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Related Concept Videos

State Space Representation01:27

State Space Representation

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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
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Discrete Fourier Transform01:15

Discrete Fourier Transform

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The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
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Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

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The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
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Linear time-invariant Systems01:23

Linear time-invariant Systems

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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
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Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

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Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
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Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

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It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
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Cross-Modal Multivariate Pattern Analysis
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Dynamic Autoregressive Tensor Factorization for Pattern Discovery of Spatiotemporal Systems.

Xinyu Chen, Dingyi Zhuang, HanQin Cai

    IEEE Transactions on Pattern Analysis and Machine Intelligence
    |June 4, 2025
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces dynamic autoregressive tensor factorization, an unsupervised machine learning framework for uncovering patterns in complex spatiotemporal systems. The method effectively reveals time-varying spatial and temporal insights from diverse real-world data.

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    Area of Science:

    • Data Science
    • Machine Learning
    • Complex Systems Analysis

    Background:

    • Spatiotemporal systems are prevalent across scientific disciplines, holding crucial data patterns.
    • Characterizing these systems using data-driven machine learning presents a fundamental challenge.
    • Existing methods may not fully capture the dynamic and multidimensional nature of spatiotemporal data.

    Purpose of the Study:

    • To introduce an unsupervised pattern discovery framework for spatiotemporal systems.
    • To enable the characterization of time-varying autoregression in multivariate and multidimensional data.
    • To discover interpretable spatial and temporal modes/patterns from complex datasets.

    Main Methods:

    • Developed dynamic autoregressive tensor factorization, an unsupervised machine learning framework.
    • Integrated tensor factorization with time-varying autoregression for pattern discovery.
    • Assumed an orthogonal spatial factor matrix for efficient modeling.

    Main Results:

    • Applied the framework to fluid dynamics, international trade, and urban mobility datasets.
    • Identified interpretable import/export patterns in international trade data.
    • Detected shifts in urban human mobility patterns between 2019 and 2022 using ridesharing data.

    Conclusions:

    • The dynamic autoregressive tensor factorization framework effectively discovers meaningful patterns in spatiotemporal systems.
    • The discovered patterns are both time-varying and multidimensional, offering significant insights.
    • The framework demonstrates versatility across various scientific domains and data types.