ𝜍: Θ(𝑂𝑈𝑂2/Δ𝜄Δ𝜍)

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[87] A. Kadyrov, A. Talepbour, and M. Petrou, \Texture Classification With Thousands of Features," in 13th British Machine Vision Conference. BMVC, 2-5 September 2002 2002, pp. 656{665. [190] S. Tabbone, L. Wendling, and J.-P. Salmon, \A new shape descriptor defined on the Radon transform," Computer Vision and Image Understanding, vol. 102, no. 1, pp.42 -51, 2006.

  • W. A. Albukhanajer et. al. “Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction,” CEC2015, Sendai, Japan.
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Multi-objective Trace Parameters Tuning

  • Parameters Tuning Using Two-Objective Optimisation

– Two-objective minimisation with ∆𝜄 𝑏𝑜𝑒 ∆𝜍 as extra parameters to be tuned in addition to the Trace functionals T, D, and C.

  • Parameters Tuning Using Three-Objective Optimisation

– Time complexity is added as a third objective:

  • Both integer and real coding for ∆𝜄 𝑏𝑜𝑒 ∆𝜍 are considered.

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  • W. A. Albukhanajer et. al. “Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction,” CEC2015, Sendai, Japan.
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Some Functionals

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  • W. A. Albukhanajer et. al. “Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction,” CEC2015, Sendai, Japan.
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Multi-objective Trace Parameters Tuning

  • Two-objective non-dominated fronts and a selection of solutions at

the knee point

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Integer coding Real coding

  • W. A. Albukhanajer et. al. “Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction,” CEC2015, Sendai, Japan.

Search converges to value of 1 (better accuracy)

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Multi-objective Trace Parameters Tuning

  • Three-objective non-dominated fronts

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Integer coding Real coding

  • W. A. Albukhanajer et. al. “Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction,” CEC2015, Sendai, Japan.
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Experimental Results

  • Two-Objective Parameters Tuning: RST with Gaussian Noise (COIL-20 database)

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  • W. A. Albukhanajer et. al. “Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction,” CEC2015, Sendai, Japan.

Integer coding Real coding

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Experimental Results

  • Three-Objective Parameters Tuning: RST with Gaussian Noise (COIL-20 database)

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  • W. A. Albukhanajer et. al. “Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction,” CEC2015, Sendai, Japan.

Integer coding Real coding

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Experimental Results

  • Average performance of three solutions of each method:

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  • W. A. Albukhanajer et. al. “Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction,” CEC2015, Sendai, Japan.
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Experimental Results

  • Time complexity of three solutions of each method:

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  • W. A. Albukhanajer et. al. “Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction,” CEC2015, Sendai, Japan.

The run time in the three-objective case is smaller than the run time in the two-objective case due to the time complexity being added as a third

  • bjective in the three-objective case,

which provides fastest features but a relatively low performance.

From Table VI, we can see there are three different T functionals in all Triple feature pairs, which are T1, T3 and T5. which are And which have a time complexity O(N).

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Summary and Conclusion

  • This paper focused on the computational complexity in evolutionary Trace transform.
  • There are five parameters were tuned, which are three functionals T, D, C, and ∆𝜄 and

∆𝜍.

  • Multi-objective parameter tuning was presented for fine-tune Trace sampling

parameters using both, integer and real coding. Both two-objective and three-objective evolutionary algorithms were used and compared.

  • In the three-objective case, the time complexity was introduced as a third objective.

Therefore, it has improved the computational complexity. On the other hand, it has impacted negatively on the accuracy. Without a constraint on the minimum acceptable level of accuracy, the resulting solutions would not be in a good performance.

  • The integer coding scheme of the two-objective case was of the best overall

performance and computational complexity compared to the original ETTN and the

  • ther multi-objective optimisation such as the real coding scheme.

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  • W. A. Albukhanajer et. al. “Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction,” CEC2015, Sendai, Japan.
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Publications

  • Journal Papers:

–

  • W. A. Albukhanajer, J. A. Briffa, and Y. Jin, “Evolutionary Multiobjective Feature Extraction in the Presence
  • f Noise,” IEEE Trans. on Cybernetics. Vol. PP, Issue 99. 26 September 2014.

http://dx.doi.org/10.1109/TCYB.2014.2360074 –

  • W. A. Albukhanajer, J. A. Briffa, and Y. Jin, “Classifier Ensembles Using Pareto Optimal Image Features ”

submitted, IEEE Transactions on Cybernetics. March 2015.

  • Peer reviewed Conference Papers:

–

  • W. A. Albukhanajer, Y. Jin, J. A. Briffa "Evolutionary Multi-Objective Feature Construction and Tuning for

Invariant Image Analysis", submitted (January 2015), 2015 IEEE Congress on Evolutionary Computation (CEC), Sendai, Japan, May 25-28, 2015. –

  • W. A. Albukhanajer, Y. Jin, and J. A. Briffa, “Neural Network Ensembles for Image Identification Using

Pareto-optimal Features,” WCCI2014 IEEE Congress on Evolutionary Computation (CEC), Beijing, China, 06-11, July 2014. Page(s): 89 - 96. http://dx.doi.org/10.1109/CEC.2014.6900349 –

  • W. A. Albukhanajer, Y. Jin, J. Briffa and G. Williams “Evolutionary Multi-Objective Optimization of Trace

Transform for Invariant Feature Extraction”, WCCI2012. IEEE Congress on Evolutionary Computation (CEC), Brisbane, Australia, June 10-15, 2012. Page(s): 1 – 8. http://dx.doi.org/10.1109/CEC.2012.6256160 –

  • W. A. Albukhanajer, Y. Jin, J. Briffa and G. Williams “A comparative study of multi-objective evolutionary

trace transform methods for robust feature extraction,” in Evolutionary Multi-Criterion Optimization, ser. Lecture Notes in Computer Science (LNCS), R. Purshouse, P. Fleming, C. Fonseca, S. Greco, and J. Shaw, Eds. Springer Berlin Heidelberg, 2013, vol. 7811, pp. 573–586. http://dx.doi.org/10.1007/978-3-642-37140- 0_43

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  • W. A. Albukhanajer et. al. “Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction,” CEC2015, Sendai, Japan.
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Thank you

Wissam A. Albukhanajer (student) E: w.albukhanajer@surrey.ac.uk T: +44(0)1483 68 6051

Q&A

Nature Inspired Computing and Engineering Department of Computing Faculty of Engineering & Physical Sciences University of Surrey Guildford, UK. GU2 7XH

http://www.surrey.ac.uk/computing/

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  • W. A. Albukhanajer et. al. “Trade-off Between Computational Complexity and Accuracy in Evolutionary Image Feature Extraction,” CEC2015, Sendai, Japan.
  • Prof. Yaochu Jin

E: yaochu.jin@surrey.ac.uk T: +44(0)1483 686037, F: +44(0)1483 68 6051 Johann A. Briffa johann.briffa@um.edu.mt