1 Background

Human collaborative processes are being revolutionized by the emergence of ubiquitous, completely portable social media. Group decision-making, social interaction, educational instruction, and many other directed and undirected cognitive interactions are now conducted without a single spoken word being exchanged.

Augmented cognition is a form of human-systems interaction in which a tight coupling between user and computer is achieved via physiological and neurophysiological sensing of a user’s cognitive state. An essential, sometimes determinative component of this state is the user’s emotional state; this not only affects his or her cognition, but the cognition of others by means of the way individual online behaviors condition the emotional context within which interactions take place.

The underlying motivating principles are:

  1. 1.

    By the term “emotional context” we mean a vector field generated by documents posted on a specific social medium. The documents are themselves within this attribute space.

  2. 2.

    Text sources (i.e., persons) can be regarded as short-memory text generators having goals and a partially-observable history.

  3. 3.

    The output text (forum posts on social media) is purposeful and sequential in time.

  4. 4.

    The output text is constrained by the medium and the medium’s linguistics.

  5. 5.

    The text is generated within an “emotional context” that both informs, and is informed by, each generator.

We take 4 above as our guiding principle, since all field theories are ultimately based upon the idea that,

“The entities whose actions are conditioned by a field are themselves its sources and sustainers.”

We begin by assuming that this is just as true of the emotion that drives social behaviors as it is of the massive objects that drive gravitational behaviors. The field can then be viewed as a mathematical device for explaining how entities influence one another without directly interacting.

2 The Data

Sirius15 has been benchmarked using two years of colloquial, natural-language discourse from an English-language blog site. No prior domain assumptions are made (e.g., the method is language independent and does not require “translation” in order to operate). Results from the benchmark indicate that content-clustering is supported, and that “social signatures” of individual posters can be characterized.

The figure below shows a short sequence of blog posts from the data used to create the benchmark.

3 Approach

The ultimate goal of this work is to extend and mature emotion-mining applications that will inform practical action, either in the real-world, or in the social medium itself.

While much work has been done (and remains to be done) in machine translation of colloquial text, relatively little formal mathematical analysis of the ambient emotional context that emerges from the interaction of humans using social media has been published. The Sirius15 application ingests bulk social media data and, by means of a six-phase procedure, infers an empirical vector field structure characterizing the emotional attributes of the discourse. This we call the media’s “Emotion Field”.

Modern text mining methods generally rely on a combination of statistical and graph-theoretic schemas for representing information. These schemas are parsed and quantified to obtain information about associations, processes, and conditional probabilities for variables of interest. While some automation exists, the semantic characterization of corpora is largely manual and ad hoc. The state of the art is described in detail in [1].

The shortcomings of current approaches arise largely because each was designed fairly specifically to overcome failures observed in others. Because a “trouble-shooting” mentality is inherently ad hoc, none of the current methods is founded upon a mathematical formalism intended to cover the entire problem space. Each of these proposed solutions has given rise to new problems. Our work re-addresses this space by employing a broader and more mature mathematical foundation.

The six-phase Sirius15 processing sequence begins by fusing a collection of document metrics to create a matrix of pair wise distances between social media posts. This can be done in a coordinate-free way, since many document metrics are statistical rather than “vectorial” in nature (e.g., Tf.idf, term histograms). The combined differences between the selected metrics are taken as a similarity measure, where greater differences imply a greater distance between the underlying documents.

From this document distance matrix is inferred a set of points in an N-dimensional Euclidean space, with each point representing a single document in the corpus. The points are developed as a set to have the same distance matrix as the corpus of documents. This embedding geometrizes the document analysis problem, facilitating the use of many mature data mining tools that require numerical (rather than nominal) input features.

The figures immediately below are snippets collected during the model building process:

All Phases of the application run under Microsoft Windows on a 1-core processor. The Sirius15 prototype operates in a “batch” mode; all posts are assumed to be present when modeling is performed.

During model construction, computational complexity is O(N2) in the number of threads (a thread is a topically heterogeneous collection of posts). Our benchmark data set contained 4,487 threads. The experiment reported below is based upon a subset of 136 threads, consisting of a total of 2,847 posts.

A large-scale processing-complexity experiment had the following results:

4 The Mathematics of the Approach

The field-theoretic approach gives a unifying mathematical framework for applications of computational linguistics to emotion mining akin to the framework Maxwell’s Equations provide for Electromagnetism: a set of field equations that provide a rigorous mathematical framework for automating aspects of currently man-intensive characterization of the “emotional context” of online social behavior. The mathematics is relatively straightforward:

The field equations give rise to a radially symmetric scalar potential, depicted in the figure on the left below. The field source is the center, which is a blog post that establishes an “energy well” that can be occupied by another document (at “7 o’clock”).

The field satisfies the superposition principle, so as additional blog posts are generated, they can just be directly added in (the figure on the right above). Further, by the methods of Differential Geometry, it can be shown that the “emotion” field is conservative. In particular, it is path-independent, which implies that we need not retain the history of a post to understand its immediate effect on the emotion field. This “statelessness” is potentially important for future work, though we have not exploited it.

The derived attribute space is a Hilbert Space of appropriate dimension that creates coordinates in a natural way using unsupervised machine learning. The method was discovered independently by our team, but was first described by [2].

The dimension of the Euclidean Space can be chosen at will (though poor choices cause convergence problems; see below). We use a variation of the Delta Rule from machine-learning for inferring the embedding.

The Delta Rule is a first-order gradient descent method. When it is written as a distance minimization expression, it can be interpreted as a differential equation describing a vector field; a solution (to coordinatize the document data) is then a set of Lagrangian Points for this differential equation. In this way, the field is an emergent property of the points it positions, and the positions are constrained by the field. Specifics are given below.

Other methods can be used to coordinatize the data from the distance matrix (e.g., Singular Value Decomposition, Lagrange Multipliers, Newton’s Method). We have found that convergence by gradient descent is usually not complete, owing largely to the fact that natural text metrics might not result in a fused distance function that is a metric (e.g., Triangle Inequality is satisfied only approximately). This is sometimes overcome by increasing the dimension of the Euclidean Space. We also use an adaptive convergence rate and an annealing schedule to speed up convergence.

Once the data are geometrized, data mining methods for data visualization, signature extraction, clustering, building classifiers, etc., can be used to complete the emotional context modeling process [3].

5 Future Work

The field-equations can be used to impose an inherent, a priori clustering of entities in the space. This clustering determines, and is determined by, the terrain geometry; these are in dynamic tension. Clusters, or cliques, correspond to “emotion plateaus” in the original feature space.

We have performed some preliminary work on the development of predictive analytics. Perhaps more interesting is the “domain segmentation” clustering provides, which might be used to identify those members of a forum most likely to engage in displays of emotive language. This is a type of Signaturing; done across the entire problem space, it constitutes a type of “Emotion Terrain-Forming.”

In looking at the details of the benchmarked data set, the techniques discussed above are able to identify cliques of posters. More importantly, the “emotional distance” between cliques might be quantified, supporting assessment of the “emotional separation” of cliques, and individuals within cliques. Further, the level of emotional impact of certain terms might be numerically estimated.