Extracting Hidden Information from Knowledge Networks

Maslov, Sergei; Zhang, Yi Cheng

doi:10.1103/physrevlett.87.248701

Cited by 98 publications

(94 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this particular case, we can compute the mean level spacing explicitly: 8) which converges to the WL Wigner surmise value for γ → ∞:…”

Section: The Wigner Surmise In the Bulkmentioning

confidence: 99%

“…It has since appeared in many different contexts, such as multivariate statistical data analysis [2], analysis of the capacity of channels with multiple antennae and receivers [3], low-energy Quantum Chromodynamics and other gauge theories [4,5], Quantum Gravity [6,7], knowledge networks [8], finance [9] and also in statistical physics problems, such as a class of (1 + 1)-dimensional directed polymer problems [10]. Very recent analytical results include statistics of large deviations for the maximum eigenvalue [11] and distributions related to entangled random pure states [12].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Power law deformation of Wishart–Laguerre ensembles of random matrices

Akemann¹,

Vivo²

2008

J. Stat. Mech.

View full text Add to dashboard Cite

We introduce a one-parameter deformation of the Wishart-Laguerre or chiral ensembles of positive definite random matrices with Dyson index β = 1, 2 and 4. Our generalised model has a fat-tailed distribution while preserving the invariance under orthogonal, unitary or symplectic transformations. The spectral properties are derived analytically for finite matrix size N × M for all three β, in terms of the orthogonal polynomials of the standard Wishart-Laguerre ensembles. For large-N in a certain double scaling limit we obtain a generalised Marčenko-Pastur distribution on the macroscopic scale, and a generalised Bessel-law at the hard edge which is shown to be universal. Both macroscopic and microscopic correlations exhibit power-law tails, where the microscopic limit depends on β and the difference M − N . In the limit where our parameter governing the power-law goes to infinity we recover the correlations of the Wishart-Laguerre ensembles. To illustrate these findings the generalised Marčenko-Pastur distribution is shown to be in very good agreement with empirical data from financial covariance matrices.

show abstract

“…In this particular case, we can compute the mean level spacing explicitly: 8) which converges to the WL Wigner surmise value for γ → ∞:…”

Section: The Wigner Surmise In the Bulkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Power law deformation of Wishart–Laguerre ensembles of random matrices

Akemann¹,

Vivo²

2008

J. Stat. Mech.

View full text Add to dashboard Cite

show abstract

“…Representative recommending techniques developed by the computer science community include collaborative filtering [11,12], singular value decomposition [13,14], content-based analysis [15], latent semantic models [16], latent Dirichlet allocation [17], principle component analysis [18], and so on. Recently, physical perspectives and approaches have also found applications in designing recommendation algorithms, including iterative refinements [19][20][21], random-walk-based algorithms [22][23][24][25][26] and heat conduction algorithms [5,27]. Generally speaking, the performance of the above-mentioned algorithms can be further improved by using a hybrid method [28,29] or ensemble learning [30], or by exploiting additional information, like time [31] and tags [32].…”

Section: Introductionmentioning

confidence: 99%

Negative ratings play a positive role in information filtering

Zeng

Zhu

Lü

et al. 2011

Physica A: Statistical Mechanics and its Applications

View full text Add to dashboard Cite

The explosive growth of information asks for advanced information filtering techniques to solve the so-called information overload problem. A promising way is the recommender system which analyzes the historical records of users' activities and accordingly provides personalized recommendations. Most recommender systems can be represented by userobject bipartite networks where users can evaluate and vote for objects, and ratings such as ''dislike'' and ''I hate it'' are treated straightforwardly as negative factors or are completely ignored in traditional approaches. Applying a local diffusion algorithm on three benchmark data sets, MovieLens, Netflix and Amazon, our study arrives at a very surprising result, namely the negative ratings may play a positive role especially for very sparse data sets. In-depth analysis at the microscopic level indicates that the negative ratings from less active users to less popular objects could probably have positive impacts on the recommendations, while the ones connecting active users and popular objects mostly should be treated negatively. We finally outline the significant relevance of our results to the two long-term challenges in information filtering: the sparsity problem and the coldstart problem.

show abstract

“…Yet the first step will be to check, whether in such a context the power map will still provide the desired noise reduction (see [36] as well); thus in the next section we shall test, in a simple model, whether noise reduction by means of the power map is effective for singular correlation matrices. Next we proceed to the main part of our results, which will be to analyze the behavior of Wishart ensembles (WE) of singular matrices [38,39], including correlated Wishart ensembles (CWE), under the power map deformations.…”

Section: Introductionmentioning

confidence: 99%

Emerging spectra of singular correlation matrices under small power-map deformations

2013

View full text Add to dashboard Cite

Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an assumption of varying and often dubious validity. The validity of the assumption improves as shorter time series are used. If many time series are used this implies an analysis of highly singular correlation matrices. We attack this problem by using the so called power map which was introduced to reduce noise. Its non-linearity breaks the degeneracy of the zero eigenvalues and we analyze the sensitivity of the so emerging spectra to correlations. This sensitivity will be demonstrated for uncorrelated and correlated Wishart ensembles.

show abstract

Extracting Hidden Information from Knowledge Networks

Cited by 98 publications

References 6 publications

Power law deformation of Wishart–Laguerre ensembles of random matrices

Power law deformation of Wishart–Laguerre ensembles of random matrices

Negative ratings play a positive role in information filtering

Emerging spectra of singular correlation matrices under small power-map deformations

Contact Info

Product

Resources

About