Question

Q1. In a digital classification process “training” a computer can be performed with supervised or unsupervised method.

(i) What then is “training”?

…………………………………………………………………………………………….

…………………………………………………………………………………………….

(ii) Maximum likelihood algorithm assumes that the bands of data have normal distributions. What is the objective of the assumption of normality in this algorithm?

………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

(iii) In maximum likelihood algorithm, about three parameters can be used to compute the statistical probability of a given pixel value being a member of a particular land cover category class. These are:

(i) ……………………………………………………….

(ii) ………………………………………………………

(iii) ………………………………………………………..

Q2. Kappa statistic is derived from the entire error matrix, which takes into consideration the off-diagonal elements.

(i)Write down the equation of the kappa.

(ii) Derive the relationship between the kappa, the overall accuracy and the expected accuracy.

(iii) Briefly state the strength of the kappa accuracy measure in relation to the overall accuracy.

Q3 (i) What is classification of remote sensing data?

……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….

(ii) How will you explain class variability?

………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………….......

(iii) Write down one feature which has less variance.

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(iv) Validating results in the classification involves (give two only)

(a) …………………………………………………………………………………………………

(b) …………………………………………………………………………………………………

(v) An error matrix is built by comparing the reference points to the classified points (in a c x c matrix). What is a reference data?

………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

(vi) Reference data may also be referred to as: …………………………………………………

Q4.

Confusion Matrix Table

A B C D Total User Accuracy

a 45 15 12 2

b 5 12 3 5

c 12 9 41 3

d 2 5 12 5

Total 64 41 68 15

Error of Omission

Producer Accuracy

The table above is a confusion matrix derived from a supervised classification.

(i) Complete the table (Total, user accuracy, error of omission and producer accuracy)

(ii) Calculate the overall accuracy of the classification.

(iii) Calculate the kappa of the classification.

Answer 1

Q1)

i.What is training then?

Answer

Given input/dataset you are training a model to predict the output.In training phase it undergoes learning.The code which is written makes the machine to learn how to fetch the numbers and select the best among them which is dominating while making decisions . In one word it's like growing a child.

ii.Maximum likelyhood algorithm assumes the bands of data have normal distributions.what is the objective of assumption of normality in this algorithm?

Answer

Maximum likelihood estimation depends on choosing an underlying statistical distribution from which the sample data should be drawn. That is, our expectation of what the data should look like depends in part on a statistical distribution that parameters that govern its shape. The most common parameters for distributions govern location (aka ‘expectation’, often the mean) and the scale (aka ‘’dispersion’, often variance). There are many different statistical distributions such as Gaussian (aka normal), Poisson, Gamma, and Beta. Crucially, probability distributions have parameter that define their shape and numerical properties.

In most of SEM, and regression for that matter, scientists often select the Gaussian distribution based on a belief that observed values tend to have a central tendency and symmetric dispersion around the tendency. Indeed, the central limit theorem posits that if a set of independent random variables is summed, the distribution approaches a normal distribution even if each variable is not Gaussian. Thus, if we imagine that the observed scores on a variable X reflect the summed contribution of many unknown latent processes, a Gaussian assumption on the resulting distribution is often quite principled and parsimonious.

Let’s focus on the univariate Gaussian distribution as a test case for thinking about parameter fitting and likelihood methods. A Gaussian distribution has a mean and standard deviation that define the location and scale, respectively, of the data it describes.

X∼N(μ,σ2)

where X is a random variable distributed as normal with mean μ and variance σ2

Normalizing data to have zero mean and unit standard deviation (subtracting the mean, then scaling by the inverse of the standard deviation) makes it possible to use the same tools on data that were originally very different. It’s frequently used as a preprocessing step in many algorithms.

iii.In maximum likelywood algorithm ,about 3 parameters can be used to compute the statstical probability of a given pixel value being a member of a particular land cover category class.These are:

Answer

Maximum likelihood classification assumes that the statistics for each class in each band are normally distributed and calculates the probability that a given pixel belongs to a specific class. Unless you select a probability threshold, all pixels are classified. Each pixel is assigned to the class that has the highest probability (that is, the maximum likelihood). If the highest probability is smaller than a threshold you specify, the pixel remains unclassified.

ENVI implements maximum likelihood classification by calculating the following discriminant functions for each pixel in the image (Richards, 1999):

where i=class

x = n-dimensional data (where n is the number of bands)

p(ω_i) = probability that class ω_i occurs in the image and is assumed the same for all classes

|Σ_i| = determinant of the covariance matrix of the data in class ω_i

Σ_i^-1 = its inverse matrix

m_i = mean vector