Abstract
Image representation is a fundamental issue in signal processing, pattern recognition, and computer vision. An efficient image representation can lead to the development of effective algorithms for the interpretation of images. Since Marr proposed the fundamental principle of the primary sketch concept of a scene, many image representations have been developed based on this concept. The primary sketch refers to the edges, lines, regions, and others in an image. These are characteristic features, which can be extracted from an image by transforming an image from the pixel-level to a higher level representation for image understanding. Many techniques developed for pattern recognition can be used for image transform and resulted in efficiently representing the characteristic features (or called intrinsic dimension). Dimensionality reduction (DR) and sparse representation (SR) are two representative schemes frequently used in the transform for reducing the dimension of a dataset. These transformations include principle component analysis (PCA), singular value decomposition (SVD), non-negative matrix factorization (NMF), and sparse coding (SC). The study of the mammal brain suggests that only a small number of active neurons encode sensory information at any given point. This finding has led to the rapid development of sparse coding which refers to a small number of nonzero entries in a feature vector. Hence, it is important to represent the sparsity for the dataset by eliminating the data redundancy for applications. The ultimate goal is to have a compact, efficient, and compressed representation of the input data.
Nature does not hurry, yet everything is accomplished.
—Lao Tzu
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aharon M, Elad M, Bruckstein A (2006) K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans Signal Process 54(11):4311–4322. https://doi.org/10.1109/TSP.2006.881199
Breen P (2009) Algorithms for sparse approximation. University of Edinburgh, School of Mathematics
Cai D, Bao H, He X (2011) Sparse concept coding for visual analysis. CVPR 2011:20–25
Castleman KR (1996) Digital image processing, Prentice Hall, New Jersey
Eggert J, Korner E (2004) Sparse coding and NMF. In: Proceedings of IEEE international joint conference on Neural Networks 2004, vol 4, pp 2529–2533
Elad M (2006) Sparse and redundant representations: from theory to applications in signal and image processing. Springer, Berlin
Gangeh MJ, Ghodsi A, Kamel MS (2011) Dictionary learning in texture classification. In: Kamel M, Campilho A (eds) Image analysis and recognition. ICIAR 2011. Lecture notes in computer science, vol 6753. Springer, Berlin
Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning: data mining, inference, and prediction, 2nd edn. Springer, Berlin
Horng MH (2009) Honey bee mating optimization vector quantization scheme in image compression. In: Deng H, Wang L, Wang FL, Lei J (eds) Artificial intelligence and computational intelligence (AICI 2009). Lecture notes in computer science, vol 5855. Springer, Berlin
Horn RA, Johnson CR (1985) Matrix Analysis, Cambridge. Cambridge University Press, England
Hotelling H (1933) Analysis of a complex of statistical variables into principal components. J Educ Psychol, 24: 417–441 and 498–520
Hughes GF (1968) On the mean accuracy of statistical pattern recognitions. IEEE Trans Inf Theory, IT-14(1)
Hung CC, Fahsi A, Tadesse W, Coleman T (1997) A comparative study of remotely sensed data classification using principal components analysis and divergence. In: Proceedings of IEEE international conference on systems, man, and cybernetics, Orlando, FL, 12–15 Oct 1997, pp 2444–2449
Hyvärinen A, Oja E (2000) Independent component analysis: algorithms and applications. Neural Netw 13(4–5):411–430
Jolliffe IT (2002) Principal component analysis, 2nd edn. Springer, New York
Kim H, Park H (2007) Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis. Bioinformatics 23(12):1495–1502
Kolman B (1980) Introductory linear algebra with applications, 2nd edn. Macmillan Publishing Company Incorporated, New York
Kuo B-C, Ho H-H, Li C-H, Hung C-C, Taur J-S (2013) A kernel-based feature selection method for SVM with RBF kernel for hyperspectral image classification. IEEE J Sel Top Appl Earth Obs Remote Sens, 7(1):317–326
Kuo B-C, Landgrebe DA (2004) Nonparametric weighted feature extraction for classification. IEEE Trans Geosci Remote Sens 42(5):1096–1105
Lee H, BattleA, Raina R, Ng AY (2006) Efficient sparse coding algorithms. Advances in neural information processing systems, pp 801–808
Linde Y, Buzo A, Gray RM (1980) An algorithm for vector quantizer design. IEEE Trans Commun, COM-28(1):84–95
Lee DD, Seung HS (1999) Learning the parts of objects by non-negative matrix factorization. Nature 401:788–791
Mallapragada S, Wong M, Hung C-C (2018) Dimensionality reduction of hyperspectral images for classification. In: Proceedings of the ninth international conference on information, pp 153–160
Mallat SG (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intell 2(7):674–693
Marial J, Bach F, Ponce J, Sapiro G (2010) Online learning for matrix factorization and sparse coding. J Mach Learn Res 11:19–60
Mairal J, Bach F, Ponce J, Sapiro G (2009) Online dictionary learning for sparse coding. In: Proceedings of the 26th international conference on machine learning, montreal, Canada
Mairal J, Bach F, Sapiro G, Zisserman A (2008) Supervised dictionary learning. INRIA
Marr D (1982) A computational investigation into the human representation and processing of visual information. MIT Press, Cambridge
Olshausen BA, Field DJ (1996) Emergence of simple cell receptive field properties by learning a sparse code for natural images. Nature 381(6583):607–609
Olshausen BA, Field DJ (2004) Sparse coding of sensory inputs. Curr Opin Neurobiol 14:481–487
Paatero P, Tapper U (1994) Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values. Environmentrics 5(2):111–126
Pearson K (1901) On lines and planes of closest fit to systems of points in space. Philos Mag 2(11):559–572 (series 6)
Richards JA, Jia X (2006) Remote sensing digital image analysis, 4th edn. Springer, Berlin
Rish I, Grabarnik GY (2015) Sparse modeling: theory, algorithms, and applications. Chapman & Hall/CRC
Rubinstein R, Bruckstein AM, Elad M (2010) Dictionaries for sparse representation modeling. Proc IEEE 98(6):1045–1057. https://doi.org/10.1109/JPROC.2010.2040551
Sarkar R (2017) Dictionary learning and sparse representation for image analysis with application to segmentation, classification and event detection. Ph.D. Dissertation, University of Virginia
Turkmen AC (2015) A review of nonnegative matrix factorization methods for clustering. Allen Institute for Artificial Intelligence, 31 Aug 2015
Wang Y-X, Zhang Y-J (2013) Nonnegative matrix factorization: a comprehensive review. IEEE Trans Knowl Data Eng 25(6):1336–1353
Yang J, Yu K, Gong Y, Huang T (2009) Linear spatial pyramid matching using sparse coding for image classification. In IEEE conference on computer vision and pattern recognition, pp 1794–1801
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Hung, CC., Song, E., Lan, Y. (2019). Dimensionality Reduction and Sparse Representation. In: Image Texture Analysis. Springer, Cham. https://doi.org/10.1007/978-3-030-13773-1_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-13773-1_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-13772-4
Online ISBN: 978-3-030-13773-1
eBook Packages: Computer ScienceComputer Science (R0)