Michael is a hybrid thinker and doer--a byproduct of being a StrengthsFinder "Learner" over time. With 20 years of engineering, design, and product experience, he helps organizations identify market needs, mobilize internal and external resources, and deliver delightful digital customer experiences that align with business goals. Michael earned his BS in Computer Science from New York Institute of Technology and his MBA from the University of Maryland, College Park. He is also a candidate to receive his MS in Applied Analytics from Columbia University.

While the strength of Topological Data Analysis has been explored in many studies on high dimensional numeric data, it is still a challenging task to apply it to text. As the primary goal in topological data analysis is to define and quantify the shapes in numeric data, defining shapes in the text is much more challenging, even though the geometries of vector spaces and conceptual spaces are clearly relevant for information retrieval and semantics. In this paper, we examine two different methods of extraction of topological features from text, using as the underlying representations of words the two most popular methods, namely word embeddings and TF-IDF vectors. To extract topological features from the word embedding space, we interpret the embedding of a text document as high dimensional time series, and we analyze the topology of the underlying graph where the vertices correspond to different embedding dimensions. For topological data analysis with the TF-IDF representations, we analyze the topology of the graph whose vertices come from the TF-IDF vectors of different blocks in the textual document. In both cases, we apply homological persistence to reveal the geometric structures under different distance resolutions. Our results show that these topological features carry some exclusive information that is not captured by conventional text mining methods. In our experiments we observe adding topological features to the conventional features in ensemble models improves the classification results (up to 5\%). On the other hand, as expected, topological features by themselves may be not sufficient for effective classification. It is an open problem to see whether TDA features from word embeddings might be sufficient, as they seem to perform within a range of few points from top results obtained with a linear support vector classifier.

The aim of this work is to provide a family of qualitative theories for spatial change in general, and for motion of spatial scenes in particular. To achieve this, we consider a spatio-temporalisation MTALC(Dx), of the well-known ALC(D) family of Description Logics (DLs) with a concrete domain: the MTALC(Dx) concepts are interpreted over infinite k-ary Sigma-trees, with the nodes standing for time points, and Sigma including, additionally to its uses in classical k-ary Sigma-trees, the description of the snapshot of an n-object spatial scene of interest; the roles split into m+n immediate-successor (accessibility) relations, which are serial, irreflexive and antisymmetric, and of which m are general, not necessarily functional, the other n functional; the concrete domain Dx is generated by an RCC8-like spatial Relation Algebra (RA) x, and is used to guide the change by imposing spatial constraints on objects of the "followed" spatial scene, eventually at different time points of the input trees. In order to capture the expressiveness of most modal temporal logics encountered in the literature, we introduce weakly cyclic Terminological Boxes (TBoxes) of MTALC(Dx), whose axioms capture the decreasing property of modal temporal operators. We show the important result that satisfiability of an MTALC(Dx) concept with respect to a weakly cyclic TBox can be reduced to the emptiness problem of a Buchi weak alternating automaton augmented with spatial constraints. In another work, complementary to this one, also submitted to this conference, we thoroughly investigate Buchi automata augmented with spatial constraints, and provide, in particular, a translation of an alternating into a nondeterministic, and an effective decision procedure for the emptiness problem of the latter.

The recent discovered spatial-temporal information processing capability of bio-inspired Spiking neural networks (SNN) has enabled some interesting models and applications. However designing large-scale and high-performance model is yet a challenge due to the lack of robust training algorithms. A bio-plausible SNN model with spatial-temporal property is a complex dynamic system. Each synapse and neuron behave as filters capable of preserving temporal information. As such neuron dynamics and filter effects are ignored in existing training algorithms, the SNN downgrades into a memoryless system and loses the ability of temporal signal processing. Furthermore, spike timing plays an important role in information representation, but conventional rate-based spike coding models only consider spike trains statistically, and discard information carried by its temporal structures. To address the above issues, and exploit the temporal dynamics of SNNs, we formulate SNN as a network of infinite impulse response (IIR) filters with neuron nonlinearity. We proposed a training algorithm that is capable to learn spatial-temporal patterns by searching for the optimal synapse filter kernels and weights. The proposed model and training algorithm are applied to construct associative memories and classifiers for synthetic and public datasets including MNIST, NMNIST, DVS 128 etc.; and their accuracy outperforms state-of-art approaches.

There has been a recent push in extraction of 3D spatial layout of scenes. In this paper, we argue for a parametric representation of objects in 3D, which allows us to incorporate volumetric constraints of the physical world. We show that augmenting current structured prediction techniques with volumetric reasoning significantly improves the performance of the state-of-the-art. Papers published at the Neural Information Processing Systems Conference.

We develop an algorithm for efficient range search when the notion of dissimilarity is given by a Bregman divergence. The range search task is to return all points in a potentially large database that are within some specified distance of a query. It arises in many learning algorithms such as locally-weighted regression, kernel density estimation, neighborhood graph-based algorithms, and in tasks like outlier detection and information retrieval. In metric spaces, efficient range search-like algorithms based on spatial data structures have been deployed on a variety of statistical tasks. Here we describe the first algorithm for range search for an arbitrary Bregman divergence.

Efficient and interpretable spatial analysis is crucial in many fields such as geology, sports, and climate science. Large-scale spatial data often contains complex higher-order correlations across features and locations. While tensor latent factor models can describe higher-order correlations, they are inherently computationally expensive to train. Furthermore, for spatial analysis, these models should not only be predictive but also be spatially coherent. However, latent factor models are sensitive to initialization and can yield inexplicable results. We develop a novel Multi-resolution Tensor Learning (MRTL) algorithm for efficiently learning interpretable spatial patterns. MRTL initializes the latent factors from an approximate full-rank tensor model for improved interpretability and progressively learns from a coarse resolution to the fine resolution for an enormous computation speedup. We also prove the theoretical convergence and computational complexity of MRTL. When applied to two real-world datasets, MRTL demonstrates 4 ~ 5 times speedup compared to a fixed resolution while yielding accurate and interpretable models.

Unsupervised text encoding models have recently fueled substantial progress in NLP. The key idea is to use neural networks to convert words in texts to vector space representations based on word positions in a sentence and their contexts, which are suitable for end-to-end training of downstream tasks. We see a strikingly similar situation in spatial analysis, which focuses on incorporating both absolute positions and spatial contexts of geographic objects such as POIs into models. A general-purpose representation model for space is valuable for a multitude of tasks. However, no such general model exists to date beyond simply applying discretization or feed-forward nets to coordinates, and little effort has been put into jointly modeling distributions with vastly different characteristics, which commonly emerges from GIS data. Meanwhile, Nobel Prize-winning Neuroscience research shows that grid cells in mammals provide a multi-scale periodic representation that functions as a metric for location encoding and is critical for recognizing places and for path-integration. Therefore, we propose a representation learning model called Space2Vec to encode the absolute positions and spatial relationships of places. We conduct experiments on two real-world geographic data for two different tasks: 1) predicting types of POIs given their positions and context, 2) image classification leveraging their geo-locations. Results show that because of its multi-scale representations, Space2Vec outperforms well-established ML approaches such as RBF kernels, multi-layer feed-forward nets, and tile embedding approaches for location modeling and image classification tasks. Detailed analysis shows that all baselines can at most well handle distribution at one scale but show poor performances in other scales. In contrast, Space2Vec's multi-scale representation can handle distributions at different scales.

We present a novel method for learning densities with bounded support which enables us to incorporate hard' topological constraints. In particular, we show how emerging techniques from computational algebraic topology and the notion of Persistent Homology can be combined with kernel based methods from Machine Learning for the purpose of density estimation. The proposed formalism facilitates learning of models with bounded support in a principled way, and -- by incorporating Persistent Homology techniques in our approach -- we are able to encode algebraic-topological constraints which are not addressed in current state-of the art probabilistic models. We study the behaviour of our method on two synthetic examples for various sample sizes and exemplify the benefits of the proposed approach on a real-world data-set by learning a motion model for a racecar. We show how to learn a model which respects the underlying topological structure of the racetrack, constraining the trajectories of the car.

This paper presents a probabilistic-graphical model that can be used to infer characteristics of instantaneous brain activity by jointly analyzing spatial and temporal dependencies observed in electroencephalograms (EEG). Specifically, we describe a factor-graph-based model with customized factor-functions defined based on domain knowledge, to infer pathologic brain activity with the goal of identifying seizure-generating brain regions in epilepsy patients. We utilize an inference technique based on the graph-cut algorithm to exactly solve graph inference in polynomial time. We validate the model by using clinically collected intracranial EEG data from 29 epilepsy patients to show that the model correctly identifies seizure-generating brain regions. Our results indicate that our model outperforms two conventional approaches used for seizure-onset localization (5-7% better AUC: 0.72, 0.67, 0.65) and that the proposed inference technique provides 3-10% gain in AUC (0.72, 0.62, 0.69) compared to sampling-based alternatives. Papers published at the Neural Information Processing Systems Conference.