308,369 research outputs found
Isometric Sliced Inverse Regression for Nonlinear Manifolds Learning
[[abstract]]Sliced inverse regression (SIR) was developed to find effective linear dimension-reduction directions for exploring the intrinsic structure of the high-dimensional data. In this study, we present isometric SIR for nonlinear dimension reduction, which is a hybrid of the SIR method using the geodesic distance approximation. First, the proposed method computes the isometric distance between data points; the resulting distance matrix is then sliced according to K-means clustering results, and the classical SIR algorithm is applied. We show that the isometric SIR (ISOSIR) can reveal the geometric structure of a nonlinear manifold dataset (e.g., the Swiss roll). We report and discuss this novel method in comparison to several existing dimension-reduction techniques for data visualization and classification problems. The results show that ISOSIR is a promising nonlinear feature extractor for classification applications.[[incitationindex]]SCI[[booktype]]紙本[[booktype]]電子
Regression Driven F--Transform and Application to Smoothing of Financial Time Series
In this paper we propose to extend the definition of fuzzy transform in order
to consider an interpolation of models that are richer than the standard fuzzy
transform. We focus on polynomial models, linear in particular, although the
approach can be easily applied to other classes of models. As an example of
application, we consider the smoothing of time series in finance. A comparison
with moving averages is performed using NIFTY 50 stock market index.
Experimental results show that a regression driven fuzzy transform (RDFT)
provides a smoothing approximation of time series, similar to moving average,
but with a smaller delay. This is an important feature for finance and other
application, where time plays a key role.Comment: IFSA-SCIS 2017, 5 pages, 6 figures, 1 tabl
Investigating complex networks with inverse models: analytical aspects of spatial leakage and connectivity estimation
Network theory and inverse modeling are two standard tools of applied
physics, whose combination is needed when studying the dynamical organization
of spatially distributed systems from indirect measurements. However, the
associated connectivity estimation may be affected by spatial leakage, an
artifact of inverse modeling that limits the interpretability of network
analysis. This paper investigates general analytical aspects pertaining to this
issue. First, the existence of spatial leakage is derived from the topological
structure of inverse operators. Then, the geometry of spatial leakage is
modeled and used to define a geometric correction scheme, which limits spatial
leakage effects in connectivity estimation. Finally, this new approach for
network analysis is compared analytically to existing methods based on linear
regressions, which are shown to yield biased coupling estimates.Comment: 19 pages, 4 figures, including 5 appendices; v2: minor edits, 1
appendix added; v3: expanded version, v4: minor edit
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