Matti Karppa

A faster subquadratic algorithm for finding outlier correlations

We study the problem of detecting outlier pairs of strongly correlated variables among a collection of n variables with otherwise weak pairwise correlations. After normalization, this task amounts to the geometric task where we are given as input a set of n vectors with unit Euclidean norm and dimension d, and for some constants 0<τ < ρ < 1, we are asked to find all the outlier pairs of vectors whose inner product is at least ρ in absolute value, subject to the promise that all but at most q pairs of vectors have inner product at most τ in absolute value. Improving on an algorithm of Valiant [FOCS 2012; J. ACM 2015], we present a randomized algorithm that for Boolean inputs ({ −1,1}-valued data normalized to unit Euclidean length) runs in time Õ((nmax,{ 1−γ +M(Δ γ ,γ),M(1−γ ,2 Δ γ)}+qdn2γ), where 0<γ < 1 is a constant tradeoff parameter and M(μ, ν) is the exponent to multiply an ⌊ nμ ⌋ × ⌊ nν ⌋ matrix with an ⌊ nν ⌋ × ⌊ nμ ⌋ matrix and Δ =1/(1−logτ ρ). As corollaries we obtain randomized algorithms that run in time Õ( (n2/ω 3−logτ ρ + qdn2/(1−logτ ρ)3=logττ ρ) and in time õ( (n4 / 2+α (1−logτ ρ)+qdn2/α (1−logτ ρ)2+α (1−logτ ρ)>), where 2≤ ω <2.38 is the exponent for square matrix multiplication and 0.3<α ≤ 1 is the exponent for rectangular matrix multiplication. The notation Õ(ṡ) hides polylogarithmic factors in n and d whose degree may depend on ρ and τ. We present further corollaries for the light bulb problem and for learning sparse Boolean functions.

Head Pose Estimation for Sign Language Video

We address the problem of estimating three head pose angles in sign language video using the Pointing04 data set as training data. The proposed model employs facial landmark points and Support Vector Regression learned from the training set to identify yaw and pitch angles independently. A simple geometric approach is used for the roll angle. As a novel development, we propose to use the detected skin tone areas within the face bounding box as additional features for head pose estimation. The accuracy level of the estimators we obtain compares favorably with published results on the same data, but the smaller number of pose angles in our setup may explain some of the observed advantage.

Detecting Hand-Head Occlusions in Sign Language Video

A large body of current linguistic research on sign language is based on analyzing large corpora of video recordings. This requires either manual or automatic annotation of the videos. In this paper we introduce methods for automatically detecting and classifying hand-head occlusions in sign language videos. Linguistically, hand-head occlusions are an important and interesting subject of study as the head is a structural place of articulation in many signs. Our method combines easily calculable local video properties with more global hand tracking. The experiments carried out with videos of the Suvi on-line dictionary of Finnish Sign Language show that the sensitivity of the proposed local method in detecting occlusion events is 92.6%. When global hand tracking is combined in the method, the specificity can reach the level of 93.7% while still maintaining the detection sensitivity above 90%.

Experiments on Recognising the Handshape in Blobs Extracted from Sign Language Videos

Handshape has an important role in sign languages. It would be inconceivable to try to understand sign language without recognising the handshapes. Over the years, numerous different approaches have been proposed for extracting the hand configuration information. The existing approaches for hand-shape recognition have problems especially with the huge sizes of modern linguistic corpora. Computationally expensive methods become easily infeasible with such large amounts of data. In this paper we examine the straightforward and efficient approach of recognising handshapes by our existing image category detection methodology, involving state-of-the-art local image descriptors. In the experiments the approach produces promising results. On the image feature side, we find that surprisingly complex hierarchical descriptors of shape primitive statistics provide the best overall performance in hand shape recognition. The accuracy of feature-wise detections can be improved by fusing together several features. Considering the temporal succession of the hand blobs markedly improves the accuracy over detecting the hand shape in each video frame in isolation.

An Adaptive Prefix-Assignment Technique for Symmetry Reduction

This paper presents a technique for symmetry reduction that adaptively assigns a prefix of variables in a system of constraints so that the generated prefix-assignments are pairwise nonisomorphic under the action of the symmetry group of the system. The technique is based on McKays canonical extension framework [J.~Algorithms 26 (1998), no.~2, 306--324]. Among key features of the technique are (i) adaptability---the prefix sequence can be user-prescribed and truncated for compatibility with the group of symmetries; (ii) parallelizability---prefix-assignments can be processed in parallel independently of each other; (iii) versatility---the method is applicable whenever the group of symmetries can be concisely represented as the automorphism group of a vertex-colored graph; and (iv) implementability---the method can be implemented relying on a canonical labeling map for vertex-colored graphs as the only nontrivial subroutine. To demonstrate the practical applicability of our technique, we have prepared an experimental open-source implementation of the technique and carry out a set of experiments that demonstrate ability to reduce symmetry on hard instances. Furthermore, we demonstrate that the implementation effectively parallelizes to compute clusters with multiple nodes via a message-passing interface.

Explicit Correlation Amplifiers for Finding Outlier Correlations in Deterministic Subquadratic Time

We derandomize G. Valiants [J. ACM 62 (2015) Art. 13] subquadratic-time algorithm for finding outlier correlations in binary data. Our derandomized algorithm gives deterministic subquadratic scaling essentially for the same parameter range as Valiants randomized algorithm, but the precise constants we save over quadratic scaling are more modest. Our main technical tool for derandomization is an explicit family of correlation amplifiers built via a family of zigzag-product expanders in Reingold, Vadhan, and Wigderson [Ann. of Math. 155 (2002) 157--187]. We say that a function

2D Appearance Based Techniques for Tracking the Signer Configuration in Sign Language Video Recordings

f:\{-1,1\}^d\rightarrow\{-1,1\}^D

SLMotion - An extensible sign language oriented video analysis tool

is a correlation amplifier with threshold

Method for visualisation and analysis of hand and head movements in sign language video

0\leq\tau\leq 1

Comparing computer vision analysis of signed language video with motion capture recordings

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