arXiv research

The paper challenges the validity of cluster validity measures in unsupervised learning.

Develops a new cluster validity index to find multiple optimal cluster numbers.

Study benchmarks 26 clustering validity measures.

New cluster validity index detects optimal number of clusters and secondary options.

New validity index for fuzzy-possibilistic c-means clustering.

Validation is one of the most important aspects of clustering, but most approaches have been batch methods. Recently, interest has grown in providing incremental alternatives. This paper extends the incremental cluster validity index (iCVI) family to include incremental versions of Calinski-Harabasz (iCH), I index and …

Introduces BCVI, a Bayesian cluster validity index for better cluster selection.

We generalize Roe's index theorem for graded generalized Dirac operators on amenable manifolds to multigraded elliptic uniform pseudodifferential operators. The generalization will follow from a local index theorem that is valid on any manifold of bounded geometry. This local formula incorporates the uniform estimates …

XGBoost predicts NEPSE Index log returns with low error and high directional accuracy.

Local constancy of index for certain gradient mappings proved.

This is an expository paper which gives a proof of the Atiyah-Singer index theorem for Dirac operators, presenting the theorem as a computation of the K-homology of a point. This paper and its follow up ("K-homology and index theory II: Elliptic Operators") was written to clear up basic points about index theory that a…

Proposes a method for valid inference in GPLSIMs with longitudinal data.

This is an expository paper which gives a proof of the Atiyah-Singer index theorem for elliptic operators. Specifcally, we compute the geometric K-cycle that corresponds to the analytic K-cycle determined by the operator. This paper and its companion ("K-homology and index theory II: Dirac Operators") was written to cl…

CDL index improves clustering validation for non-convex data.

Kernelized bandit algorithm tackles adaptive contextual bandits with single-index models.

Cluster analysis is used to explore structure in unlabeled data sets in a wide range of applications. An important part of cluster analysis is validating the quality of computationally obtained clusters. A large number of different internal indices have been developed for validation in the offline setting. However, thi…

CAF-HFCM automatically forms a cluster hierarchy and optimizes the number of clusters without trial-and-validation.

Novel method for multiclass ROC curves using multidimensional Gini index.

A new concordance loss improves model performance and reliability in survival prediction.

Prediction of future movement of stock prices has been a subject matter of many research work. In this work, we propose a hybrid approach for stock price prediction using machine learning and deep learning-based methods. We select the NIFTY 50 index values of the National Stock Exchange of India, over a period of four …

Configuration spaces for computer systems can be challenging for traditional and automatic tuning strategies. Injecting task-specific knowledge into the tuner for a task may allow for more efficient exploration of candidate configurations. We apply this idea to the task of index set selection to accelerate database wor…

Paper introduces SCI to distinguish market signals from coordination.

The paper evaluates index-based allocation policies using data from randomized control trials.

In this paper we formulate a regression problem to predict realized volatility by using option price data and enhance VIX-styled volatility indices' predictability and liquidity. We test algorithms including regularized regression and machine learning methods such as Feedforward Neural Networks (FNN) on S&P 500 Index a…

AGMMNs improve learning of copula models by adaptively selecting kernels.

Paper introduces a new robust method for estimating Pareto tail index from grouped data.

We find many examples of compact Riemannian manifolds $(M,g)$ whose closed minimal hypersurfaces satisfy a lower bound on their index that is linear in their first Betti number. Moreover, we show that these bounds remain valid when the metric $g$ is replaced with $g'$ in a neighbourhood of $g$. Our examples $(M,g)$ con…

A new method tracks index using topological data analysis for sparse portfolios.

Let $M$ be a compact manifold. and $D$ a Dirac type differential operator on $M$. Let $A$ be a $C^*$-algebra. Given a bundle $W$ of $A$-modules over $M$ (with connection), the operator $D$ can be twisted with this bundle. One can then use a trace on $A$ to define numerical indices of this twisted operator. We prove an …

Gradient descent dynamics studied for DEQs in linear and single-index models.

ASRI index detects crypto market risks with high precision and lead time.

Well-defined formal definitions for sentiment and opinion are extended to incorporate the necessary elements to provide a formal quantitative definition of reputation. This definition takes the form of a time-based index, in which each element is a function of a collection of opinions mined during a given time period. …

While invasively recorded brain activity is known to provide detailed information on motor commands, it is an open question at what level of detail information about positions of body parts can be decoded from non-invasively acquired signals. In this work it is shown that index finger positions can be differentiated fr…

A new CVI called DSI evaluates clustering results without true labels.

This paper proposes a governing equation for stock market indexes that accounts for non-stationary effects. This is a linear Fokker-Planck equation (FPE) that describes the time evolution of the probability distribution function (PDF) of the price return. By applying Ito's lemma, this FPE is associated with a stochasti…

Rigidity theorem for critical points of Allen-Cahn equation on S³.

iCVI-ARTMAP accelerates clustering with adaptive resonance theory and validity indices.

Heavy-tailed distributions emerge in SGD's parameter evolution.

It has been noticed that some external CVIs exhibit a preferential bias towards a larger or smaller number of clusters which is monotonic (directly or inversely) in the number of clusters in candidate partitions. This type of bias is caused by the functional form of the CVI model. For example, the popular Rand index (R…

HD-BWDM improves clustering validation in high-dimensional data.

The authors previously found a model of universal quantum computation by making use of the coset structure of subgroups of a free group $G$ with relations. A valid subgroup $H$ of index $d$ in $G$ leads to a 'magic' state $\left|ψ\right\rangle$ in $d$-dimensional Hilbert space that encodes a minimal informationally com…

Cluster analysis is widely used in the areas of machine learning and data mining. Fuzzy clustering is a particular method that considers that a data point can belong to more than one cluster. Fuzzy clustering helps obtain flexible clusters, as needed in such applications as text categorization. The performance of a clu…

Unified framework predicts S&P500 index direction using transfer learning and causal graph.

New method optimizes policies without assuming known link functions between preferences and rewards.

Paper develops new conformal prediction methods for sum or average of unknown labels.

Single Index Models (SIMs) are simple yet flexible semi-parametric models for classification and regression. Response variables are modeled as a nonlinear, monotonic function of a linear combination of features. Estimation in this context requires learning both the feature weights, and the nonlinear function. While met…

Paper uses deep Ritz method for solving stationary Schrödinger equation, proving convergence and feature emergence.

Over the years, there has been growing interest in using Machine Learning techniques for biomedical data processing. When tackling these tasks, one needs to bear in mind that biomedical data depends on a variety of characteristics, such as demographic aspects (age, gender, etc) or the acquisition technology, which migh…