Separating Topological Noise from Features Using Persistent Entropy

Topology is the branch of mathematics that studies shapes and maps among them. From the algebraic definition of topology a new set of algorithms have been derived. These algorithms are identified with “computational topology” or often pointed out as Topological Data Analysis (TDA) and are used for investigating high-dimensional data in a quantitative manner. Persistent homology appears as a fundamental tool in Topological Data Analysis. It studies the evolution of k−dimensional holes along a sequence of simplicial complexes (i.e. a filtration). The set of intervals representing birth and death times of k−dimensional holes along such sequence is called the persistence barcode. k−dimensional holes with short lifetimes are informally considered to be topological noise, and those with a long lifetime are considered to be topological feature associated to the given data (i.e. the filtration). In this paper, we derive a simple method for separating topological noise from topological features using a novel measure for comparing persistence barcodes called persistent entropy.Ministerio de Economía y Competitividad MTM2015-67072-

Towards personalized diagnosis of Glioblastoma in Fluid-attenuated inversion recovery (FLAIR) by topological interpretable machine learning

Glioblastoma multiforme (GBM) is a fast-growing and highly invasive brain tumour, it tends to occur in adults between the ages of 45 and 70 and it accounts for 52 percent of all primary brain tumours. Usually, GBMs are detected by magnetic resonance images (MRI). Among MRI, Fluid-attenuated inversion recovery (FLAIR) sequence produces high quality digital tumour representation. Fast detection and segmentation techniques are needed for overcoming subjective medical doctors (MDs) judgment. In the present investigation, we intend to demonstrate by means of numerical experiments that topological features combined with textural features can be enrolled for GBM analysis and morphological characterization on FLAIR. To this extent, we have performed three numerical experiments. In the first experiment, Topological Data Analysis (TDA) of a simplified 2D tumour growth mathematical model had allowed to understand the bio-chemical conditions that facilitate tumour growth: the higher the concentration of chemical nutrients the more virulent the process. In the second experiment topological data analysis was used for evaluating GBM temporal progression on FLAIR recorded within 90 days following treatment (e.g., chemo-radiation therapy - CRT) completion and at progression. The experiment had confirmed that persistent entropy is a viable statistics for monitoring GBM evolution during the follow-up period. In the third experiment we had developed a novel methodology based on topological and textural features and automatic interpretable machine learning for automatic GBM classification on FLAIR. The algorithm reached a classification accuracy up to the 97%.Comment: 22 pages; 16 figure

Topological classifier for detecting the emergence of epileptic seizures

Objective An innovative method based on topological data analysis is introduced for classifying EEG recordings of patients affected by epilepsy. We construct a topological space from a collection of EEGs signals using Persistent Homology; then, we analyse the space by Persistent entropy, a global topological feature, in order to classify healthy and epileptic signals. Results The performance of the resulting one-feature-based linear topological classifier is tested by analysing the Physionet dataset. The quality of classification is evaluated in terms of the Area Under Curve (AUC) of the receiver operating characteristic curve. It is shown that the linear topological classifier has an AUC equal to 97.2% while the performance of a classifier based on Sample Entropy has an AUC equal to 62.0%

Using Topological Data Analysis for diagnosis pulmonary embolism

Pulmonary Embolism (PE) is a common and potentially lethal condition. Most patients die within the first few hours from the event. Despite diagnostic advances, delays and underdiagnosis in PE are common.To increase the diagnostic performance in PE, current diagnostic work-up of patients with suspected acute pulmonary embolism usually starts with the assessment of clinical pretest probability using plasma d-Dimer measurement and clinical prediction rules. The most validated and widely used clinical decision rules are the Wells and Geneva Revised scores. We aimed to develop a new clinical prediction rule (CPR) for PE based on topological data analysis and artificial neural network. Filter or wrapper methods for features reduction cannot be applied to our dataset: the application of these algorithms can only be performed on datasets without missing data. Instead, we applied Topological data analysis (TDA) to overcome the hurdle of processing datasets with null values missing data. A topological network was developed using the Iris software (Ayasdi, Inc., Palo Alto). The PE patient topology identified two ares in the pathological group and hence two distinct clusters of PE patient populations. Additionally, the topological netowrk detected several sub-groups among healthy patients that likely are affected with non-PE diseases. TDA was further utilized to identify key features which are best associated as diagnostic factors for PE and used this information to define the input space for a back-propagation artificial neural network (BP-ANN). It is shown that the area under curve (AUC) of BP-ANN is greater than the AUCs of the scores (Wells and revised Geneva) used among physicians. The results demonstrate topological data analysis and the BP-ANN, when used in combination, can produce better predictive models than Wells or revised Geneva scores system for the analyzed cohortComment: 18 pages, 5 figures, 6 tables. arXiv admin note: text overlap with arXiv:cs/0308031 by other authors without attributio

On the Intersection of Explainable and Reliable AI for physical fatigue prediction

In the era of Industry 4.0, the use of Artificial Intelligence (AI) is widespread in occupational settings. Since dealing with human safety, explainability and trustworthiness of AI are even more important than achieving high accuracy. eXplainable AI (XAI) is investigated in this paper to detect physical fatigue during manual material handling task simulation. Besides comparing global rule-based XAI models (LLM and DT) to black-box models (NN, SVM, XGBoost) in terms of performance, we also compare global models with local ones (LIME over XGBoost). Surprisingly, global and local approaches achieve similar conclusions, in terms of feature importance. Moreover, an expansion from local rules to global rules is designed for Anchors, by posing an appropriate optimization method (Anchors coverage is enlarged from an original low value, 11%, up to 43%). As far as trustworthiness is concerned, rule sensitivity analysis drives the identification of optimized regions in the feature space, where physical fatigue is predicted with zero statistical error. The discovery of such “non-fatigue regions” helps certifying the organizational and clinical decision making

Identification of functional sets in mechanical assembly models

Easy retrieval of product data and related information is extremely important for knowledge and data reuse in new product development. Nowadays the adoption of PDM (Product Data Management) systems makes the reuse easy providing means for documenting all the data related to a product, thus making possible their retrieval through the inserted metadata. Unfortunately, large datasets are available in which data are not documented; therefore, retrieval systems based on content similarities according to different criteria would be beneficial. In this paper, we face the problem of identifying functional sets. The main difficulties relay in the variety in terms of shape and representation of the components that can achieve the same functionality. To overcome this issue, we present a multi-step approach, which considers a component embedded in the whole assembly model, improving component characterization

CAD Assembly Retrieval and Browsing

This paper presents a method for the retrieval and inspection of similar CAD assemblies in a database according to a user query. The method exploits the information on components’ shape and relationships (e.g. contacts and regular patterns) automatically extracted from the STEP descriptions of CAD assemblies and stored in the so-called Enriched Assembly Model. It evaluates the similarity among assemblies in terms of the components’ shapes and joints. A graphical interface highlighting the elements in the assembly similar to the query has been developed to facilitate the inspection of the obtained results