# Pattern Recognition Winter 2022 GTU Paper Solution | 3171613

Here, We provide Pattern Recognition GTU Paper Solution Winter 2022. Read the Full PR GTU paper solution given below.

Pattern Recognition GTU Old Paper Winter 2022 [Marks : 70] : Click Here

(a) Define the term: “Auto-correlation”.

Autocorrelation is a statistical method used to measure the degree of similarity between a time series and a lagged version of itself over successive time intervals. In simpler terms, it refers to the correlation of a signal with itself, where the signal is delayed by a certain time lag. The degree of correlation between the signal and its delayed version at different time lags can reveal underlying patterns and trends in the data. It is a common method used in time series analysis and signal processing.

(b) What is meant by “dimensionality reduction” of attributes? Explain its
significance.

(c) What is a “pattern”? Briefly discuss applications of Pattern Recognition.

(a) Explain “Maximum a Posteriori” estimation with respect to Bayes’
theorem.

Maximum a Posteriori (MAP) estimation is a method used in Bayesian inference to estimate the most probable value of a parameter given some data. It is based on Bayes’ theorem, which describes the relationship between the conditional probabilities of two events:

P(A|B) = P(B|A) * P(A) / P(B)

where A and B are two events, and P(A|B) is the probability of event A given that event B has occurred. In the context of MAP estimation, A represents the parameter to be estimated and B represents the observed data.

MAP estimation involves finding the value of the parameter that maximizes the posterior probability distribution P(A|B). This is equivalent to finding the mode of the distribution, which represents the most probable value of the parameter given the data. Mathematically, this can be expressed as:

A_MAP = argmax P(A|B) = argmax P(B|A) * P(A)

where argmax is the value of A that maximizes the expression.

The term P(B|A) is the likelihood function, which describes the probability of observing the data given a particular value of the parameter. The term P(A) is the prior probability distribution, which represents our prior knowledge or beliefs about the parameter before observing the data. The term P(B) is the evidence, which is a normalization constant that ensures that the posterior probability distribution integrates to one.

MAP estimation is commonly used in various fields, including machine learning, signal processing, and image analysis. It can be used for tasks such as parameter estimation, classification, and denoising. One advantage of MAP estimation over other estimation methods is that it allows us to incorporate prior knowledge or beliefs about the parameter into the estimation process, which can improve the accuracy of the estimates.

(b) Find the eigenvalues and corresponding eigenvectors for the matrix A =
[2 2]
[5 −1].

(c) Explain the Principal Component Analysis method for dimensionality
reduction. What are the advantages of this method?

(c) With the help of suitable example explain the ‘k-means’ clustering
algorithm. What are the limitations of this algorithm?

(a) Explain Minimum-error-rate classification in brief.

Minimum-error-rate classification is a type of classification algorithm used in machine learning and pattern recognition to classify data into different categories or classes. The goal of the algorithm is to minimize the probability of classification errors, which is achieved by choosing a decision rule that minimizes the overall probability of misclassification.

The minimum-error-rate classification algorithm uses a probabilistic approach to classify data, where each data point is assigned a probability of belonging to a particular class. The algorithm then compares these probabilities and assigns the data point to the class with the highest probability.

To determine the decision rule that minimizes the probability of misclassification, the algorithm uses a cost matrix that specifies the cost of classifying a data point into each possible class. The cost matrix is used to calculate the expected cost of misclassification for each decision rule, and the decision rule with the lowest expected cost is chosen as the optimal decision rule.

In summary, minimum-error-rate classification is a probabilistic approach to classification that aims to minimize the probability of classification errors by choosing a decision rule that minimizes the expected cost of misclassification.

(b) Give differences between supervised and unsupervised learning.

(c) Write a short note on Hierarchical clustering.

OR

(a) Define the term: “stationary process”.

A stationary process is a stochastic process whose statistical properties such as the mean, variance, and autocorrelation remain constant over time. In other words, the distribution of the process remains the same over time. A stationary process is often considered as a key assumption in many time-series analysis techniques. The strict stationary process requires that the joint distribution of any set of observations is independent of the starting time. A less strict version of a stationary process is a weakly stationary process, which requires the first two moments (mean and variance) to be constant over time and the autocovariance function to depend only on the time lag between observations.

(b) Explain main characteristics of Fisher’s linear discriminant analysis.

(c) Enlist and explain any two criterion functions for clustering.

(a) With the help of a diagram explain the working of a Perceptron.

The perceptron is a type of neural network used for classification tasks. It takes a set of inputs, processes them, and produces an output. A single perceptron can be used for binary classification tasks where the input belongs to one of two classes.

The perceptron has multiple inputs, each input is associated with a weight, and the output is a binary value based on the weighted sum of the inputs. The weights and bias are updated during the training process to minimize the error in classification. The following diagram illustrates the working of a perceptron:

``````      Input Layer       Weights
+-----------+    +-------+
|  Input 1  |----| W1    |
+-----------+    |       |
|  Input 2  |----| W2    |
+-----------+    |       |
|     .     |    |   .   |
+-----------+    |   .   |
|     .     |    |   .   |
+-----------+    |       |
|  Input n  |----| Wn    |
+-----------+    +-------+
|
v
Weighted Sum
+-------+
|       |
|       |
|  ∑ xi wi + b |
|       |
|       |
+-------+
|
v
Output
+-------+
|       |
|       |
|    1   | if ∑ xi wi + b > 0
|       |
|    0   | if ∑ xi wi + b <= 0
|       |
+-------+
``````

Here, the input layer consists of n inputs, each input is multiplied with its corresponding weight, and the sum of these weighted inputs is added to the bias. If the weighted sum is greater than zero, then the output is 1, otherwise, the output is 0.

During the training process, the weights and bias are updated using the error between the predicted output and the actual output. This is done by minimizing the error function using gradient descent or other optimization techniques.

The perceptron is limited to linearly separable problems and may not work well for non-linear problems. Also, it can only classify inputs into two classes. To classify inputs into more than two classes, multiple perceptrons can be used in a multi-layer perceptron (MLP) architecture.

(b) Explain the Expectation-Maximization method for parameter
estimation.

(c) With the help of a neat diagram, discuss the topology of a multi-layer
feedforward neural network.

OR

(a) Define the following terms with respect to classification:
(i) training set (ii) testing set

(i) Training set: A training set is a subset of a dataset used to train a machine learning model. It is a collection of input-output pairs used to train the model. The model learns from the training set by adjusting its parameters to minimize the error between its predicted output and the actual output.

(ii) Testing set: A testing set is a subset of a dataset used to evaluate the performance of a trained machine learning model. It is a collection of input-output pairs that were not used during the training phase. The model is tested on the testing set to check how well it generalizes to new, unseen data. The performance of the model on the testing set is used to estimate its accuracy or error rate.

(b) Explain classification using Support Vector Machines.

(c) Write a short note on dictionary learning methods.

(a) What is k-NN learning?

k-NN (k-Nearest Neighbors) is a machine learning algorithm used for classification and regression analysis. It is a non-parametric method that stores all available cases and classifies new cases based on a similarity measure (e.g., distance functions). In k-NN, the “k” refers to the number of nearest neighbors that are considered when predicting the class of a new data point.

For example, suppose we have a set of labeled data points (also called a training set) that belong to two classes, A and B. When we get a new unlabeled data point, we can use k-NN to predict its class based on the classes of the k nearest labeled data points to the new data point. The class with the majority vote among the k neighbors is assigned to the new data point.

The value of k in k-NN is typically chosen by cross-validation, i.e., by splitting the training set into multiple folds and testing the performance of the algorithm for different values of k. One of the advantages of k-NN is that it does not assume any underlying distribution of the data and can be used for both binary and multi-class classification problems.

(b) When does a Decision Tree require pruning? How can pruning be done?

(c) Write a short note on Hidden Markov models.

OR

(a) Explain “gradient descent” using a suitable analogy.

Gradient descent is an optimization algorithm used to find the minimum of a function. It works by starting at a random point on the function and iteratively taking steps in the direction of steepest descent until it reaches the minimum.

An analogy to understand gradient descent is climbing down a mountain. Imagine you are standing on top of a mountain and your goal is to reach the bottom. You have no idea which direction to go in, so you take a step in a random direction. You then look around and see which direction is steepest downhill, and take a step in that direction. You repeat this process, taking steps in the direction of steepest descent, until you reach the bottom of the mountain.

In the same way, gradient descent starts at a random point on a function and calculates the gradient (or slope) of the function at that point. It then takes a step in the direction of steepest descent (i.e., the negative of the gradient) and repeats this process, iteratively moving towards the minimum of the function.

(b) Write a short note on Convolutional Neural Networks.

(c) Discuss Decision Tree learning based on the CART approach.

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