Slow Feature Analysis: A Theoretical Analysis of Optimal Free Responses

2003 ◽  
Vol 15 (9) ◽  
pp. 2147-2177 ◽  
Author(s):  
Laurenz Wiskott
Keyword(s):  
Simple Model ◽  
Theoretical Analysis ◽  
Visual System ◽  
Efficient Algorithm ◽  
Optimization Problem ◽  
Feature Analysis ◽  
Slow Feature Analysis ◽  
Input Signals ◽  
Invariant Representations ◽  
Simulation Results

Temporal slowness is a learning principle that allows learning of invariant representations by extracting slowly varying features from quickly varying input signals. Slow feature analysis (SFA) is an efficient algorithm based on this principle and has been applied to the learning of translation, scale, and other invariances in a simple model of the visual system. Here, a theoretical analysis of the optimization problem solved by SFA is presented, which provides a deeper understanding of the simulation results obtained in previous studies.

A Theory of Slow Feature Analysis for Transformation-Based Input Signals with an Application to Complex Cells

2011 ◽  
Vol 23 (2) ◽  
pp. 303-335 ◽  
Author(s):  
Henning Sprekeler ◽  
Laurenz Wiskott
Keyword(s):  
Frequency Tuning ◽  
Receptive Fields ◽  
Direction Selectivity ◽  
Feature Analysis ◽  
Translation Invariance ◽  
Complex Cells ◽  
Slow Feature Analysis ◽  
Input Signals ◽  
Good Agreement ◽  
Group Theoretical Analysis

We develop a group-theoretical analysis of slow feature analysis for the case where the input data are generated by applying a set of continuous transformations to static templates. As an application of the theory, we analytically derive nonlinear visual receptive fields and show that their optimal stimuli, as well as the orientation and frequency tuning, are in good agreement with previous simulations of complex cells in primary visual cortex (Berkes and Wiskott, 2005 ). The theory suggests that side and end stopping can be interpreted as a weak breaking of translation invariance. Direction selectivity is also discussed.

scholarly journals Slow Feature Analysis: Unsupervised Learning of Invariances

2002 ◽  
Vol 14 (4) ◽  
pp. 715-770 ◽  
Author(s):  
Laurenz Wiskott ◽  
Terrence J. Sejnowski
Keyword(s):  
Input Signal ◽  
Recognition Performance ◽  
Training Stimulus ◽  
Time Derivative ◽  
Optimal Solution ◽  
Principal Component ◽  
Feature Analysis ◽  
Slow Feature Analysis ◽  
Input Signals ◽  
Complex Features

Invariant features of temporally varying signals are useful for analysis and classification. Slow feature analysis (SFA) is a new method for learning invariant or slowly varying features from a vectorial input signal. It is based on a nonlinear expansion of the input signal and application of principal component analysis to this expanded signal and its time derivative. It is guaranteed to find the optimal solution within a family of functions directly and can learn to extract a large number of decor-related features, which are ordered by their degree of invariance. SFA can be applied hierarchically to process high-dimensional input signals and extract complex features. SFA is applied first to complex cell tuning properties based on simple cell output, including disparity and motion. Then more complicated input-output functions are learned by repeated application of SFA. Finally, a hierarchical network of SFA modules is presented as a simple model of the visual system. The same unstructured network can learn translation, size, rotation, contrast, or, to a lesser degree, illumination invariance for one-dimensional objects, depending on only the training stimulus. Surprisingly, only a few training objects suffice to achieve good generalization to new objects. The generated representation is suitable for object recognition. Performance degrades if the network is trained to learn multiple invariances simultaneously.

Exploiting the Homomorphic Property of Visual Cryptography

2017 ◽  
Vol 9 (2) ◽  
pp. 45-56 ◽  
Author(s):  
Xuehu Yan ◽  
Yuliang Lu ◽  
Lintao Liu ◽  
Song Wan ◽  
Wanmeng Ding ◽  
...  
Keyword(s):  
Cloud Computing ◽  
Signal Processing ◽  
Theoretical Analysis ◽  
Visual System ◽  
Human Visual System ◽  
Visual Cryptography ◽  
Secret Image ◽  
Simulation Results ◽  
Cryptographic Scheme

In this paper, homomorphic visual cryptographic scheme (HVCS) is proposed. The proposed HVCS inherits the good features of traditional VCS, such as, loss-tolerant (e.g., (k, n) threshold) and simply reconstructed method, where simply reconstructed method means that the decryption of the secret image is based on human visual system (HVS) without any cryptographic computation. In addition, the proposed HVCS can support signal processing in the encrypted domain (SPED), e.g., homomorphic operations and authentication, which can protect the user's privacy as well as improve the security in some applications, such as, cloud computing and so on. Both the theoretical analysis and simulation results demonstrate the effectiveness and security of the proposed HVCS.

scholarly journals Exploiting the Homomorphic Property of Visual Cryptography

Cryptography ◽  
2020 ◽  
pp. 416-427
Author(s):  
Xuehu Yan ◽  
Yuliang Lu ◽  
Lintao Liu ◽  
Song Wan ◽  
Wanmeng Ding ◽  
...  
Keyword(s):  
Cloud Computing ◽  
Signal Processing ◽  
Theoretical Analysis ◽  
Visual System ◽  
Human Visual System ◽  
Visual Cryptography ◽  
Secret Image ◽  
Simulation Results ◽  
Cryptographic Scheme

In this paper, homomorphic visual cryptographic scheme (HVCS) is proposed. The proposed HVCS inherits the good features of traditional VCS, such as, loss-tolerant (e.g., (k, n) threshold) and simply reconstructed method, where simply reconstructed method means that the decryption of the secret image is based on human visual system (HVS) without any cryptographic computation. In addition, the proposed HVCS can support signal processing in the encrypted domain (SPED), e.g., homomorphic operations and authentication, which can protect the user's privacy as well as improve the security in some applications, such as, cloud computing and so on. Both the theoretical analysis and simulation results demonstrate the effectiveness and security of the proposed HVCS.

scholarly journals An application of slow feature analysis to the genetic sequences of coronaviruses and influenza viruses

2021 ◽  
Vol 15 (1) ◽  
Author(s):  
Anastasios A. Tsonis ◽  
Geli Wang ◽  
Lvyi Zhang ◽  
Wenxu Lu ◽  
Aristotle Kayafas ◽  
...  
Keyword(s):  
Mathematical Method ◽  
Dna Sequence ◽  
Dna Sequences ◽  
Transmission Rate ◽  
Complex Structure ◽  
Mortality Rates ◽  
Influenza Viruses ◽  
Feature Analysis ◽  
Slow Feature Analysis ◽  
Genetic Sequences

Abstract Background Mathematical approaches have been for decades used to probe the structure of DNA sequences. This has led to the development of Bioinformatics. In this exploratory work, a novel mathematical method is applied to probe the DNA structure of two related viral families: those of coronaviruses and those of influenza viruses. The coronaviruses are SARS-CoV-2, SARS-CoV-1, and MERS. The influenza viruses include H1N1-1918, H1N1-2009, H2N2-1957, and H3N2-1968. Methods The mathematical method used is the slow feature analysis (SFA), a rather new but promising method to delineate complex structure in DNA sequences. Results The analysis indicates that the DNA sequences exhibit an elaborate and convoluted structure akin to complex networks. We define a measure of complexity and show that each DNA sequence exhibits a certain degree of complexity within itself, while at the same time there exists complex inter-relationships between the sequences within a family and between the two families. From these relationships, we find evidence, especially for the coronavirus family, that increasing complexity in a sequence is associated with higher transmission rate but with lower mortality. Conclusions The complexity measure defined here may hold a promise and could become a useful tool in the prediction of transmission and mortality rates in future new viral strains.

scholarly journals Latency-Optimal Computational Offloading Strategy for Sensitive Tasks in Smart Homes

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2347
Author(s):  
Yanyan Wang ◽  
Lin Wang ◽  
Ruijuan Zheng ◽  
Xuhui Zhao ◽  
Muhua Liu
Keyword(s):  
Queue Length ◽  
Optimization Problem ◽  
Time Slot ◽  
Smart Homes ◽  
Back Pressure ◽  
Smart Devices ◽  
Smart Device ◽  
Simulation Results ◽  
Computational Offloading ◽  
The Stability

In smart homes, the computational offloading technology of edge cloud computing (ECC) can effectively deal with the large amount of computation generated by smart devices. In this paper, we propose a computational offloading strategy for minimizing delay based on the back-pressure algorithm (BMDCO) to get the offloading decision and the number of tasks that can be offloaded. Specifically, we first construct a system with multiple local smart device task queues and multiple edge processor task queues. Then, we formulate an offloading strategy to minimize the queue length of tasks in each time slot by minimizing the Lyapunov drift optimization problem, so as to realize the stability of queues and improve the offloading performance. In addition, we give a theoretical analysis on the stability of the BMDCO algorithm by deducing the upper bound of all queues in this system. The simulation results show the stability of the proposed algorithm, and demonstrate that the BMDCO algorithm is superior to other alternatives. Compared with other algorithms, this algorithm can effectively reduce the computation delay.

scholarly journals Current-Mode Third-Order Quadrature Oscillator Using CDTAs

2009 ◽  
Vol 2009 ◽  
pp. 1-5 ◽  
Author(s):  
Jiun-Wei Horng
Keyword(s):  
Theoretical Analysis ◽  
Phase Difference ◽  
Oscillation Frequency ◽  
Current Mode ◽  
Third Order ◽  
Quadrature Oscillator ◽  
Oscillation Condition ◽  
Transconductance Amplifiers ◽  
Simulation Results ◽  
A Current

This paper describes a current-mode third-order quadrature oscillator based on current differencing transconductance amplifiers (CDTAs). Outputs of two current-mode sinusoids with90°phase difference are available in the quadrature oscillator circuit. The oscillation condition and oscillation frequency are orthogonal controllable. The proposed circuit employs only grounded capacitors and is ideal for integration. Simulation results are included to confirm the theoretical analysis.

Structure-Aware Slow Feature Analysis for Age Estimation

2016 ◽  
Vol 23 (12) ◽  
pp. 1702-1706 ◽  
Author(s):  
Zhouzhou He ◽  
Xi Li ◽  
Zhongfei Zhang ◽  
Yaqing Zhang ◽  
Jun Xiao ◽  
...  
Keyword(s):  
Age Estimation ◽  
Feature Analysis ◽  
Slow Feature Analysis
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