Cropping is a fundamental image data augmentation technique used to artificially increase the size of a training dataset. By taking multiple random crops from a single source image, a data scientist can generate numerous new, slightly different training samples. This process not only expands the dataset but also helps the model improve its robustness and generalizability by learning to recognize objects in various positions and scales within the frame. This is particularly effective when the initial dataset is limited in size.

A. Clipping is a normalization process that limits pixel intensity values to a predefined range (e.g., 0-255); it does not create new training samples.

C. Masking involves obscuring parts of an image to train a model to handle occlusions, which modifies an image but does not typically generate new, distinct samples to increase dataset size.

D. Scaling resizes an entire image. While it can be used in an augmentation pipeline, it modifies the existing sample rather than creating new, unique samples from subsections of the original.

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1. Shorten

C.

& Khoshgoftaar

T. M. (2019). A survey on Image Data Augmentation for Deep Learning. Journal of Big Data

6(1)

60. In Section 3.1

"Geometric transformations

" the paper explicitly discusses cropping as a common data augmentation method where a section of the original image is taken to create a new sample. DOI: https://doi.org/10.1186/s40537-019-0197-0

2. Stanford University. (n.d.). CS231n: Convolutional Neural Networks for Visual Recognition

Course Notes

Data Augmentation. Stanford Computer Science. Retrieved from https://cs231n.github.io/transfer-learning/. The section on Data Augmentation details the practice of resizing an image and then taking random crops to generate multiple training examples from one image.

3. TensorFlow Authors. (n.d.). Core > Guides > Keras > Data augmentation. TensorFlow Official Documentation. Retrieved from https://www.tensorflow.org/tutorials/images/dataaugmentation. The official documentation provides code examples and explanations for using random cropping (tf.image.randomcrop) as a primary technique to augment an image dataset.

The primary requirement is to use a clustering algorithm that does not need the number of clusters to be specified in advance. DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is a density-based algorithm that groups together points that are closely packed, marking as outliers points that lie alone in low-density regions. A key advantage of DBSCAN is that it automatically determines the number of clusters based on the data's density and connectivity, making it ideal for scenarios where the cluster count is unknown.

B. k-nearest neighbors: This is a supervised learning algorithm for classification and regression, not an unsupervised clustering method.

C. k-means: This is a popular clustering algorithm, but it explicitly requires the user to pre-specify the number of clusters ('k') as an input parameter.

D. Logistic regression: This is a supervised classification algorithm used to predict a categorical dependent variable; it does not perform clustering.

1. Ester

M.

Kriegel

H. P.

Sander

J.

& Xu

X. (1996). A density-based algorithm for discovering clusters in large spatial databases with noise. In Proceedings of the Second International Conference on Knowledge Discovery and Data Mining (KDD'96). AAAI Press

pp. 226–231. The paper introduces DBSCAN and states in its abstract

"The proposed algorithm DBSCAN is designed to discover the clusters and the noise in a spatial database... it does not require the number of clusters as input."

2. Scikit-learn Developers. (2023). 2.3. Clustering - 2.3.7. DBSCAN. Scikit-learn 1.3.2 documentation. In the overview of the algorithm

the documentation notes

"In contrast to k-means

DBSCAN does not require the number of clusters to be specified in advance."

3. Leskovec

J.

Rajaraman

A.

& Ullman

J. D. (2020). Mining of Massive Datasets. Cambridge University Press. In Chapter 7

"Clustering

" Section 7.4

the authors describe DBSCAN as a method that can find non-spherical clusters and does not require the number of clusters to be known beforehand

contrasting it with methods like k-means. DOI: https://doi.org/10.1017/9781108684160

A greedy algorithm is an algorithmic paradigm that builds up a solution piece by piece, always choosing the next piece that offers the most obvious and immediate benefit. This approach makes the choice that seems best at the current moment—the "locally optimal" choice—without regard for future consequences. In machine learning, this is seen in algorithms like decision tree induction (e.g., ID3, C4.5), where at each node, the algorithm greedily selects the feature split that provides the highest information gain at that step, hoping this series of local optima leads to a good overall tree.

A. This describes Bayesian inference or online learning, where a model's parameters are updated sequentially as new data arrives.

B. This describes an exhaustive or brute-force search, which is computationally expensive and the opposite of a greedy strategy's efficiency.

C. This refers to parametric models, a classification of statistical models, not an algorithmic strategy like the greedy approach.

1. Cormen

T. H.

Leiserson

C. E.

Rivest

R. L.

& Stein

C. (2009). Introduction to Algorithms (3rd ed.). MIT Press. In Chapter 16

"Greedy Algorithms

" the introduction states

"A greedy algorithm always makes the choice that looks best at the moment... It makes a locally optimal choice in the hope that this choice will lead to a globally optimal solution." (p. 414).

2. Demaine

E. & Devadas

S. (2011). 6.006 Introduction to Algorithms

Fall 2011. Massachusetts Institute of Technology: MIT OpenCourseWare. Lecture 16 notes define the strategy: "A greedy algorithm builds a solution step-by-step

and at each step

it makes a 'locally optimal' choice." (URL: https://ocw.mit.edu/courses/6-006-introduction-to-algorithms-fall-2011/pages/lecture-notes/

Lecture 16: Greedy Algorithms).

3. Roughgarden

T. (n.d.). CS161: Design and Analysis of Algorithms

Lecture #13: Greedy Algorithms. Stanford University. The lecture notes state

"A greedy algorithm is one that

in a series of steps

always makes the choice that is locally optimal." (p. 1).

The most fundamental architecture for an artificial neural network (ANN) that can learn non-linear patterns is the Multi-Layer Perceptron (MLP). This structure minimally consists of three types of layers. The input layer receives the raw data or features. At least one hidden layer processes the inputs through a series of weighted connections and activation functions, enabling the network to learn complex relationships. Finally, the output layer produces the final prediction or classification. This input-hidden-output sequence forms the simplest complete feedforward neural network.

A: Pooling layers are specialized components used for down-sampling, primarily in Convolutional Neural Networks (CNNs), and are not a fundamental requirement for a basic ANN.

B: Convolutional layers are also specialized, designed for feature extraction from grid-like data (e.g., images), and are not part of a minimal, general-purpose ANN.

D: A dropout layer is a regularization technique to prevent overfitting, not a core computational layer. This option also critically omits the essential output layer.

1. Goodfellow

I.

Bengio

Y.

& Courville

A. (2016). Deep Learning. MIT Press. In Chapter 6

"Deep Feedforward Networks

" Section 6.1 describes the basic model as consisting of an input layer

one or more hidden layers

and an output layer. The simplest non-trivial example shown requires all three.

2. Nielsen

M. A. (2015). Neural Networks and Deep Learning. Determination Press. Chapter 1

"Using neural nets to recognize handwritten digits

" introduces the standard network architecture: "The leftmost layer... is called the input layer... The rightmost or output layer... The middle layer is called a hidden layer."

3. Stanford University. (n.d.). CS231n: Convolutional Neural Networks for Visual Recognition - Module 1: Neural Networks Part 1: Setting up the Architecture. The course notes define a "2-layer Neural Network" as having one hidden layer

which implies the full structure of an input layer

one hidden layer

and an output layer.

Principal Component Analysis (PCA) is a fundamental unsupervised learning technique used for dimensionality reduction. Its primary goal is to transform a high-dimensional dataset into a lower-dimensional space by identifying a new set of orthogonal axes, known as principal components. These components are ordered such that the first few retain most of the variation present in the original data. By discarding the components that capture the least variance, PCA reduces the number of features while minimizing information loss. This is invaluable for data visualization, noise filtering, and improving the efficiency of subsequent machine learning models.

B. Classification is a supervised learning task for predicting categorical labels; PCA is an unsupervised transformation technique, not a predictive model.

C. Regression is a supervised learning task for predicting continuous numerical values, which is not the direct purpose of PCA.

D. While PCA can be a preprocessing step in some recommendation systems, its core function is data reduction, not the recommendation logic itself.

1. Ng

A. (n.d.). CS229 Lecture Notes: Principal Component Analysis. Stanford University. Retrieved from http://cs229.stanford.edu/notes/cs229-notes10.pdf. In Section 1

"Application 1: Dimensionality reduction" (p. 2)

the notes explicitly state

"By far the most common application of PCA is for dimensionality reduction."

2. Shlens

J. (2014). A Tutorial on Principal Component Analysis. arXiv:1404.1100 [cs.LG]. In the Abstract (p. 1)

the author states

"Principal component analysis (PCA) is a mainstay of modern data analysis - a black box that is widely used but poorly understood. The goal of this paper is to dispel the magic behind this black box. This manuscript focuses on building a solid intuition for how and why principal component analysis works. This is accomplished by forging connections between the underlying statistics and geometry of PCA. This tutorial avoids the use of heavy mathematical notation and instead focuses on building a visual

intuitive framework for what PCA is actually doing. With minimal additional effort

PCA provides a roadmap for how to reduce a complex data set to a lower dimension to reveal the sometimes hidden

simplified dynamics that often underlie it."

3. Scikit-learn Developers. (n.d.). 2.5. Decomposing signals in components (matrix factorization problems). Scikit-learn 1.4.2 documentation. In Section 2.5.1

"Principal component analysis (PCA)

" the documentation introduces PCA as a method to "...decompose a multivariate dataset in a set of successive orthogonal components that explain a maximum amount of the variance." This decomposition is the basis for its use in dimensionality reduction.