Search

A major archetype of artificial intelligence is developing algorithms facilitating temporal efficiency and accuracy while boosting the generalization performance. Even with the latest developments in machine learning, a key limitation has been the inefficient feature extraction from the initial data, which is essential in performance optimization. Here, we introduce a feature extraction method inspired by sensory cortical networks in the brain. Dubbed as bioinspired cortex, the algorithm provides convergence to orthogonal features from streaming signals with superior computational efficiency while processing data in compressed form. We demonstrate the performance of the new algorithm using artificially created complex data by comparing it with the commonly used traditional clustering algorithms, such as Birch, GMM, and K-means. While the data processing time is significantly reduced, seconds versus hours, encoding distortions remain essentially the same in the new algorithm providing a basis for better generalization. Although we show herein the superior performance of the cortex model in clustering and vector quantization, it also provides potent implementation opportunities for machine learning fundamental components, such as reasoning, anomaly detection and classification in large scope applications, e.g., finance, cybersecurity, and healthcare., Comment: 17 pages, 6 Figures in Main Text, 5 Figures in Methods plus Appendix, and 54 references cited

The generalized mean-square fractional integrals $\mathcal{J}_{\rho,\lambda,u+;\omega}^{\sigma}$ and $\mathcal{J}_{\rho,\lambda,v-;\omega}^{\sigma}$ of the stochastic process $X$ are introduced. Then, for Jensen-convex and strongly convex stochastic proceses, the generalized fractional Hermite--Hadamard inequality is establish via generalized stochastic fractional integrals., Comment: Published at https://doi.org/10.15559/18-VMSTA117 in the Modern Stochastics: Theory and Applications (https://vmsta.org/) by VTeX (http://www.vtex.lt/)

In the present work we give several new integral inequalities of the type Riemann-Liouville fractional integral via Montgomery identities integrals., Comment: 6 pages

In this paper, using functions whose derivatives absolute values are strongly $\Phi_{h}$-convex with modulus c>0, we obtained new inequalities releted to the right and left side of Hermite-Hadamard inequality by using new integral identities, Comment: 15 pages

In this paper, we extend some estimates of the right hand side of a Hermite- Hadamard type inequality for nonconvex functions whose second derivatives absolute values are \phi-convex, log-\phi-convex, and quasi-\phi-convex., Comment: arXiv admin note: text overlap with arXiv:1203.2282

In this paper, we introduce the notion of log-{\varphi}-convex functions and present some properties and representation of such functions. We obtain some results of the Hermite Hadamard inequalities for product log-{\varphi}-convex functions.

In this paper, we introduce the notion of strongly {\varphi}-convex functions with respect to c>0 and present some properties and representation of such functions. We obtain a characterization of inner product spaces involving the notion of strongly {\varphi}-convex functions. Finaly, a version of Hermite Hadamard-type inequalities for strongly {\varphi}-convex functions are established.

In this paper, we extend some estimates of the left hand side of a Hermite- Hadamard type inequality for nonconvex functions whose derivatives absolute values are preinvex and log-preinvex.

In this paper, we have established Ostrowski type inequalities involving the right Caputo fractional derivatives belong to L_{p} spaces (1\leq p \leq \infty) via the right Caputo fractional Taylor formula with integral remainder.

In this paper, we use the Riemann-Liouville fractional integrals to establish some new integral inequalities of Ostrowski-Gr\"uss type. From our results, the classical Ostrowski-Gr\"uss type inequalities can be deduced as some special cases.

In this paper, we improve and further generalize some Ostrowski-Gr\"uss type inequalities for the fractional integrals by using new Montogomery identities.

In this paper, the notation of strongly log-convex functions with respect to c>0 is introduced and versions of Hermite Hadamard-type inequalities for strongly logarithmic convex functions are established.

In this paper, new integral inequalities of Hadamard type involving several differentiable \Phi-r-convex functions are given.

In this paper, we extend the weighted Montogomery identities for the Riemann-Liouville fractional integrals. We also use this Montogomery identities to establish some new Ostrowski type integral inequalities.

In this paper, we extend some estimates of the right and left hand side of a Hermite-Hadamard type inequality for nonconvex functions whose derivatives absolute values are \Phi-convex and quasi-\Phi-convex was introduced by Noor in Noor1., Comment: Mathematical Sciences And Applications E-Notes, in press. arXiv admin note: substantial text overlap with arXiv:1204.0923; and overlap with arXiv:1205.6657 by other authors

This paper has been withdrawn by the author due to a missing figure, Comment: This paper has been withdrawn by the author due to a missing figure

Some new inequalities of Ostrowski type for twice differentiable mappings whose derivatives in absolute value are s-convex in the second sense are given.Applications for special means are also provided.

In this paper, we establish several new inequalities for some twice differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided., Comment: Accepted by Nonlinear Analysis Forum