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 .
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
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.
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.
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.
Plant species identification is time consuming, costly, and requires lots of efforts, and expertise knowledge. In recent, many researchers use deep learning methods to classify plants directly using plant images. While deep learning models have achieved a great success, the lack of interpretability limit their widespread application. To overcome this, we explore the use of interpretable, measurable and computer-aided features extracted from plant leaf images. Image processing is one of the most challenging, and crucial steps in feature-extraction. The purpose of image processing is to improve the leaf image by removing undesired distortion. The main image processing steps of our algorithm involves: i) Convert original image to RGB (Red-Green-Blue) image, ii) Gray scaling, iii) Gaussian smoothing, iv) Binary thresholding, v) Remove stalk, vi) Closing holes, and vii) Resize image. The next step after image processing is to extract features from plant leaf images. We introduced 52 computationally efficient features to classify plant species. These features are mainly classified into four groups as: i) shape-based features, ii) color-based features, iii) texture-based features, and iv) scagnostic features. Length, width, area, texture correlation, monotonicity and scagnostics are to name few of them. We explore the ability of features to discriminate the classes of interest under supervised learning and unsupervised learning settings. For that, supervised dimensionality reduction technique, Linear Discriminant Analysis (LDA), and unsupervised dimensionality reduction technique, Principal Component Analysis (PCA) are used to convert and visualize the images from digital-image space to feature space. The results show that the features are sufficient to discriminate the classes of interest under both supervised and unsupervised learning settings.
Feature ranking and selection is a widely used approach in various applications of supervised dimensionality reduction in discriminative machine learning. Nevertheless there exists significant evidence on feature ranking and selection algorithms based on any criterion leading to potentially sub-optimal solutions for class separability. In that regard, we introduce emerging information theoretic feature transformation protocols as an end-to-end neural network training approach. We present a dimensionality reduction network (MMINet) training procedure based on the stochastic estimate of the mutual information gradient. The network projects high-dimensional features onto an output feature space where lower dimensional representations of features carry maximum mutual information with their associated class labels. Furthermore, we formulate the training objective to be estimated non-parametrically with no distributional assumptions. We experimentally evaluate our method with applications to high-dimensional biological data sets, and relate it to conventional feature selection algorithms to form a special case of our approach.
We explore the application of linear discriminant analysis (LDA) to the features obtained in different layers of pretrained deep convolutional neural networks (CNNs). The advantage of LDA compared to other techniques in dimensionality reduction is that it reduces dimensions while preserving the global structure of data, so distances in the low-dimensional structure found are meaningful. The LDA applied to the CNN features finds that the centroids of classes corresponding to the similar data lay closer than classes corresponding to different data. We applied the method to a modification of the MNIST dataset with ten additional classes, each new class with half of the images from one of the standard ten classes. The method finds the new classes close to the corresponding standard classes we took the data form. We also applied the method to a dataset of images of butterflies to find that related subspecies are found to be close. For both datasets, we find a performance similar to state-of-the-art methods.
Dimensionality reduction is an important operation in information visualization, feature extraction, clustering, regression, and classification, especially for processing noisy high dimensional data. However, most existing approaches preserve either the global or the local structure of the data, but not both. Approaches that preserve only the global data structure, such as principal component analysis (PCA), are usually sensitive to outliers. Approaches that preserve only the local data structure, such as locality preserving projections, are usually unsupervised (and hence cannot use label information) and uses a fixed similarity graph. We propose a novel linear dimensionality reduction approach, supervised discriminative sparse PCA with adaptive neighbors (SDSPCAAN), to integrate neighborhood-free supervised discriminative sparse PCA and projected clustering with adaptive neighbors. As a result, both global and local data structures, as well as the label information, are used for better dimensionality reduction. Classification experiments on nine high-dimensional datasets validated the effectiveness and robustness of our proposed SDSPCAAN.
Does adding a theorem to a paper affect its chance of acceptance? Does labeling a post with the author's gender affect the post popularity? This paper develops a method to estimate such causal effects from observational text data, adjusting for confounding features of the text such as the subject or writing quality. We assume that the text suffices for causal adjustment but that, in practice, it is prohibitively high-dimensional. To address this challenge, we develop causally sufficient embeddings, low-dimensional document representations that preserve sufficient information for causal identification and allow for efficient estimation of causal effects. Causally sufficient embeddings combine two ideas. The first is supervised dimensionality reduction: causal adjustment requires only the aspects of text that are predictive of both the treatment and outcome. The second is efficient language modeling: representations of text are designed to dispose of linguistically irrelevant information, and this information is also causally irrelevant. Our method adapts language models (specifically, word embeddings and topic models) to learn document embeddings that are able to predict both treatment and outcome. We study causally sufficient embeddings with semi-synthetic datasets and find that they improve causal estimation over related embedding methods. We illustrate the methods by answering the two motivating questions---the effect of a theorem on paper acceptance and the effect of a gender label on post popularity. Code and data available at https://github.com/vveitch/causal-text-embeddings-tf2}{github.com/vveitch/causal-text-embeddings-tf2
The vast majority of Dimensionality Reduction (DR) techniques rely on second-order statistics to define their optimization objective. Even though this provides adequate results in most cases, it comes with several shortcomings. The methods require carefully designed regularizers and they are usually prone to outliers. In this work, a new DR framework, that can directly model the target distribution using the notion of similarity instead of distance, is introduced. The proposed framework, called Similarity Embedding Framework, can overcome the aforementioned limitations and provides a conceptually simpler way to express optimization targets similar to existing DR techniques. Deriving a new DR technique using the Similarity Embedding Framework becomes simply a matter of choosing an appropriate target similarity matrix. A variety of classical tasks, such as performing supervised dimensionality reduction and providing out-of-of-sample extensions, as well as, new novel techniques, such as providing fast linear embeddings for complex techniques, are demonstrated in this paper using the proposed framework. Six datasets from a diverse range of domains are used to evaluate the proposed method and it is demonstrated that it can outperform many existing DR techniques.