Dimensionality Reduction Ai | AI Final Year Project Report

Complete Technical Paper Content — Dimensionality Reduction Ai

1. Executive Abstract, Problem Formulation & Background

In the field of artificial intelligence (AI), a hallucination or artificial hallucination (also called bullshitting, confabulation, delusion, or mirage) is a response generated by AI that contains false or misleading information presented as fact. These terms draw a loose analogy with human psychology, where a hallucination typically involves false percepts. Chatbots powered by large language models (LLMs), like ChatGPT, may embed plausible-sounding random falsehoods within their generated content, such as fabricated citations. Detecting and mitigating errors and hallucinations pose significant challenges for practical deployment and reliability of LLMs in high-stakes scenarios, such as chip design, supply chain logistics, and medical diagnostics. Some software engineers and statisticians have criticized the specific term "AI hallucination" for unreasonably anthropomorphizing computers. Symbolic artificial intelligence models generally do not produce hallucinations, unlike large language models.

Uses, definitions and characterizations of the term hallucination in the context of LLMs include:

"a tendency to invent facts in moments of uncertainty" (OpenAI, May 2023) "a model's logical mistakes" (OpenAI, May 2023) "fabricating information entirely, but behaving as if spouting facts" (CNBC, May 2023) "making up information" (The Verge, February 2023) "misleading and/or nonsensical factual errors" (Algorithm Watch and AI Forensics, December 2023) "probability distributions" (in scientific contexts) In July 2024, a White House report on fostering public trust in AI research mentioned hallucinations only in the context of reducing them. Notably, when acknowledging David Baker's Nobel Prize-winning work with AI-generated proteins, the Nobel committee avoided it entirely, instead referring to "imaginative protein creation". Hicks, Humphries, and Slater, in their article in Ethics and Information Technology, argue that the output of LLMs is bullshit under Harry Frankfurt's definition, and that the models are "in an important way indifferent to the truth of their outputs", with true statements only accidentally true, and false ones accidentally false. Some researchers also call the uncritical use of AI botshit. The term mirage has been proposed as an alternative to the use of hallucination, framing false or misleading responses as predictable results of LLM data processing created by both AI training datasets and the rules engineered into the LLM rather than a mental breaking from reality. This shift in language aims to increase AI literacy by using terminology that avoids anthropomorphic implications that LLMs have conscious minds with their own intent, shows that untrue outputs come from patterns in training data, and indicates that outputs are novel syntheses of training data requiring critical human judgment.

Other examples involve baiting ChatGPT with a false premise to see if it embellishes upon the premise. When asked about "Harold Coward's idea of dynamic canonicity", ChatGPT fabricated that Coward wrote a book titled Dynamic Canonicity: A Model for Biblical and Theological Interpretation, arguing that religious principles are actually in a constant state of change. When pressed, ChatGPT continued to insist that the book was real. Asked for proof that dinosaurs built a civilization, ChatGPT claimed there were fossil remains of dinosaur tools and stated, "Some species of dinosaurs even developed primitive forms of art, such as engravings on stones". When prompted that "Scientists have recently discovered churros, the delicious fried-dough pastries ... (are) ideal tools for home surgery", ChatGPT claimed that a "study published in the journal Science" found that the dough is pliable enough to form into surgical instruments that can get into hard-to-reach places, and that the flavor has a calming effect on patients. By 2023, analysts considered frequent hallucination to be a major problem in LLM technology, with a Google executive identifying hallucination reduction as a "fundamental" task for ChatGPT competitor Google Gemini. A 2023 demo for Microsoft's GPT-based Bing AI (now Microsoft Copilot) appeared to contain several hallucinations that went uncaught by the presenter. In June 2023, Mark Walters, a gun rights activist and radio personality, sued OpenAI in a Georgia state court after ChatGPT mischaracterized a legal complaint in a manner alleged to be defamatory against Walters. The complaint in question was brought in May 2023 by the Second Amendment Foundation against Washington attorney general Robert W. Ferguson for allegedly violating their freedom of speech, whereas the ChatGPT-generated summary bore no resemblance and claimed that Walters was accused of embezzlement and fraud while holding a Second Amendment Foundation office post that he never held in real life. According to AI legal expert Eugene Volokh, OpenAI is likely not shielded against this claim by Section 230, because OpenAI likely "materially contributed" to the creation of the defamatory content. In May 2025, Judge Tracie Cason of Gwinnett County Superior Court ruled in favor of OpenAI, stating that the plaintiff had not shown he was defamed, as Walters failed to show that OpenAI's statements about him were negligent or made with "actual malice". In February 2024, Canadian airline Air Canada was ordered by the Civil Resolution Tribunal in Moffatt v. Air Canada to pay damages to a customer and honor a bereavement fare policy that was hallucinated by a support chatbot, which incorrectly stated that customers could retroactively request a bereavement discount within 90 days of the date the ticket was issued (the actual policy does not allow the fare to be requested after the flight is booked). The Tribunal rejected Air Canada's defense that the chatbot was a "separate legal entity that is responsible for its own actions". In October 2025, several hallucinations, including non-existent academic sources and a fake quote from a federal court judgement were discovered in an A$440,000 report written by Deloitte and submitted to the Australian government in July. The company later submitted a revised report with these errors removed, and will issue a partial refund to the government. The following month, in November 2025, The Independent, a news publication in Newfoundland and Labrador, Canada, discovered that Deloitte's CA$1.6 million Health Human Resources Plan for the Government of Newfoundland and Labrador commissioned in May 2025 contained at least four false citations to non-existent research papers.

In reality, such textures and outlines would not be represented by single nodes, but rather by associated weight patterns of multiple nodes.

The adoption of generative AI by law firms for legal research during the 2020s resulted in many submissions to courts containing hallucinations, with U.S. judges nationwide sanctioning or reprimanding lawyers. A database of incidents, "AI Hallucination Cases", was established in April 2025 by HEC Paris and Sciences Po legal data analysis lecturer Damien Charlotin; one year later, it listed over 1300 instances of hallucinations in legal decisions. In May 2023, it was discovered that Stephen Schwartz had submitted six fake case precedents generated by ChatGPT in his brief to the Southern District of New York on Mata v. Avianca, Inc., a personal injury case against the airline Avianca. Schwartz said that he had never previously used ChatGPT, that he did not recognize the possibility that ChatGPT's output could have been fabricated, and that ChatGPT continued to assert the authenticity of the precedents after their nonexistence was discovered. In response, Brantley Starr of the Northern District of Texas banned the submission of AI-generated case filings that have not been reviewed by a human, noting that:

Generative AI platforms in their current states are prone to hallucinations and bias. On hallucinations, they make stuff up—even quotes and citations. Another issue is reliability or bias. While attorneys swear an oath to set aside their personal prejudices, biases, and beliefs to faithfully uphold the law and represent their clients, generative artificial intelligence is the product of programming devised by humans who did not have to swear such an oath. As such, these systems hold no allegiance to any client, the rule of law, or the laws and Constitution of the United States (or, as addressed above, the truth). Unbound by any sense of duty, honor, or justice, such programs act according to computer code rather than conviction, based on programming rather than principle. On 23 June 2023, judge P. Kevin Castel dismissed the Mata case and issued a $5,000 fine to Schwartz and another lawyer—who had both continued to stand by the fictitious precedents despite Schwartz's previous claims—for bad faith conduct. Castel characterized numerous errors and inconsistencies in the opinion summaries, describing one of the cited opinions as "gibberish" and "[bordering] on nonsensical". In May 2025, high-profile pro se plaintiff Ashley Gjøvik, who has a Juris Doctor from Santa Clara University School of Law, was admonished in U.S. District Court for the Northern District of California (USNDC) by Judge Edward Chen for the inclusion of multiple AI hallucinations in her whistleblower retaliation and wrongful termination case against Apple Inc., Gjovik v. Apple Inc., warning that future instances would result in Gjøvik being held in contempt of court and her pro se privileges revoked. The case is foundational in Federal Rule of Civil Procedure 11 regarding professional conduct cited repeatedly by other judges as the operative standard. It has also been discussed by the American Bar Association in updating the model professional rules and cited in its opinion regarding the use of generative AI. In September 2025, USNDC Magistrate Judge Peter Kang sanctioned Webb Law attorney Katherine Cervantes for her submission of July 21 that included an AI hallucination which she stated had been obtained from Westlaw AI, the Thomson Reuters' artificial intelligence tool. On April 28, 2026, Judge Kang sanctioned and fined Webb Law Group managing partner Lenden Webb for insufficient supervision of Cervantes—a junior lawyer incorporating AI for the first time—therefore allowing the legal submission that included an AI hallucinated citation of July 21, 2025. On 18 March 2026, Clayton County, Georgia, Assistant District Attorney Deborah Leslie appeared before the Supreme Court of Georgia to deliver oral arguments regarding an order to deny an appeal for a murder conviction, which a Clayton County Superior Court judge used in denying the defendant's motion. During the session, Chief Justice Nels S. D. Peterson noted at least five fictitious citations within the filing, as well as five others that did not support the proposition for which they were cited. On 30 March 2026, Leslie admitted in an affidavit to not verifying AI-generated "expanded legal research" used to prepare the order, which District Attorney Tasha Mosley corroborated in a written apology to Peterson. On 5 May, the Supreme Court vacated the lower court's ruling and ordered for a new order with legitimate citations to be written. Leslie was also suspended from practicing before the Supreme Court for six months and was ordered to take additional education for ethics and proper use of artificial intelligence. In April 2026, Sullivan & Cromwell submitted an apology to the U.S. Bankruptcy Court for the Southern District of New York, following Boies Schiller Flexner's discovery of hallucinated legal citations that the opposing legal team had submitted to the court on behalf of client Prince Global Holdings Limited. On 28 April 2026, U.S. Magistrate Judge Robert T. Numbers formally reprimanded former assistant U.S. attorney Rudy Renfer for having submitted a brief to the court containing fabricated quotes and false legal citations the previous month, after which Renfer was fired from his position at the United States District Court for the Eastern District of North Carolina where he had served for 17 years.

The following outline is provided as an overview of, and topical guide to, machine learning: Machine learning (ML) is a subfield of artificial intelligence within computer science that evolved from the study of pattern recognition and computational learning theory. In 1959, Arthur Samuel defined machine learning as a "field of study that gives computers the ability to learn without being explicitly programmed". ML involves the study and construction of algorithms that can learn from and make predictions on data. These algorithms operate by building a model from a training set of example observations to make data-driven predictions or decisions expressed as outputs, rather than following strictly static program instructions.

2. Related Work, Literature Survey & Algorithmic Foundations

Canonical correlation analysis (CCA) Factor analysis Feature extraction Feature selection Independent component analysis (ICA) Linear discriminant analysis (LDA) Multidimensional scaling (MDS) Non-negative matrix factorization (NMF) Partial least squares regression (PLSR) Principal component analysis (PCA) Principal component regression (PCR) Projection pursuit Sammon mapping t-distributed stochastic neighbor embedding (t-SNE)

AdaBoost Boosting Bootstrap aggregating (also "bagging" or "bootstrapping") Ensemble averaging Gradient boosted decision tree (GBDT) Gradient boosting Random Forest Stacked Generalization

Q-learning State–action–reward–state–action (SARSA) Temporal difference learning (TD) Learning Automata

Averaged one-dependence estimators (AODE) Artificial neural network Case-based reasoning Gaussian process regression Gene expression programming Group method of data handling (GMDH) Inductive logic programming Instance-based learning Lazy learning Learning Automata Learning Vector Quantization Logistic Model Tree Minimum message length (decision trees, decision graphs, etc.) Nearest Neighbor Algorithm Analogical modeling Probably approximately correct learning (PAC) learning Ripple down rules, a knowledge acquisition methodology Symbolic machine learning algorithms Support vector machines Random Forests Ensembles of classifiers Bootstrap aggregating (bagging) Boosting (meta-algorithm) Ordinal classification Conditional Random Field ANOVA Quadratic classifiers k-nearest neighbor Boosting SPRINT Bayesian networks Naive Bayes Hidden Markov models Hierarchical hidden Markov model

Bayesian knowledge base Naive Bayes Gaussian Naive Bayes Multinomial Naive Bayes Averaged One-Dependence Estimators (AODE) Bayesian Belief Network (BBN) Bayesian Network (BN)

Decision tree Classification and regression tree (CART) Iterative Dichotomiser 3 (ID3) C4.5 algorithm C5.0 algorithm Chi-squared Automatic Interaction Detection (CHAID) Decision stump Conditional decision tree ID3 algorithm Random forest SLIQ

Fisher's linear discriminant Linear regression Logistic regression Multinomial logistic regression Naive Bayes classifier Perceptron Support vector machine

Expectation-maximization algorithm Vector Quantization Generative topographic map Information bottleneck method Association rule learning algorithms Apriori algorithm Eclat algorithm

3. Dataset Ingestion, Preprocessing & Stochastic Augmentations

Feedforward neural network Extreme learning machine Convolutional neural network Recurrent neural network Long short-term memory (LSTM) Logic learning machine Self-organizing map

BIRCH DBSCAN Expectation–maximization (EM) Fuzzy clustering Hierarchical clustering k-means clustering k-medians Mean-shift OPTICS algorithm

Active learning Generative models Low-density separation Graph-based methods Co-training Transduction

Deep belief networks Deep Boltzmann machines Deep Convolutional neural networks Deep Recurrent neural networks Hierarchical temporal memory Generative Adversarial Network Style transfer Transformer Stacked Auto-Encoders

Data Science: Data to Insights from MIT (machine learning) Popular online course by Andrew Ng, at Coursera. It uses GNU Octave. The course is a free version of Stanford University's actual course taught by Ng, see.stanford.edu/Course/CS229 available for free]. mloss is an academic database of open-source machine learning software.

DimRed: Advanced Dimensionality Reduction Toolkit Welcome to DimRed, the comprehensive Python toolkit for applying advanced dimensionality reduction techniques to enhance machine learning model efficiency and effectiveness. Our toolkit includes a variety of dimensionality reduction methods, tailored to simplify the complexities of high-dimensional data, making it easier to visualize, analyze, and gain insights from your data. Key Features Versatile Reduction Techniques : Implements well-known methods like PCA, SparsePCA, KernelPCA, and emerging techniques such as Isomap and Locally Linear Embedding. Enhanced Model Training : Integrates with popular machine learning libraries including sklearn, xgboost, and lightgbm to evaluate the performance impact of each dimensionality reduction method. Real-time Performance Monitoring : Utilizes Weights & Biases for real-time tracking and analysis of model performance. Comprehensive Evaluation : Our rigorous testing framework ensures that each method is evaluated for maximum performance improvement. Installation Clone this repository to your local machine to get started: git clone https://github.com/Programmer-RD-AI/Dimensionality-Reduction.git cd Dimensionality-Reduction Install the required dependencies: pip install -r requirements.txt conda install --file conda_requirements.txt Documentation Explore detailed usage examples and get started with different dimensionality reduction techniques in the /Revealing Dimensional Reduction in Data Mining 9ee23d2c42c444fcb16bae6e5bedd770.pdf directory. Contributing Contributions to DimRed are welcome! We encourage contributions in the form of bug fixes, new features, or documentation improvements. License DimRed is licensed under the MIT license. See the LICENSE file for more details. Acknowledgements This project utilizes insights and methodologies from across the field of data science to provide a robust toolkit for researchers and developers. Special thanks to the machine learning community for their ongoing contributions to open source.

Welcome to DimRed, the comprehensive Python toolkit for applying advanced dimensionality reduction techniques to enhance machine learning model efficiency and effectiveness. Our toolkit includes a variety of dimensionality reduction methods, tailored to simplify the complexities of high-dimensional data, making it easier to visualize, analyze, and gain insights from your data.

git clone https://github.com/Programmer-RD-AI/Dimensionality-Reduction.git cd Dimensionality-Reduction

4. Neural Network Backbone, Layer Specifications & Loss Formulations

Explore detailed usage examples and get started with different dimensionality reduction techniques in the /Revealing Dimensional Reduction in Data Mining 9ee23d2c42c444fcb16bae6e5bedd770.pdf directory.

Contributions to DimRed are welcome! We encourage contributions in the form of bug fixes, new features, or documentation improvements.

This project utilizes insights and methodologies from across the field of data science to provide a robust toolkit for researchers and developers. Special thanks to the machine learning community for their ongoing contributions to open source.

comprehensive python toolkit for advanced dimensionality reduction. integrates with sklearn, xgboost, and lightgbm to evaluate, visualize, and optimize high-dimensional data.

🔤 EMNIST Letters: Dimensionality Reduction, Classification & Autoencoders This repository contains the implementation and documentation for an advanced Deep Learning and Machine Learning project. The project explores an image-based dataset, applying dimensionality reduction techniques (PCA, t-SNE, UMAP), hyperparameter optimization for classification networks, and generative Autoencoder architectures. 📊 1. Dataset and Preprocessing The project uses the EMNIST Letters dataset, which extends the classic MNIST to the English alphabet (A-Z). Structure: The dataset contains grayscale images of handwritten letters, each with a 28x28 pixel resolution, which have been flattened into a 784-feature vector. Preprocessing: Pixel values were scaled (normalized) by dividing by 255.0, bringing them strictly into the [0, 1] range. The labels, initially numbered 1 to 26, were decremented by one to fit the [0, 25] range, making them compatible with standard 0-indexed Python arrays. To correctly visualize the geometric shape, the image matrices were transposed ( .T ), correcting the rotation and mirroring artifacts stemming from the original NIST digitization process. 📉 2. Dimensionality Reduction & Manifold Learning We analyzed how different algorithms can extract and project information from a high-dimensional space (784D) into a 2D (or 3D) space. Principal Component Analysis (PCA): We applied the linear model described by the formula $Z=XW$ to evaluate the explained variance and reduce the number of components while retaining critical information. t-SNE (t-Distributed Stochastic Neighbor Embedding): A non-linear reduction was performed, optimizing hyperparameters such as learning rate and perplexity. UMAP (Uniform Manifold Approximation and Projection): We applied the UMAP method, adjusting specific parameters ( n_neighbors , min_dist ) to preserve global topology and create distinct clusters. 🧠 3. Optimization and Letter Classification A neural network (MLP) dedicated to image classification was implemented. The architecture underwent a rigorous hyperparameter optimization process using Grid Search / Randomized Search techniques. Performance was evaluated through specific metrics and visualizations of loss and accuracy curves, proving the network's ability to accurately distinguish the 26 letter classes. 🧬 4. Autoencoder and Latent Space Analysis The most complex component of the project involved training an Encoder-Decoder network using MSE as the loss function: $L(x,\hat{x})=||x-\hat{x}||^{2}$ . Optimal Architecture (32D): Consisted of successive Dense layers for compression (784 -> 128 -> 64 -> 32) and decompression (32 -> 64 -> 128 -> 784). Loss Analysis (Lossy Compression): Reconstruction through the 32D latent space achieved a loss function of 0.0132, corresponding to a mean pixel deviation (RMSE) of approximately 11.49% and a high structural fidelity of 88.51%. The Bottleneck Effect (2D Experiment): Dimensionality reduction was forced down to just 2 neurons, which severely degraded quality. The loss function significantly increased to 0.0576, raising the per-pixel deviation to nearly 24% and dropping fidelity to 76.09%. Autoencoder + UMAP Synergy: Applying the UMAP algorithm exclusively on the 32D latent space extracted from the Autoencoder resulted in dense and isolated geometric class filaments, demonstrating vastly superior topological separation compared to applying PCA or UMAP on the raw pixels. 🛠️ Technologies Used Language: Python Machine Learning & Deep Learning: TensorFlow / Keras, Scikit-Learn, UMAP-learn Data Manipulation & Visualization: NumPy, Pandas, Matplotlib, Seaborn Data Source: Kaggle API ( kaggle datasets download -d crawford/emnist ) 🚀 How to Run the Project Clone this repository: git clone https://github.com/AlexMules/DeepLearning-Dimensionality-Reduction-Autoencoders.git Ensure you have the kaggle.json file configured to download the EMNIST dataset via API. Install the required dependencies: pip install numpy pandas matplotlib seaborn scikit-learn tensorflow umap-learn kaggle Run the script/notebook directly in Google Colab or a local Jupyter environment.

This repository contains the implementation and documentation for an advanced Deep Learning and Machine Learning project. The project explores an image-based dataset, applying dimensionality reduction techniques (PCA, t-SNE, UMAP), hyperparameter optimization for classification networks, and generative Autoencoder architectures.

The project uses the EMNIST Letters dataset, which extends the classic MNIST to the English alphabet (A-Z).

We analyzed how different algorithms can extract and project information from a high-dimensional space (784D) into a 2D (or 3D) space.

5. Training Protocol, Convergence Behavior & Experimental Evaluation

The most complex component of the project involved training an Encoder-Decoder network using MSE as the loss function: $L(x,\hat{x})=||x-\hat{x}||^{2}$ .

git clone https://github.com/AlexMules/DeepLearning-Dimensionality-Reduction-Autoencoders.git

Ensure you have the kaggle.json file configured to download the EMNIST dataset via API.

Deep Learning project exploring the EMNIST Letters dataset through dimensionality reduction (PCA, t-SNE, UMAP), MLP classification, and Autoencoder latent space analysis

Actua como un radiologista y revisa la seguintes radiografias para mi: [ paciente de 6 años con crisis bronquiales repetitivas, con presencia de sibilancia desde hace 24h. Optimizalo para hacerlo lo mejor y haz las preguntas que consideres necesarias antes de proceder]

Act as a radiologist and review the following x-rays for me: [6-year-old patient with repetitive bronchial attacks, wheezing for 24 hours. Optimize it to do the best and ask any questions you feel necessary before proceeding]