Isometric Multi-Manifolds Learning

Isometric feature mapping (Isomap) is a promising manifold learning method. However, Isomap fails to work on data which distribute on clusters in a single manifold or manifolds. Many works have been done on extending Isomap to multi-manifolds learning. In this paper, we first proposed a new multi-manifolds learning algorithm (M-Isomap) with help of a general procedure. The new algorithm preserves intra-manifold geodesics and multiple inter-manifolds edges precisely. Compared with previous methods, this algorithm can isometrically learn data distributed on several manifolds. Secondly, the original multi-cluster manifold learning algorithm first proposed in \cite{DCIsomap} and called D-C Isomap has been revised so that the revised D-C Isomap can learn multi-manifolds data. Finally, the features and effectiveness of the proposed multi-manifolds learning algorithms are demonstrated and compared through experiments

An Explicit Nonlinear Mapping for Manifold Learning

Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data manifold to the output embedding. This prohibits the application of manifold learning methods in many practical problems such as classification and target detection. Previously, in order to provide explicit mappings for manifold learning methods, many methods have been proposed to get an approximate explicit representation mapping with the assumption that there exists a linear projection between the high-dimensional data samples and their low-dimensional embedding. However, this linearity assumption may be too restrictive. In this paper, an explicit nonlinear mapping is proposed for manifold learning, based on the assumption that there exists a polynomial mapping between the high-dimensional data samples and their low-dimensional representations. As far as we know, this is the first time that an explicit nonlinear mapping for manifold learning is given. In particular, we apply this to the method of Locally Linear Embedding (LLE) and derive an explicit nonlinear manifold learning algorithm, named Neighborhood Preserving Polynomial Embedding (NPPE). Experimental results on both synthetic and real-world data show that the proposed mapping is much more effective in preserving the local neighborhood information and the nonlinear geometry of the high-dimensional data samples than previous work

Intrinsic dimension estimation of data by principal component analysis

Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however, becomes ineffective when data have a nonlinear structure. In this paper, we propose a new PCA-based method to estimate intrinsic dimension of data with nonlinear structures. Our method works by first finding a minimal cover of the data set, then performing PCA locally on each subset in the cover and finally giving the estimation result by checking up the data variance on all small neighborhood regions. The proposed method utilizes the whole data set to estimate its intrinsic dimension and is convenient for incremental learning. In addition, our new PCA procedure can filter out noise in data and converge to a stable estimation with the neighborhood region size increasing. Experiments on synthetic and real world data sets show effectiveness of the proposed method.Comment: 8 pages, submitted for publicatio

Towards A Deep Insight into Landmark-based Visual Place Recognition: Methodology and Practice

In this paper, we address the problem of landmark-based visual place recognition. In the state-of-the-art method, accurate object proposal algorithms are first leveraged for generating a set of local regions containing particular landmarks with high confidence. Then, these candidate regions are represented by deep features and pairwise matching is performed in an exhaustive manner for the similarity measure. Despite its success, conventional object proposal methods usually produce massive landmark-dependent image patches exhibiting significant distribution variance in scale and overlap. As a result, the inconsistency in landmark distributions tends to produce biased similarity between pairwise images yielding the suboptimal performance. In order to gain an insight into the landmark-based place recognition scheme, we conduct a comprehensive study in which the influence of landmark scales and the proportion of overlap on the recognition performance is explored. More specifically, we thoroughly study the exhaustive search based landmark matching mechanism, and thus derive three-fold important observations in terms of the beneficial effect of specific landmark generation strategies. Inspired by the above observations, a simple yet effective dense sampling based scheme is presented for accurate place recognition in this paper. Different from the conventional object proposal strategy, we generate local landmarks of multiple scales with uniform distribution from entire image by dense sampling, and subsequently perform multi-scale fusion on the densely sampled landmarks for similarity measure. The experimental results on three challenging datasets demonstrate that the recognition performance can be significantly improved by our efficient method in which the landmarks are appropriately produced for accurate pairwise matching

Chiral orbital magnetism of pp-orbital bosons in optical lattices

Chiral magnetism is a fascinating quantum phenomena that has been found in low-dimensional magnetic materials. It is not only interesting for understanding the concept of chirality, but also important for potential applications in spintronics. Past studies show that chiral magnets require both lack of the inversion symmetry and spin-orbit coupling to induce the Dzyaloshinskii-Moriya (DM) interaction. Here we report that the combination of inversion symmetry breaking and quantum degeneracy of orbital degrees of freedom will provide a new paradigm to achieve the chiral orbital magnetism. By means of the density matrix renormalization group (DMRG) calculation, we demonstrate that the chiral orbital magnetism can be found when considering bosonic atoms loaded in the $p$-band of an optical lattice in the Mott regime. The high tunability of our scheme is also illustrated through simply manipulating the inversion symmetry of the system for the cold atom experimental conditions.Comment: 7 pages, 4 figures, including Supplementary Materia

Probing the dynamical behavior of dark energy

We investigate dynamical behavior of the equation of state of dark energy $w_{de}$ by employing the linear-spline method in the region of low redshifts from observational data (SnIa, BAO, CMB and 12 $H(z)$ data). The redshift is binned and $w_{de}$ is approximated by a linear expansion of redshift in each bin. We leave the divided points of redshift bins as free parameters of the model, the best-fitted values of divided points will represent the turning positions of $w_{de}$ where $w_{de}$ changes its evolving direction significantly (if there exist such turnings in our considered region). These turning points are natural divided points of redshift bins, and $w_{de}$ between two nearby divided points can be well approximated by a linear expansion of redshift. We find two turning points of $w_{de}$ in $z\in(0,1.8)$ and one turning point in $z\in (0,0.9)$, and $w_{de}(z)$ could be oscillating around $w=-1$. Moreover, we find that there is a $2\sigma$ deviation of $w_{de}$ from -1 around $z=0.9$ in both correlated and uncorrelated estimates.Comment: Accepted by JCAP; 16 pages, 3 figure

Features in Dark Energy Equation of State and Modulations in the Hubble Diagram

We probe the time dependence of the dark energy equation of state (EOS) in light of three-year WMAP (WMAP3) and the combination with other tentative cosmological observations from galaxy clustering (SDSS) and Type Ia Supernova (SNIa). We mainly focus on cases where the EOS is oscillating or with local bumps. By performing a global analysis with the Markov Chain Monte Carlo (MCMC) method, we find the current observations, in particular the WMAP3 + SDSS data combination, allow large oscillations of the EOS which can leave oscillating features on the (residual) Hubble diagram, and such oscillations are potentially detectable by future observations like SNAP, or even by the CURRENTLY ONGOING SNIa observations. Local bumps of dark energy EOS can also leave imprints on CMB, LSS and SNIa. In cases where the bumps take place at low redshifts and the effective EOS are close to -1, CMB and LSS observations cannot give constraints on such possibilities. However, geometrical observations like (future) SNIa can possibly detect such features. On the other hand when the local bumps take place at higher redshifts beyond the detectability of SNIa, future precise observations like Gamma-ray bursts, CMB and LSS may possibly detect such features. In particular, we find that bump-like dark energy EOS on high redshifts might be responsible for the features of WMAP on ranges l \sim 30-50, which is interesting and deserves addressing further.Comment: 14 pages, 7 figures Revtex

Scalar graviton in the healthy extension of Ho\v{r}ava-Lifshitz theory

In this note we study the linear dynamics of scalar graviton in a de Sitter background in the infrared limit of the healthy extension of Ho\v{r}ava-Lifshitz gravity with the dynamical critical exponent $z=3$. Both our analytical and numerical results show that the non-zero Fourier modes of scalar graviton oscillate with an exponentially damping amplitude on the sub-horizon scale, while on the super-horizon scale, the phases are frozen and they approach to some asymptotic values. In addition, as the case of the non-zero modes on super-horizon scale, the zero mode also initially decays exponentially and then approaches to an asymptotic constant value.Comment: 12 pages, 1 figure, ghost free condition addressed, accepted by Phys. Rev.

Acoustic signatures in the Cosmic Microwave Background bispectrum from primordial magnetic fields

Using the full radiation transfer function, we numerically calculate the CMB angular bispectrum seeded by the compensated magnetic scalar density mode. We find that, for the string inspired primordial magnetic fields characterized by index $n_B=-2.9$ and mean-field amplitude B_{\lam}=9{\rm nG}, the angular bispectrum is dominated by two primordial magnetic shapes. The first magnetic shape looks similar to the one from local-type primordial curvature perturbations, so both the amplitude and profile of the Komatsu-Spergel estimator (reduced bispectrum) seeded by this shape are almost the same as those of the primary CMB anisotropies. However, for different parameter sets ($l_1,l_2$), this "local-type" reduced bispectrum oscillates around different asymptotic values in the high-$l_3$ regime because of the effect of the Lorentz force, which is exerted by the primordial magnetic fields on the charged baryons. This feature is different from the standard case where all modes approach to zero asymptotically in the high-$l$ limit. On the other hand, the second magnetic shape appears only in the primordial magnetic field model. The amplitude of the Komatsu-Spergel estimator sourced by the second shape diverges in the low-$l$ regime because of the negative slope of shape. In the high-$l$ regime, this amplitude is approximately equal to that of the first estimator, but with a reversal phase.Comment: 37 pages, 11 figures, version published in JHE

Cosmic ray e+e−e^{+} e^{-} spectrum excess and peak feature observed by the DAMPE experiment from dark matter

The Chinese satellite Wukong, also known as the DArk Matter Particle Explorer (DAMPE), has released its observation data of the cosmic ray (CR) electrons and positrons. The data shows an excess in the energy spectrum up to TeV energy, and possibly a peak-like fine structure at \sim 1.4 \TeV. We investigate the scenario that the source of the excess comes from dark matter annihilation or decay. We find that the annihilation or decay of diffuse dark matter particles in the Galactic halo can give excellent ($W^+W^-$ channel) or at least good (double $\tau^+\tau^-$ channel) fits to the broad excess. However, the annihilation cross-section is 10^{-23}\cm^3s^{-1}, larger than required for getting the correct relic abundance. We then study whether the narrow peak at \sim 1.4\TeV could be explained by a nearby subhalo, which thanks to the smaller distance, could supply $e^+e^-$ within a narrow energy range. We find that in order to produce a peak width less than the energy bin width (0.2 TeV), the source must be located within r\lsim 0.53~\kpc. Our global fit models do not produce the peak-like feature, instead at 1.4 TeV the spectrum show either a slope or a cliff-like feature. However, if less than optimal fit is allowed, the peak-like feature could be generated. Furthermore, an excellent fit with peak could be obtained with model B if the background is rescaled. If the dark matter decay and annihilation rates are determined using the broad excess, the required subhalo mass $\sim10^{5}~M_\odot$ for decay model, or \sim10^{4.5}\Msun for annihilation model and a shallower density profile slope $\alpha=1.2$, or \sim10^{2.5}\Msun for the steep density profile $\alpha=1.7$. However, the probability for the existence of a such nearby subhalo as massive as given above is very low.Comment: 17 pages, 17 figures, replaced with PRD accepted versio