The meaning conveyed by a sentence often depends on the context in which it appears. Despite the progress of sentence embedding methods, it remains unclear how to best modify a sentence embedding conditioned on its context. To address this problem, we propose Condition-Aware Sentence Embeddings (CASE), an efficient and accurate method to create an embedding for a sentence under a given condition. First, CASE creates an embedding for the condition using a Large Language Model (LLM), where the sentence influences the attention scores computed for the tokens in the condition during pooling. Next, a supervised nonlinear projection is learned to reduce the dimensionality of the LLM-based text embeddings. We show that CASE significantly outperforms previously proposed Conditional Semantic Textual Similarity (C-STS) methods on an existing standard benchmark dataset. We find that subtracting the condition embedding consistently improves the C-STS performance of LLM-based text embeddings. Moreover, we propose a supervised dimensionality reduction method that not only reduces the dimensionality of LLM-based embeddings but also significantly improves their performance.
We present a supervised dimensionality reduction technique called Convex Linear Discriminant Analysis (ConvexLDA). The proposed model optimizes a multi-objective cost function by balancing two complementary terms. The first term pulls the samples of a class towards its centroid by minimizing a sample's distance from its class-centroid in low dimensional space. The second term pushes the classes far apart by maximizing their hyperellipsoid scattering volume via the logarithm of the determinant (\textit{log det}) of the outer product matrix formed by the low-dimensional class-centroids. Using the negative of the \textit{log det}, we pose the final cost as a minimization problem, which balances the two terms using a hyper-parameter $\lambda$. We demonstrate that the cost function is convex. Unlike Fisher LDA, the proposed method doesn't require to compute the inverse of a matrix, hence avoiding any ill-conditioned problem where data dimension is very high, e.g. RNA-seq data. ConvexLDA doesn't require pair-wise distance calculation, making it faster and more easily scalable. Moreover, the convex nature of the cost function ensures global optimality, enhancing the reliability of the learned embedding. Our experimental evaluation demonstrates that ConvexLDA outperforms several popular linear discriminant analysis (LDA)-based methods on a range of high-dimensional biological data, image data sets, etc.
Supervised dimensionality reduction aims to map labeled data to a low-dimensional feature space while maximizing class discriminability. Directly computing discriminability is often impractical, so an alternative approach is to learn features that maximize a distance or dissimilarity measure between classes. The Fisher-Rao distance is an important information geometry distance in statistical manifolds. It is induced by the Fisher information metric, a tool widely used for understanding neural representations. Despite its theoretical and pratical appeal, Fisher-Rao distances between classes have not been used as a maximization objective in supervised feature learning. Here, we present Supervised Quadratic Feature Analysis (SQFA), a linear dimensionality reduction method that maximizes Fisher-Rao distances between class distributions, by exploiting the information geometry of the symmetric positive definite manifold. SQFA maximizes distances using first- and second-order statistics, and its features allow for quadratic discriminability (i.e. QDA performance) matching or surpassing state-of-the-art methods on real-world datasets. We theoretically motivate Fisher-Rao distances as a proxy for quadratic discriminability, and compare its performance to other popular distances (e.g. Wasserstein distances). SQFA provides a flexible state-of-the-art method for dimensionality reduction. Its successful use of Fisher-Rao distances between classes motivates future research directions.
Robustness is a fundamental aspect for developing safe and trustworthy models, particularly when they are deployed in the open world. In this work we analyze the inherent capability of one-stage object detectors to robustly operate in the presence of out-of-distribution (OoD) data. Specifically, we propose a novel detection algorithm for detecting unknown objects in image data, which leverages the features extracted by the model from each sample. Differently from other recent approaches in the literature, our proposal does not require retraining the object detector, thereby allowing for the use of pretrained models. Our proposed OoD detector exploits the application of supervised dimensionality reduction techniques to mitigate the effects of the curse of dimensionality on the features extracted by the model. Furthermore, it utilizes high-resolution feature maps to identify potential unknown objects in an unsupervised fashion. Our experiments analyze the Pareto trade-off between the performance detecting known and unknown objects resulting from different algorithmic configurations and inference confidence thresholds. We also compare the performance of our proposed algorithm to that of logits-based post-hoc OoD methods, as well as possible fusion strategies. Finally, we discuss on the competitiveness of all tested methods against state-of-the-art OoD approaches for object detection models over the recently published Unknown Object Detection benchmark. The obtained results verify that the performance of avant-garde post-hoc OoD detectors can be further improved when combined with our proposed algorithm.
The performance of deep neural networks scales with dataset size and label quality, rendering the efficient mitigation of low-quality data annotations crucial for building robust and cost-effective systems. Existing strategies to address label noise exhibit severe limitations due to computational complexity and application dependency. In this work, we propose WANN, a Weighted Adaptive Nearest Neighbor approach that builds on self-supervised feature representations obtained from foundation models. To guide the weighted voting scheme, we introduce a reliability score $\eta$, which measures the likelihood of a data label being correct. WANN outperforms reference methods, including a linear layer trained with robust loss functions, on diverse datasets of varying size and under various noise types and severities. WANN also exhibits superior generalization on imbalanced data compared to both Adaptive-NNs (ANN) and fixed k-NNs. Furthermore, the proposed weighting scheme enhances supervised dimensionality reduction under noisy labels. This yields a significant boost in classification performance with 10x and 100x smaller image embeddings, minimizing latency and storage requirements. Our approach, emphasizing efficiency and explainability, emerges as a simple, robust solution to overcome inherent limitations of deep neural network training. The code is available at https://github.com/francescodisalvo05/wann-noisy-labels .
The value of supervised dimensionality reduction lies in its ability to uncover meaningful connections between data features and labels. Common dimensionality reduction methods embed a set of fixed, latent points, but are not capable of generalizing to an unseen test set. In this paper, we provide an out-of-sample extension method for the random forest-based supervised dimensionality reduction method, RF-PHATE, combining information learned from the random forest model with the function-learning capabilities of autoencoders. Through quantitative assessment of various autoencoder architectures, we identify that networks that reconstruct random forest proximities are more robust for the embedding extension problem. Furthermore, by leveraging proximity-based prototypes, we achieve a 40% reduction in training time without compromising extension quality. Our method does not require label information for out-of-sample points, thus serving as a semi-supervised method, and can achieve consistent quality using only 10% of the training data.
A fundamental problem in supervised learning is to find a good set of features or distance measures. If the new set of features is of lower dimensionality and can be obtained by a simple transformation of the original data, they can make the model understandable, reduce overfitting, and even help to detect distribution drift. We propose a supervised dimensionality reduction method Gradient Boosting Mapping (GBMAP), where the outputs of weak learners -- defined as one-layer perceptrons -- define the embedding. We show that the embedding coordinates provide better features for the supervised learning task, making simple linear models competitive with the state-of-the-art regressors and classifiers. We also use the embedding to find a principled distance measure between points. The features and distance measures automatically ignore directions irrelevant to the supervised learning task. We also show that we can reliably detect out-of-distribution data points with potentially large regression or classification errors. GBMAP is fast and works in seconds for dataset of million data points or hundreds of features. As a bonus, GBMAP provides a regression and classification performance comparable to the state-of-the-art supervised learning methods.
A new dimensional reduction (DR) and data visualization method, Curvature-Augmented Manifold Embedding and Learning (CAMEL), is proposed. The key novel contribution is to formulate the DR problem as a mechanistic/physics model, where the force field among nodes (data points) is used to find an n-dimensional manifold representation of the data sets. Compared with many existing attractive-repulsive force-based methods, one unique contribution of the proposed method is to include a non-pairwise force. A new force field model is introduced and discussed, inspired by the multi-body potential in lattice-particle physics and Riemann curvature in topology. A curvature-augmented force is included in CAMEL. Following this, CAMEL formulation for unsupervised learning, supervised learning, semi-supervised learning/metric learning, and inverse learning are provided. Next, CAMEL is applied to many benchmark datasets by comparing existing models, such as tSNE, UMAP, TRIMAP, and PacMap. Both visual comparison and metrics-based evaluation are performed. 14 open literature and self-proposed metrics are employed for a comprehensive comparison. Conclusions and future work are suggested based on the current investigation. Related code and demonstration are available on https://github.com/ymlasu/CAMEL for interested readers to reproduce the results and other applications.
Providing a model that achieves a strong predictive performance and is simultaneously interpretable by humans is one of the most difficult challenges in machine learning research due to the conflicting nature of these two objectives. To address this challenge, we propose a modification of the radial basis function neural network model by equipping its Gaussian kernel with a learnable precision matrix. We show that precious information is contained in the spectrum of the precision matrix that can be extracted once the training of the model is completed. In particular, the eigenvectors explain the directions of maximum sensitivity of the model revealing the active subspace and suggesting potential applications for supervised dimensionality reduction. At the same time, the eigenvectors highlight the relationship in terms of absolute variation between the input and the latent variables, thereby allowing us to extract a ranking of the input variables based on their importance to the prediction task enhancing the model interpretability. We conducted numerical experiments for regression, classification, and feature selection tasks, comparing our model against popular machine learning models, the state-of-the-art deep learning-based embedding feature selection techniques, and a transformer model for tabular data. Our results demonstrate that the proposed model does not only yield an attractive prediction performance compared to the competitors but also provides meaningful and interpretable results that potentially could assist the decision-making process in real-world applications. A PyTorch implementation of the model is available on GitHub at the following link. https://github.com/dannyzx/Gaussian-RBFNN
Manifold learning approaches seek the intrinsic, low-dimensional data structure within a high-dimensional space. Mainstream manifold learning algorithms, such as Isomap, UMAP, $t$-SNE, Diffusion Map, and Laplacian Eigenmaps do not use data labels and are thus considered unsupervised. Existing supervised extensions of these methods are limited to classification problems and fall short of uncovering meaningful embeddings due to their construction using order non-preserving, class-conditional distances. In this paper, we show the weaknesses of class-conditional manifold learning quantitatively and visually and propose an alternate choice of kernel for supervised dimensionality reduction using a data-geometry-preserving variant of random forest proximities as an initialization for manifold learning methods. We show that local structure preservation using these proximities is near universal across manifold learning approaches and global structure is properly maintained using diffusion-based algorithms.
We propose a new supervised dimensionality reduction technique called Supervised Linear Centroid-Encoder (SLCE), a linear counterpart of the nonlinear Centroid-Encoder (CE) \citep{ghosh2022supervised}. SLCE works by mapping the samples of a class to its class centroid using a linear transformation. The transformation is a projection that reconstructs a point such that its distance from the corresponding class centroid, i.e., centroid-reconstruction loss, is minimized in the ambient space. We derive a closed-form solution using an eigendecomposition of a symmetric matrix. We did a detailed analysis and presented some crucial mathematical properties of the proposed approach. %We also provide an iterative solution approach based solving the optimization problem using a descent method. We establish a connection between the eigenvalues and the centroid-reconstruction loss. In contrast to Principal Component Analysis (PCA) which reconstructs a sample in the ambient space, the transformation of SLCE uses the instances of a class to rebuild the corresponding class centroid. Therefore the proposed method can be considered a form of supervised PCA. Experimental results show the performance advantage of SLCE over other supervised methods.
State-of-the-art hypergraph partitioners follow the multilevel paradigm that constructs multiple levels of progressively coarser hypergraphs that are used to drive cut refinement on each level of the hierarchy. Multilevel partitioners are subject to two limitations: (i) hypergraph coarsening processes rely on local neighborhood structure without fully considering the global structure of the hypergraph; and (ii) refinement heuristics risk entrapment in local minima. In this paper, we describe K-SpecPart, a supervised spectral framework for multi-way partitioning that directly tackles these two limitations. K-SpecPart relies on the computation of generalized eigenvectors and supervised dimensionality reduction techniques to generate vertex embeddings. These are computational primitives that are fast and capture global structural properties of the hypergraph that are not explicitly considered by existing partitioners. K-SpecPart then converts the vertex embeddings into multiple partitioning solutions. K-SpecPart introduces the idea of ''ensembling'' multiple solutions via a cut-overlay clustering technique that often enables the use of computationally demanding partitioning methods such as ILP (integer linear programming). Using the output of a standard partitioner as a supervision hint, K-SpecPart effectively combines the strengths of established multilevel partitioning techniques with the benefits of spectral graph theory and other combinatorial algorithms. K-SpecPart significantly extends ideas and algorithms that first appeared in our previous work on the bipartitioner SpecPart. Our experiments demonstrate the effectiveness of K-SpecPart. For bipartitioning, K-SpecPart produces solutions with up to 15% cutsize improvement over SpecPart. For multi-way partitioning, K-SpecPart produces solutions with up to 20% cutsize improvement over leading partitioners hMETIS and KaHyPar.
Efficient surrogate modelling is a key requirement for uncertainty quantification in data-driven scenarios. In this work, a novel approach of using Sparse Random Features for surrogate modelling in combination with self-supervised dimensionality reduction is described. The method is compared to other methods on synthetic and real data obtained from crashworthiness analyses. The results show a superiority of the here described approach over state of the art surrogate modelling techniques, Polynomial Chaos Expansions and Neural Networks.
Due to the effectiveness of using machine learning in physics, it has been widely received increased attention in the literature. However, the notion of applying physics in machine learning has not been given much awareness to. This work is a hybrid of physics and machine learning where concepts of physics are used in machine learning. We propose the supervised Gravitational Dimensionality Reduction (GDR) algorithm where the data points of every class are moved to each other for reduction of intra-class variances and better separation of classes. For every data point, the other points are considered to be gravitational particles, such as stars, where the point is attracted to the points of its class by gravity. The data points are first projected onto a spacetime manifold using principal component analysis. We propose two variants of GDR -- one with the Newtonian gravity and one with the Einstein's general relativity. The former uses Newtonian gravity in a straight line between points but the latter moves data points along the geodesics of spacetime manifold. For GDR with relativity gravitation, we use both Schwarzschild and Minkowski metric tensors to cover both general relativity and special relativity. Our simulations show the effectiveness of GDR in discrimination of classes.
After the development of different machine learning and manifold learning algorithms, it may be a good time to put them together to make a powerful mind for machine. In this work, we propose affective manifolds as components of a machine's mind. Every affective manifold models a characteristic group of mind and contains multiple states. We define the machine's mind as a set of affective manifolds. We use a learning model for mapping the input signals to the embedding space of affective manifold. Using this mapping, a machine or a robot takes an input signal and can react emotionally to it. We use deep metric learning, with Siamese network, and propose a loss function for affective manifold learning. We define margins between states based on the psychological and philosophical studies. Using triplets of instances, we train the network to minimize the variance of every state and have the desired distances between states. We show that affective manifolds can have various applications for machine-machine and human-machine interactions. Some simulations are also provided for verification of the proposed method. It is possible to have as many affective manifolds as required in machine's mind. More affective manifolds in the machine's mind can make it more realistic and effective. This paper opens the door; we invite the researchers from various fields of science to propose more affective manifolds to be inserted in machine's mind.
The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a Convolutional Autoencoder for dimensionality reduction and a classifier composed by a Fully Connected Network, are combined to simultaneously produce supervised dimensionality reduction and predictions. It turned out that this methodology can also be greatly beneficial in enforcing explainability of deep learning architectures. Additionally, the resulting Latent Space, optimized for the classification task, can be utilized to improve traditional, interpretable classification algorithms. The experimental results, showed that the proposed methodology achieved competitive results against the state of the art deep learning methods, while being much more efficient in terms of parameter count. Finally, it was empirically justified that the proposed methodology introduces advanced explainability regarding, not only the data structure through the produced latent space, but also about the classification behaviour.
Deep neural network (DNN) classifiers are often overconfident, producing miscalibrated class probabilities. In high-risk applications like healthcare, practitioners require $\textit{fully calibrated}$ probability predictions for decision-making. That is, conditioned on the prediction $\textit{vector}$, $\textit{every}$ class' probability should be close to the predicted value. Most existing calibration methods either lack theoretical guarantees for producing calibrated outputs, reduce classification accuracy in the process, or only calibrate the predicted class. This paper proposes a new Kernel-based calibration method called KCal. Unlike existing calibration procedures, KCal does not operate directly on the logits or softmax outputs of the DNN. Instead, KCal learns a metric space on the penultimate-layer latent embedding and generates predictions using kernel density estimates on a calibration set. We first analyze KCal theoretically, showing that it enjoys a provable $\textit{full}$ calibration guarantee. Then, through extensive experiments across a variety of datasets, we show that KCal consistently outperforms baselines as measured by the calibration error and by proper scoring rules like the Brier Score.
Existing methods for explaining black box learning models often focus on building local explanations of model behaviour for a particular data item. It is possible to create global explanations for all data items, but these explanations generally have low fidelity for complex black box models. We propose a new supervised manifold visualisation method, SLISEMAP, that simultaneously finds local explanations for all data items and builds a (typically) two-dimensional global visualisation of the black box model such that data items with similar local explanations are projected nearby. We provide a mathematical derivation of our problem and an open source implementation implemented using the GPU-optimised PyTorch library. We compare SLISEMAP to multiple popular dimensionality reduction methods and find that SLISEMAP is able to utilise labelled data to create embeddings with consistent local white box models. We also compare SLISEMAP to other model-agnostic local explanation methods and show that SLISEMAP provides comparable explanations and that the visualisations can give a broader understanding of black box regression and classification models.
A lot of prognostication methodologies have been formulated for early detection of Polycystic Ovary Syndrome also known as PCOS using Machine Learning. PCOS is a binary classification problem. Dimensionality Reduction methods impact the performance of Machine Learning to a greater extent and using a Supervised Dimensionality Reduction method can give us a new edge to tackle this problem. In this paper we present Discriminant Analysis in different dimensions with Linear and Quadratic form for binary classification along with metrics. We were able to achieve good accuracy and less variation with Discriminant Analysis as compared to many commonly used classification algorithms with training accuracy reaching 97.37% and testing accuracy of 95.92% using Quadratic Discriminant Analysis. Paper also gives the analysis of data with visualizations for deeper understanding of problem.
Dimensionality reduction methods have found vast application as visualization tools in diverse areas of science. Although many different methods exist, their performance is often insufficient for providing quick insight into many contemporary datasets, and the unsupervised mode of use prevents the users from utilizing the methods for dataset exploration and fine-tuning the details for improved visualization quality. We present BlosSOM, a high-performance semi-supervised dimensionality reduction software for interactive user-steerable visualization of high-dimensional datasets with millions of individual data points. BlosSOM builds on a GPU-accelerated implementation of the EmbedSOM algorithm, complemented by several landmark-based algorithms for interfacing the unsupervised model learning algorithms with the user supervision. We show the application of BlosSOM on realistic datasets, where it helps to produce high-quality visualizations that incorporate user-specified layout and focus on certain features. We believe the semi-supervised dimensionality reduction will improve the data visualization possibilities for science areas such as single-cell cytometry, and provide a fast and efficient base methodology for new directions in dataset exploration and annotation.