Publications

• Selected publications
• Ph.D. thesis
• Papers in preparation

Downloadable publications

A.M.Nikiforov, G.V. Nikiforova (1992) Statistical analysis with ARCaDa. Moscow, "Dialogue", 171 + 30 p.

• Download the book in Russian (Word 5.0)
• Download the ARCaDa system (DOS, English version with the tutorial)

A.M. Nikiforov (1991) Statistical analysis of incomplete data: theory, techniques and software. Preface and supplement to the Russian edition of Little R.J.A., Rubin D.B. Statistical Analysis with Missing Data. Moscow, Finansy i Statistika, pp. 3-5, 284-332.

• Download the paper (in English)
• Download the paper (in Russian, the full version)
• Download the EM-algorithm for multivariate normal distribution

A.M. Nikiforov (1994) Algorithm AS 288: Exact two-sample Smirnov test for arbitrary distributions. Appl.Stat., vol.43, No. 1. pp.265-270.

• Download detailed version of the paper (Postscript)
• Download algorithm with driver programs etc.
• Download additional remarks and comments

Update (June 2006): be cautious when using the GSMIRN version of the routine for large samples (use instead GSMIRN2 for sample sizes over approx. 10,000). Thanks to Diab Jerius (http://hea-www.harvard.edu/~dj/) for discovering the effect. Click here for analysis of the problem.

A.M.Nikiforov (1991) Robustness of the nonparametric approach in statistical analysis with missing data. The Forth USSR seminar "Software and Algorithms for applied multivariate statistical analysis" in Cahkadzor (Armenia). Moscow, CEMI. Part 2, pp. 200-202.

A new type of robustness is introduced. Nonparametric procedures require much weaker assumptions on gap distributions than their parametric counterparts, which require normally MAR or MCAR conditions to hold.
• Download the abstract (MS Word)

M. Malioutov, A. M. Nikiforov, R. Protassov (2001). MultiTarget estimation in noise and clutter. Proceedings, International Conference "Fusion 2001", Montreal, August 7-10, 2001. pp. 17-25.

• Download the paper

M. Malioutov, A. M. Nikiforov (2002) Tracking Multiple Distributed Regression Motions with EM-algorithm. Proceedings, International Conference on Statistics, Combinatorics and Related Topics, Indian Institute of Technology, Bombay, December 19-21, 2000.

In this paper we deal with tracking the motions described by parametric regression models in noise. The first efficient method solving this, namely Symmetric Functions Measurement (SFM), was proposed in seventies for Soviet anti-missile defense (Bernstein (1973)). Here we describe another approach to tracking parametric regression models in noise and some random targets loss mechanism based on the EM-algorithm that is more effective and has a wider applicability range than the SFM-method.
• Download the paper

A.M. Nikiforov, M. Malioutov, R.Mirchev, D.Golan (2002) Estimation from a series of noisy images with the EM-algorithm. Proceedings, International Conference on Statistics, Combinatorics and Related Topics, Indian Institute of Technology, Bombay, December 19-21, 2000.

The paper deals with a series of noisy images generated from a moving object or several objects. An estimation procedure for the object location, shape and some other parameters is proposed that is based on the EM-algorithm.
• Download the paper

Selected chapters from Ph.D. thesis (1987)
"Pattern recognition with mixture analysis and statistical analysis of incomplete data: theory and algorithms"

1. "Consistent estimates of number of classes in mixture analysis".
   Two algorithms for estimation of number of classes are presented. Multiple extrema problem is also concerned.
   
   "Mixture analysis of distributions from mixed parametric families".
   The identifiability and estimation of such mixtures (exotic ones at first sight) is studied. It appears in the multivariate cluster analysis context, that mixture models can be successfully used when the shape of clusters is far from traditional for mixture-based cluster analysis (convex etc).
   

   "Maximum likelihood theory for incomplete data".
   Use of marginal distributions when data are incomplete still lacks theoretical validation. Necessary theorems are proven.
   

   "Analysis of autoregression with missing data".
   The relevant distributions under autoregression model are concerned for incomplete data. Explicit equations are derived for AR (1).
   

   "Classification with missing data".
   Optimal rule is given for classification with missing data in the parametric case.

Papers in preparation

"Fast duration modeling in HMM for speech recognition"
The model of duration of [sub]phoneme state using hazard function is proposed. Parametric approach uses unimodal distributions (Weibull, Gamma). Some semi-parametric models also perform well in tests. Estimates are easy to EM-train. Viterbi search (or full probability computation) became in average only 20% slower compared pure HMM, but performance was significantly better in experiments.

Download



"Tree-dependence covariance models in HMM".
In speech recognition, two representations of the covariance matrix are used most often: either diagonal or unconstrained matrix. The first is often an over-simplification, the second requires large amount of training data to obtain reliable estimates and is ineffective computationally. Tree-dependence model for covariance matrix provides algorithms that are only 20-30% slower than diagonal model in computations while almost fully retaining dependencies between variables.



"Image scale transforms with uniform frequency response".
Usual simple image scale / resampling transform techniques ([bilnear] interpolation, etc) introduce distortions. A simple alternative to more advanced rescaling techniques is proposed.



"Multivariate symmetry and Friedman test".
A nonparametric test for the two-way variance analysis based on multivariate symmetry properties is proposed. Unlike the Friedman test the proposed test is consistent against all alternatives.



"Robust adaptive 2D filters"
2D locally adaptive filters are considered. Examples are given for fingerprint images. Extremely good image enhancement is available via robust adaptive 2D sharpening and smoothing filters.



A note on autoregression analysis with missing data and the EM-algorithm.
The problem of analysis of univariate autoregression processes with missing data following the "marginal" technique is concerned. Exact closed-form solutions for the AR(1) and AR(2) models are given.


• Download the postscript paper with comments.




"Fast adaptive local equalization"
Global equalization can be poor for if the mean local intensity of the image is not uniform. Local equalization works properly in this situation but takes long time, even with effective "cumulative" calculations. An adaptive procedure is proposed that is only 3-4 times slower than global equalization and approximates local equalization with any given accuracy.



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Patents

Two patents on fingerprint image processing (assigned to BIO-key International, Inc.)

Co-authored the patent on BIO-key's fast ID search technology (pending)