Search results for "Subspace topology"

Boosting Hankel matrices for face emotion recognition and pain detection

2017

HighligthsDynamics of face expression descriptors are modeled for emotion recognition.A set of Hankel matrices is built upon several multi-scale face representations.Boosting and random subspace projection are used for dynamics selection.Dynamics of Haar-like features and Gabor Energies are compared.Fine-grained dynamics of subtle expressions can be modeled at small spatial scales. Studies in psychology have shown that the dynamics of emotional expressions play an important role in face emotion recognition in humans. Motivated by these studies, in this paper the dynamics of face expressions are modeled and used for automatic emotion recognition and pain detection.Given a temporal sequence o…

A subspace based fault diagnose method and its application on mechatronics systems

2014

The mechatronics systems are widely used in modern society. This paper presents a novel data-driven scheme which can be used for fault diagnose of mechatronics systems. The proposed method is based on the subspace identification of parity vector. By constructing the output observer, critical variables can be acquired by soft sensors. This makes the fault diagnoses free from the limitation of online measurement. A diagnose observer is designed directly from the parity vector. Finally, the proposed scheme is tested by the Simulink benchmark of vehicle suspension and shows its good performance.

Fast Graph Filters for Decentralized Subspace Projection

2020

A number of inference problems with sensor networks involve projecting a measured signal onto a given subspace. In existing decentralized approaches, sensors communicate with their local neighbors to obtain a sequence of iterates that asymptotically converges to the desired projection. In contrast, the present paper develops methods that produce these projections in a finite and approximately minimal number of iterations. Building upon tools from graph signal processing, the problem is cast as the design of a graph filter which, in turn, is reduced to the design of a suitable graph shift operator. Exploiting the eigenstructure of the projection and shift matrices leads to an objective whose…

Asymptotic and bootstrap tests for subspace dimension

2022

Most linear dimension reduction methods proposed in the literature can be formulated using an appropriate pair of scatter matrices, see e.g. Ye and Weiss (2003), Tyler et al. (2009), Bura and Yang (2011), Liski et al. (2014) and Luo and Li (2016). The eigen-decomposition of one scatter matrix with respect to another is then often used to determine the dimension of the signal subspace and to separate signal and noise parts of the data. Three popular dimension reduction methods, namely principal component analysis (PCA), fourth order blind identification (FOBI) and sliced inverse regression (SIR) are considered in detail and the first two moments of subsets of the eigenvalues are used to test…

Fast Distributed Subspace Projection via Graph Filters

2018

A significant number of linear inference problems in wireless sensor networks can be solved by projecting the observed signal onto a given subspace. Decentralized approaches avoid the need for performing such an operation at a central processor, thereby reducing congestion and increasing the robustness and the scalability of the network. Unfortunately, existing decentralized approaches either confine themselves to a reduced family of subspace projection tasks or need an infinite number of iterations to obtain the exact projection. To remedy these limitations, this paper develops a framework for computing a wide class of subspace projections in a decentralized fashion by relying on the notio…

Quantum systems with fractal spectra

2002

Abstract We study Hamiltonians with singular spectra of Cantor type with a constant ratio of dissection and show strict connections between the decay properties of the states in the singular subspace and the algebraic number theory. More specifically, we study the decay properties of free n-particle systems and the computability of decaying and non-decaying states in the singular continuous subspace.

Concurrent and Distributed Projection through Local Interference for Wireless Sensor Networks

2012

In this paper we use a gossip algorithm to obtain the projection of the observed signal into a subspace of lower dimension. Gossip algorithms allow distributed, fast and efficient computations on a Wireless Sensor Network and they can be properly modified to evaluate the sought projection. By combining computation coding with gossip algorithms we proposed a novel strategy that leads to important saving on convergence time as well as exponentially decreasing energy consumption, as the size of the network increases.

2014

This paper deals with designing the controller of LTI system based on data-driven techniques. We propose a scheme embedding a residual generator into control loop based on realization of the Youla parameterization for advanced controller design. Basic idea of the proposed scheme is constructing the residual generator by using the solution of the Luenberger equations as well as the well-established relationship between diagnosis observer (DO) and the parity vector. Besides, the core of the above idea is straightly using the process measurements to obtain the parity space based on the Subspace Identification Method (SIM), rather than establishing the system model. At last, a simulation based …

Fast Decentralized Linear Functions via Successive Graph Shift Operators

2019

Decentralized signal processing performs learning tasks on data distributed over a multi-node network which can be represented by a graph. Implementing linear transformations emerges as a key task in a number of applications of decentralized signal processing. Recently, some decentralized methods have been proposed to accomplish that task by leveraging the notion of graph shift operator, which captures the local structure of the graph. However, existing approaches have some drawbacks such as considering special instances of linear transformations, or reducing the family of transformations by assuming that a shift matrix is given such that a subset of its eigenvectors spans the subspace of i…

Description of the retention behaviour of solutes in micellar liquid chromatography with organic modifiers: Comparison of two methods

1995

Two methods for the description of the retention behaviour of solutes in micellar liquid chromatography are compared. One of them divides the parameter space into triangular subspaces, fitting a different equation in each subspace. The second method makes use of a unique equation, valid in the whole parameter space. In both cases, equations of the type log k=f (μ, ϕ), and 1/k=f (μ, ϕ), (μ and ϕ are the concentration of surfactant and alcohol, respectively), were used to describe the retention. The use of the hyperbolic function, 1/k=c0+c1μ+c3μϕ, to describe the whole parameter space yielded the best prediction. When a small portion of the parameter space was modelled, a simpler hyperbolic f…