Search Results (4)

Classic machine learning and regime identification methods applied to financial time series lack theoretical guarantees and exhibit systematic failure modes: heavy-tails invalidate moment-based geometry, rendering distances and centroids dominated by extremes or unstable; jumps violate smoothness, destabilizing local regressions, kernel methods, and gradient-based learning; and non-stationarity disrupts neighborhood relations, so distances in classical feature spaces no longer reflect meaningful proximity. To address these challenges, we propose a topology-based machine-learning framework grounded on probabilistic reconstruction of state-space geometry, which replaces moment- and smoothness-dependent representations with deformation-stable summaries of state-space geometry, preserving neighborhoods, adjacency, and topology. The finite-sample validity of homeomorphic state-space reconstruction, required for topology-based machine learning, is assessed through numerical studies on synthetic data with heavy tails, jumps, and known ground-truth regimes. Further diagnostics of local invertibility and bounded geometric distortion quantify when embedding windows are consistent with local diffeomorphic behavior, enabling metric-sensitive, geometry-aware learning. Clustering of Hilbert-space summaries accurately recovers underlying market tail-risk regimes with robust results across selected filtrations. Temporal, feature-space, and cluster-label null tests confirm that topology-based clustering captures genuine topological structure rather than noise or artifacts, and encodes temporal dependencies at local, mesoscopic, and network levels associated with market regimes. Full article

Fault diagnosis of rotating machinery plays an important role in modern industrial machines. In this paper, a modified sparse Bayesian classification model (i.e., Standard_SBC) is utilized to construct the fault diagnosis system of rotating machinery. The features are extracted and adopted as the input of the SBC-based fault diagnosis system, and the kernel neighborhood preserving embedding (KNPE) is proposed to fuse the features. The effectiveness of the fault diagnosis system of rotating machinery based on KNPE and Standard_SBC is validated by utilizing two case studies: rolling bearing fault diagnosis and rotating shaft fault diagnosis. Experimental results show that base on the proposed KNPE, the feature fusion method shows superior performance. The accuracy of case1 and case2 is improved from 93.96% to 99.92% and 98.67% to 99.64%, respectively. To further prove the superiority of the KNPE feature fusion method, the kernel principal component analysis (KPCA) and relevance vector machine (RVM) are utilized, respectively. This study lays the foundation for the feature fusion and fault diagnosis of rotating machinery. Full article

Synthetic aperture radar (SAR) image classification is an important task in remote sensing applications. However, it is challenging due to the speckle embedding in SAR imaging, which significantly degrades the classification performance. To address this issue, a new SAR image classification framework based on multi-feature fusion and adaptive kernel combination is proposed in this paper. Expressing pixel similarity by non-negative logarithmic likelihood difference, the generalized neighborhoods are newly defined. The adaptive kernel combination is designed on them to dynamically explore multi-feature information that is robust to speckle noise. Then, local consistency optimization is further applied to enhance label spatial smoothness during classification. By simultaneously utilizing adaptive kernel combination and local consistency optimization for the first time, the texture feature information, context information within features, generalized spatial information between features, and complementary information among features is fully integrated to ensure accurate and smooth classification. Compared with several state-of-the-art methods on synthetic and real SAR images, the proposed method demonstrates better performance in visual effects and classification quality, as the image edges and details are better preserved according to the experimental results. Full article

Face recognition is one of the most popular techniques to achieve the goal of figuring out the identity of a person. This study has been conducted to develop a new non-linear subspace learning method named “supervised kernel locality-based discriminant neighborhood embedding,” which performs data classification by learning an optimum embedded subspace from a principal high dimensional space. In this approach, not only nonlinear and complex variation of face images is effectively represented using nonlinear kernel mapping, but local structure information of data from the same class and discriminant information from distinct classes are also simultaneously preserved to further improve final classification performance. Moreover, in order to evaluate the robustness of the proposed method, it was compared with several well-known pattern recognition methods through comprehensive experiments with six publicly accessible datasets. Experiment results reveal that our method consistently outperforms its competitors, which demonstrates strong potential to be implemented in many real-world systems. Full article