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Uncertainty: Overview

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

Classification of Systems-I

Classification of Systems-I

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:

Classification of Systems-II

Classification of Systems-II

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,

Force Classification

Force Classification

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,...

Uncertainty: Confidence Intervals

Uncertainty: Confidence Intervals

The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...

Classification of Signals

Classification of Signals

In signal processing, signals are classified based on various characteristics: continuous-time versus discrete-time, periodic versus aperiodic, analog versus digital, and causal versus noncausal. Each category highlights distinct properties crucial for understanding and manipulating signals.
A continuous-time signal holds a value at every instant in time, representing information seamlessly. In contrast, a discrete-time signal holds values only at specific moments, often denoted as x(n), where...

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Related Experiment Video

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Deep Neural Networks for Image-Based Dietary Assessment

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Published on: March 13, 2021

Uncertainty Assessment of Hyperspectral Image Classification: Deep Learning vs. Random Forest.

Majid Shadman Roodposhti¹, Jagannath Aryal¹, Arko Lucieer¹

¹Discipline of Geography and Spatial Sciences, School of Technology, Environments and Design, University of Tasmania, Hobart 7018, Australia.

Entropy (Basel, Switzerland)

|December 3, 2020

Summary

This summary is machine-generated.

This study introduces novel uncertainty assessment techniques for hyperspectral image classification, outperforming traditional methods. Deep neural networks (DNNs) with Shannon entropy provide superior pixel-level accuracy estimates compared to random forests (RF).

Keywords:

Shannon entropy deep neural network random forest uncertainty assessment

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Area of Science:

Remote Sensing
Geospatial Data Analysis
Machine Learning for Earth Observation

Background:

Traditional accuracy assessment for image classification relies on confusion matrices and test data, failing to capture spatial error variations.
Existing methods are limited by test data availability and cannot spatially characterize classification accuracy before validation.
Assessing error propagation within classified imagery products is crucial for reliable geospatial data.

Purpose of the Study:

To apply and compare two novel uncertainty assessment techniques for hyperspectral image classification.
To evaluate techniques that do not require test data and enable spatial characterization of classification accuracy.
To compare the performance of deep neural networks (DNNs) against random forest (RF) using these uncertainty measures.

Main Methods:

Implemented Shannon entropy calculation on class probabilities predicted by DNN and RF for each pixel.
Quantified classification uncertainties for DNN and RF on the Salinas and Indian Pines hyperspectral datasets.
Compared derived uncertainty estimates against classification accuracy using a modified root mean square error (RMSE).

Main Results:

The Shannon entropy-based uncertainty assessment effectively characterizes spatial classification accuracy without test data.
Deep neural networks (DNNs) demonstrated superior performance in estimating classification accuracy compared to random forests (RF).
Pixel-level uncertainty derived from DNNs using Shannon entropy proved to be a better indicator of classification accuracy.

Conclusions:

Emerging deep neural networks (DNNs) offer enhanced capabilities for accurate hyperspectral image classification.
Shannon entropy is a robust metric for pixel-level uncertainty estimation in image classification.
The proposed uncertainty assessment methods improve the reliability and spatial understanding of classification accuracy in remote sensing.