Vadim Mazalov

Digital ink compression via functional approximation

Representing digital ink traces as points in a function space has proven useful for online recognition. Ink trace coordinates or their integral invariants are written as parametric functions and approximated by truncated orthogonal series. This representation captures the shape of the ink traces with a small number of coefficients in a form quite compact and independent of device resolution, and various geometric techniques may be employed for recognition. The simplicity and high performance of this method lead us to ask whether the same idea can be applied to another important aspect in online handwriting – the compression of digital ink strokes. We have investigated Chebyshev, Legendre and Legendre-Sobolev orthogonal polynomial bases as well as Fourier series and have found that Chebyshev representation is the most suitable apparatus for compressing digital curves. We obtain compression rates of 30* to 50* and have the added benefit that the Legendre- Sobolev form, used for recognition, may be obtained by a single linear transformation.

Toward affine recognition of handwritten mathematical characters

We address the problem of handwritten symbol classification in the presence of distortions modeled by affine transformations. We consider shear, rotation, scaling and translation, since these types of transformations occur most often in practice, and focus most on shear within this framework. We present a distance-based classification method, in which feature vectors are constructed from Legendre-Sobolev expansions of the coordinate functions and of the affine integral invariants of the curves given by the symbols ink strokes. We analyze different size normalization methods and conclude that integral invariants provide the most robust norm. Finally, we propose a new parameterization, a combination of arc length and time, insensitive to variations in curve tracing speed and affine distortion.

Distance-based High-frequency Trading☆

Abstract The present paper approaches high-frequency trading from a computational science perspective, presenting a pattern recognition model to predict price changes of stock market assets. The technique is based on the feature-weighted Euclidean distance to the centroid of a training cluster. A set of micro technical indicators, traditionally employed by professional scalpers, is used in this setting. We describe procedures for removal of outliers, normalization of feature points, computation of weights of features, and classification of test points. The complexity of computation at each quote received is proportional to the number of features. In addition, processing of indicators is parallelizable and, therefore, suitable in high-frequency domains. Experiments are presented for different prediction time intervals and confidence thresholds. Predictions made 10 to 2000 milliseconds before a price change resulted in an accuracy that ranged monotonically from 97% to 75%. Finally, we observed an empirical relation between Euclidean distance in the feature space and prediction accuracy.

A streaming digital ink framework for multi-party collaboration

We present a framework for pen-based, multi-user, online collaboration in mathematical domains. This environment provides participants, who may be in the same room or across the planet, with a shared whiteboard and voice channel. The digital ink stream is transmitted as InkML, allowing special recognizers for different content types, such as mathematics and diagrams. Sessions may be recorded and stored for later playback, analysis or annotation. The framework is currently structured to use the popular Skype and Google Talk services for the communications channel, but other transport mechanisms could be used. The goal of the work is to support computer-enhanced distance collaboration, where domain-specific recognizers handle different kinds of digital ink input and editing. The first of these recognizers is for mathematics, which allows converting math input into machine-understandable format. This supports multi-party collaboration, with sessions recorded in rich formats that allow semantic analysis and manipulation of the content.

Linear Compression of Digital Ink via Point Selection

We present a method to compress digital ink based on piecewise-linear approximation within a given error threshold. The objective is to achieve good compression ratio with very fast execution. The method is especially effective on types of handwriting that have large portions with nearly linear parts, e.g. hand drawn geometric objects. We compare this method with an enhanced version of our earlier functional approximation method, finding the new technique to give slightly worse compression while performing significantly faster. This suggests the presented method can be used in applications where speed of processing is of higher priority than the compression ratio.

Writing on clouds

While writer-independent handwriting recognition systems are now achieving good recognition rates, writer-dependent systems will always do better. We expect this difference in performance to be even larger for certain applications, such as mathematical handwriting recognition, with large symbol sets, symbols that are often poorly written, and no fixed dictionary. In the past, to use writer-dependent recognition software, a writer would train the system on a particular computing device without too much inconvenience. Today, however, each user will typically have multiple devices used in different settings, or even simultaneously. We present an architecture to share training data among devices and, as a side benefit, to collect writer corrections over time to improve personal writing recognition. This is done with the aid of a handwriting profile server to which various handwriting applications connect, reference, and update. The user’s handwriting profile consists of a cloud of sample points, each representing one character in a functional basis. This provides compact storage on the server, rapid recognition on the client, and support for handwriting neatening. This work uses the word “cloud” in two senses. First, it is used in the sense of cloud storage for information to be shared across several devices. Secondly, it is used to mean clouds of handwriting sample points in the function space representing curve traces. We “write on clouds” in both these senses.

A Structure for Adaptive Handwriting Recognition

We present an adaptive approach to the recognition of handwritten mathematical symbols, in which a recognition weight is associated with each training sample. The weight is computed from the distance to a test character in the space of coefficients of functional approximation of symbols. To determine the average size of the training set to achieve certain classification accuracy, we model the error drop as a function of the number of training samples in a class and compute the average parameters of the model with respect to all classes in the collection. The size is maintained by removing a training sample with the minimal average weight after each addition of a recognized symbol to the repository. Experiments show that the method allows rapid adaptation of a default training dataset to the handwriting of an author with efficient use of the storage space.

Recognition of Relatively Small Handwritten Characters or "Size Matters"

Shape-based online handwriting recognition suffers on small characters, in which the distortions and variations are often commensurate in size with the characters themselves. This problem is emphasized in settings where characters may have widely different sizes and there is no absolute scale. We propose methods that use size information to adjust shape-based classification to take this phenomenon appropriately into account. These methods may be thought of as a pre-classification in a size-based feature space and are general in nature, avoiding hand-tuned heuristics based on particular characters.

Message visualizer: a visualization tool for chat messages

We present a work-in-progress visualization tool for facilitation of multi-user online collaboration over text-, voice-, and video-chats. The idea is based on graphical representation of the key concepts of the conversation, e.g. objectives, rationale, important facts, etc. Such visualization promotes goal-oriented and productive teamwork, and improves interactive user experience. The proposed idea is developed in Java, as a modification of Jitsi, an open source IM client.