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Ordinal Level of Measurement00:55

Ordinal Level of Measurement

23.7K
The way a set of data is measured is called its level of measurement. Correct statistical procedures depend on a researcher being familiar with levels of measurement. For analysis, data are classified into four levels of measurement—nominal, ordinal, interval, and ratio.
Data measured using an ordinal scale are similar to nominal scale data, but there is one major difference. The ordinal scale data can be ordered. An example of ordinal scale data is a list of the top five national parks...
23.7K
Classification of Systems-II01:31

Classification of Systems-II

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Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
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Aggregates Classification01:29

Aggregates Classification

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Aggregate classification is generally based on its size, petrographic characteristics, weight, and source. Size classification ranges from coarse to fine aggregates, defined by the size of the particles. Coarse aggregates are particles that do not pass through ASTM sieve No. 4, and aggregates that pass through the sieve are fine aggregates.
Petrographic classification groups aggregates based on common mineralogical characteristics. Some of the common mineral groups found in aggregates are...
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Classification of Systems-I01:26

Classification of Systems-I

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Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
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How Data are Classified: Categorical Data01:11

How Data are Classified: Categorical Data

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A variable, usually notated by capital letters such as X and Y, is a characteristic or measurement that can be determined for each member of a population. Data are the actual values of variables. They may be numbers, or they may be words. Datum is a single value.
Data are classified based on whether they are measurable or not. Categorical data cannot be measured; instead, it can be divided into categories. For example, if Y denotes a person's party affiliation, some examples of Y include...
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Force Classification01:22

Force Classification

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Forces play a crucial role in the study of physics and engineering. They are essential in describing the motion, behavior, and equilibrium of objects in the physical world. Forces can be classified based on their origin, type, and direction of action.
Contact and non-contact forces are two of the most widely used categories of forces. As the name suggests, contact forces require physical contact between two objects to act upon each other. Examples of contact forces include frictional,...
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Related Experiment Video

Updated: Jul 3, 2025

Author Spotlight: Enhancement of Salient Object Detection for Smart Grid Applications
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Learning Ordinal-Hierarchical Constraints for Deep Learning Classifiers.

Riccardo Rosati, Luca Romeo, Victor Manuel Vargas

    IEEE Transactions on Neural Networks and Learning Systems
    |February 13, 2024
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces novel deep learning (DL) models, the hierarchical cumulative link model (HCLM) and hierarchical-ordinal binary decomposition (HOBD), to address complex classification tasks with hierarchical and ordinal structures, improving generalization performance.

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    Area of Science:

    • Machine Learning
    • Artificial Intelligence
    • Data Science

    Background:

    • Real-world classification often involves categories with inherent hierarchical and ordinal relationships.
    • Existing deep learning (DL) models struggle to simultaneously capture these hierarchical and ordinal constraints, limiting generalization performance.

    Purpose of the Study:

    • To propose novel DL methodologies that effectively model both hierarchical and ordinal structures in classification.
    • To enhance generalization performance in complex classification problems by integrating these constraints.

    Main Methods:

    • Introduced two new ordinal-hierarchical DL methodologies: hierarchical cumulative link model (HCLM) and hierarchical-ordinal binary decomposition (HOBD).
    • Decomposed the problem into local and global graph paths to encode ordinal constraints at each hierarchical level.
    • Framed the problem as minimizing combined global and local losses, utilizing ordinal binary decomposition (OBD) and cumulative link model (CLM) for constraint setting.

    Main Results:

    • The proposed HCLM and HOBD models demonstrated statistically significant improvements over state-of-the-art methods.
    • Effectiveness was validated across diverse real-world datasets from industrial, biomedical, computer vision, and financial domains.
    • The models successfully captured and leveraged both hierarchical and ordinal label structures.

    Conclusions:

    • The novel ordinal-hierarchical DL approaches offer a significant advancement for classification tasks with complex label structures.
    • These methodologies provide a robust framework for improving generalization in real-world applications across various scientific and industrial fields.