event detect
word trajectori
aperiod event
period event
word signal
spectral analysi
topic detect
topic track
text stream
new stream
time seri
featur categor
dft
gaussian

Analyzing Feature Trajectories for Event Detection Qi He qihe@pmail.ntu.edu.sg Kuiyu Chang ASKYChang@ntu.edu.sg Ee-Peng Lim ASEPLim@ntu.edu.sg School of Computer Engineering Nanyang Technological University Block N4, Nanyang Avenue, Singapore 639798 ABSTRACT We consider the problem of analyzing word trajectories in both time and frequency domains, with the specific goal of identifying important and less-reported, periodic and aperiodic words.
A set of words with identical trends can be grouped together to reconstruct an event in a completely unsupervised manner.
The document frequency of each word across time is treated like a time series, where each element is the document frequency - inverse document frequency (DFIDF) score at one time point.
In this paper, we 1) first applied spectral analysis to categorize features for different event characteristics: important and less-reported, periodic and aperiodic; 2) modeled aperiodic features with Gaussian density and periodic features with Gaussian mixture densities, and subsequently detected each feature``s burst by the truncated Gaussian approach; 3) proposed an unsupervised greedy event detection algorithm to detect both aperiodic and periodic events.
All of the above methods can be applied to time series data in general.
We extensively evaluated our methods on the 1-year Reuters News Corpus [3] and showed that they were able to uncover meaningful aperiodic and periodic events.
Categories and Subject Descriptors: H.3.3 [Information Storage and Retrieval]: Information Search and Retrieval General Terms: Algorithms, Experimentation.
1.
INTRODUCTION There are more than 4,000 online news sources in the world.
Manually monitoring all of them for important events has become difficult or practically impossible.
In fact, the topic detection and tracking (TDT) community has for many years been trying to come up with a practical solution to help people monitor news effectively.
Unfortunately, the holy grail is still elusive, because the vast majority of TDT solutions proposed for event detection [20, 5, 17, 4, 21, 7, 14, 10] are either too simplistic (based on cosine similarity [5]) or impractical due to the need to tune a large number of parameters [9].
The ineffectiveness of current TDT technologies can be easily illustrated by subscribing to any of the many online news alerts services such as the industryleading Google News Alerts [2], which generates more than 50% false alarms [10].
As further proof, portals like Yahoo take a more pragmatic approach by requiring all machine generated news alerts to go through a human operator for confirmation before sending them out to subscribers.
Instead of attacking the problem with variations of the same hammer (cosine similarity and TFIDF), a fundamental understanding of the characteristics of news stream data is necessary before any major breakthroughs can be made in TDT.
Thus in this paper, we look at news stories and feature trends from the perspective of analyzing a time-series word signal.
Previous work like [9] has attempted to reconstruct an event with its representative features.
However, in many predictive event detection tasks (i.e., retrospective event detection), there is a vast set of potential features only for a fixed set of observations (i.e., the obvious bursts).
Of these features, often only a small number are expected to be useful.
In particular, we study the novel problem of analyzing feature trajectories for event detection, borrowing a well-known technique from signal processing: identifying distributional correlations among all features by spectral analysis.
To evaluate our method, we subsequently propose an unsupervised event detection algorithm for news streams.
0 0.2 0.4 0.6 0.8 8/20/1996 12/8/1996 3/28/1997 7/16/1997 Easter April (a) aperiodic event 0 0.1 0.2 0.3 0.4 8/20/1996 12/8/1996 3/28/1997 7/16/1997 Unaudited Ended (b) periodic event Figure 1: Feature correlation (DFIDF:time) between a) Easter and April b) Unaudited and Ended.
As an illustrative example, consider the correlation between the words Easter and April from the Reuters Corpus1 .
From the plot of their normalized DFIDF in Figure 1(a), we observe the heavy overlap between the two words circa 04/1997, which means they probably both belong to the same event during that time (Easter feast).
In this example, the hidden event Easter feast is a typical important aperiodic event over 1-year data.
Another example is given by Figure 1(b), where both the words Unaudited and Ended 1 Reuters Corpus is the default dataset for all examples.
exhibit similar behaviour over periods of 3 months.
These two words actually originated from the same periodic event, net income-loss reports, which are released quarterly by publicly listed companies.
Other observations drawn from Figure 1 are: 1) the bursty period of April is much longer than Easter, which suggests that April may exist in other events during the same period; 2) Unaudited has a higher average DFIDF value than Ended, which indicates Unaudited to be more representative for the underlying event.
These two examples are but the tip of the iceberg among all word trends and correlations hidden in a news stream like Reuters.
If a large number of them can be uncovered, it could significantly aid TDT tasks.
In particular, it indicates the significance of mining correlating features for detecting corresponding events.
To summarize, we postulate that: 1) An event is described by its representative features.
A periodic event has a list of periodic features and an aperiodic event has a list of aperiodic features; 2) Representative features from the same event share similar distributions over time and are highly correlated; 3) An important event has a set of active (largely reported) representative features, whereas an unimportant event has a set of inactive (less-reported) representative features; 4) A feature may be included by several events with overlaps in time frames.
Based on these observations, we can either mine representative features given an event or detect an event from a list of highly correlated features.
In this paper, we focus on the latter, i.e., how correlated features can be uncovered to form an event in an unsupervised manner.
1.1 Contributions This paper has three main contributions: • To the best of our knowledge, our approach is the first to categorize word features for heterogenous events.
Specifically, every word feature is categorized into one of the following five feature types based on its power spectrum strength and periodicity: 1) HH (high power and high/long periodicity): important aperiodic events, 2) HL (high power and low periodicity): important periodic events, 3) LH (low power and high periodicity): unimportant aperiodic events, 4) LL (low power and low periodicity): non-events, and 5) SW (stopwords), a higher power and periodicity subset of LL comprising stopwords, which contains no information.
• We propose a simple and effective mixture densitybased approach to model and detect feature bursts.
• We come up with an unsupervised event detection algorithm to detect both aperiodic and periodic events.
Our algorithm has been evaluated on a real news stream to show its effectiveness.
2.
RELATED WORK This work is largely motivated by a broader family of problems collectively known as Topic Detection and Tracking (TDT) [20, 5, 17, 4, 21, 7, 14, 10].
Moreover, most TDT research so far has been concerned with clustering/classifying documents into topic types, identifying novel sentences [6] for new events, etc., without much regard to analyzing the word trajectory with respect to time.
Swan and Allan [18] first attempted using co-occuring terms to construct an event.
However, they only considered named entities and noun phrase pairs, without considering their periodicities.
On the contrary, our paper considers all of the above.
Recently, there has been significant interest in modeling an event in text streams as a burst of activities by incorporating temporal information.
Kleinberg``s seminal work described how bursty features can be extracted from text streams using an infinite automaton model [12], which inspired a whole series of applications such as Kumar``s identification of bursty communities from Weblog graphs [13], Mei``s summarization of evolutionary themes in text streams [15], He``s clustering of text streams using bursty features [11], etc..
Nevertheless, none of the existing work specifically identified features for events, except for Fung et al. [9], who clustered busty features to identify various bursty events.
Our work differs from [9] in several ways: 1) we analyze every single feature, not only bursty features; 2) we classify features along two categorical dimensions (periodicity and power), yielding altogether five primary feature types; 3) we do not restrict each feature to exclusively belong to only one event.
Spectral analysis techniques have previously been used by Vlachos et al. [19] to identify periodicities and bursts from query logs.
Their focus was on detecting multiple periodicities from the power spectrum graph, which were then used to index words for query-by-burst search.
In this paper, we use spectral analysis to classify word features along two dimensions, namely periodicity and power spectrum, with the ultimate goal of identifying both periodic and aperiodic bursty events.
3.
DATA REPRESENTATION Let T be the duration/period (in days) of a news stream, and F represents the complete word feature space in the classical static Vector Space Model (VSM).
3.1 Event Periodicity Classification Within T, there may exist certain events that occur only once, e.g., Tony Blair elected as Prime Minister of U.K., and other recurring events of various periodicities, e.g., weekly soccer matches.
We thus categorize all events into two types: aperiodic and periodic, defined as follows.
Definition 1.
(Aperiodic Event) An event is aperiodic within T if it only happens once.
Definition 2.
(Periodic Event) If events of a certain event genre occur regularly with a fixed periodicity P ≤ T/2 , we say that this particular event genre is periodic, with each member event qualified as a periodic event.
Note that the definition of aperiodic is relative, i.e., it is true only for a given T, and may be invalid for any other T > T. For example, the event Christmas feast is aperiodic for T ≤ 365 but periodic for T ≥ 730.
3.2 Representative Features Intuitively, an event can be described very concisely by a few discriminative and representative word features and vice-versa, e.g., hurricane, sweep, and strike could be representative features of a Hurricane genre event.
Likewise, a set of strongly correlated features could be used to reconstruct an event description, assuming that strongly correlated features are representative.
The representation vector of a word feature is defined as follows: Definition 3.
(Feature Trajectory) The trajectory of a word feature f can be written as the sequence yf = [yf (1), yf (2), ... , yf (T)], where each element yf (t) is a measure of feature f at time t, which could be defined using the normalized DFIDF score2 yf (t) = DFf (t) N(t) × log( N DFf ), where DFf (t) is the number of documents (local DF) containing feature f at day t, DFf is the total number of documents (global DF) containing feature f over T, N(t) is the number of documents for day t, and N is the total number of documents over T. 4.
IDENTIFYING FEATURES FOR EVENTS In this section, we show how representative features can be extracted for (un)important or (a)periodic events.
4.1 Spectral Analysis for Dominant Period Given a feature f, we decompose its feature trajectory yf = [yf (1), yf (2), ..., yf (T)] into the sequence of T complex numbers [X1, ... , XT ] via the discrete Fourier transform (DFT): Xk = T t=1 yf (t)e− 2πi T (k−1)t , k = 1, 2, ... , T. DFT can represent the original time series as a linear combination of complex sinusoids, which is illustrated by the inverse discrete Fourier transform (IDFT): yf (t) = 1 T T k=1 Xke 2πi T (k−1)t , t = 1, 2, ... , T, where the Fourier coefficient Xk denotes the amplitude of the sinusoid with frequency k/T.
The original trajectory can be reconstructed with just the dominant frequencies, which can be determined from the power spectrum using the popular periodogram estimator.
The periodogram is a sequence of the squared magnitude of the Fourier coefficients, Xk 2 , k = 1, 2, ... , T/2 , which indicates the signal power at frequency k/T in the spectrum.
From the power spectrum, the dominant period is chosen as the inverse of the frequency with the highest power spectrum, as follows.
Definition 4.
(Dominant Period) The dominant period (DP) of a given feature f is Pf = T/ arg max k Xk 2 .
Accordingly, we have Definition 5.
(Dominant Power Spectrum) The dominant power spectrum (DPS) of a given feature f is Sf = Xk 2 , with Xk 2 ≥ Xj 2 , ∀j = k. 4.2 Categorizing Features The DPS of a feature trajectory is a strong indicator of its activeness at the specified frequency; the higher the DPS, the more likely for the feature to be bursty.
Combining DPS with DP, we therefore categorize all features into four types: 2 We normalize yf (t) as yf (t) = yf (t)/ T i=1 yf (i) so that it could be interpreted as a probability.
• HH: high Sf , aperiodic or long-term periodic (Pf > T/2 ); • HL: high Sf , short-term periodic (Pf ≤ T/2 ); • LH: low Sf , aperiodic or long-term periodic; • LL: low Sf , short-term periodic.
The boundary between long-term and short-term periodic is set to T/2 .
However, distinguishing between a high and low DPS is not straightforward, which will be tackled later.
Properties of Different Feature Sets To better understand the properties of HH, HL, LH and LL, we select four features, Christmas, soccer, DBS and your as illustrative examples.
Since the boundary between high and low power spectrum is unclear, these chosen examples have relative wide range of power spectrum values.
Figure 2(a) shows the DFIDF trajectory for Christmas with a distinct burst around Christmas day.
For the 1-year Reuters dataset, Christmas is classified as a typical aperiodic event with Pf = 365 and Sf = 135.68, as shown in Figure 2(b).
Clearly, the value of Sf = 135.68 is reasonable for a well-known bursty event like Christmas.
0 0.5 1 1.5 8/20/1996 12/8/1996 3/28/1997 7/16/1997 (a) Christmas(DFIDF:time) 0 50 100 150 0.00 0.13 0.25 0.37 0.50 P=365 S=135.68 (b) Christmas(S:frequency) Figure 2: Feature Christmas with relative high Sf and long-term Pf .
The DFIDF trajectory for soccer is shown in Figure 3(a), from which we can observe that there is a regular burst every 7 days, which is again verified by its computed value of Pf = 7, as shown in Figure 3(b).
Using the domain knowledge that soccer games have more matches every Saturday, which makes it a typical and heavily reported periodic event, we thus consider the value of Sf = 155.13 to be high.
0 0.2 0.4 0.6 8/20/1996 12/8/1996 3/28/1997 7/16/1997 (a) soccer(DFIDF:time) 0 50 100 150 200 0.00 0.13 0.25 0.37 0.50 P=7 S=155.13 (b) soccer(S:frequency) Figure 3: Feature soccer with relative high Sf and short-term Pf .
From the DFIDF trajectory for DBS in Figure 4(a), we can immediately deduce DBS to be an infrequent word with a trivial burst on 08/17/1997 corresponding to DBS Land Raﬄes Holdings plans.
This is confirmed by the long period of Pf = 365 and low power of Sf = 0.3084 as shown in Figure 4(b).
Moreover, since this aperiodic event is only reported in a few news stories over a very short time of few days, we therefore say that its low power value of Sf = 0.3084 is representative of unimportant events.
The most confusing example is shown in Figure 5 for the word feature your, which looks very similar to the graph for soccer in Figure 3.
At first glance, we may be tempted to group both your and soccer into the same category of HL or LL since both distributions look similar and have the same dominant period of approximately a week.
However, further 0 0.05 0.1 0.15 8/20/1996 12/8/1996 3/28/1997 7/16/1997 (a) DBS(DFIDF:time) 0 0.1 0.2 0.3 0.4 0.00 0.13 0.25 0.37 0.50 P=365 S=0.3084 (b) DBS(S:frequency) Figure 4: Feature DBS with relative low Sf and long-term Pf .
analysis indicates that the periodicity of your is due to the differences in document counts for weekdays (average 2,919 per day) and weekends3 (average 479 per day).
One would have expected the periodicity of a stopword like your to be a day.
Moreover, despite our DFIDF normalization, the weekday/weekend imbalance still prevailed; stopwords occur 4 times more frequently on weekends than on weekdays.
Thus, the DPS remains the only distinguishing factor between your (Sf = 9.42) and soccer (Sf = 155.13).
However, it is very dangerous to simply conclude that a power value of S = 9.42 corresponds to a stopword feature.
0 0.05 0.1 0.15 0.2 8/20/1996 12/8/1996 3/28/1997 7/16/1997 (a) your(DFIDF:time) 0 5 10 0.00 0.13 0.25 0.37 0.50 P=7 S=9.42 (b) your(S:frequency) Figure 5: Feature your as an example confusing with feature soccer.
Before introducing our solution to this problem, let``s look at another LL example as shown in Figure 6 for beenb, which is actually a confirmed typo.
We therefore classify beenb as a noisy feature that does not contribute to any event.
Clearly, the trajectory of your is very different from beenb, which means that the former has to be considered separately.
0 0.001 0.002 0.003 0.004 8/20/1996 12/8/1996 3/28/1997 7/16/1997 (a) beenb(DFIDF:time) 1.20E-05 1.20E-05 1.20E-05 1.20E-05 1.20E-05 0.003 0.126 0.249 0.373 0.496 P=8 S=1.20E-05 (b) beenb(S:frequency) Figure 6: Feature beenb with relative low Sf and short-term Pf .
Stop Words (SW) Feature Set Based on the above analysis, we realize that there must be another feature set between HL and LL that corresponds to the set of stopwords.
Features from this set has moderate DPS and low but known dominant period.
Since it is hard to distinguish this feature set from HL and LL only based on DPS, we introduce another factor called average DFIDF (DFIDF).
As shown in Figure 5, features like your usually have a lower DPS than a HL feature like soccer, but have a much higher DFIDF than another LL noisy feature such as beenb.
Since such properties are usually characteristics of stopwords, we group features like your into the newly defined stopword (SW) feature set.
Since setting the DPS and DFIDF thresholds for identifying stopwords is more of an art than science, we proposed a heuristic HS algorithm, Algorithm 1.
The basic idea is to only use news stories from weekdays to identify stopwords.
3 The weekends here also include public holidays falling on weekdays.
The SW set is initially seeded with a small set of 29 popular stopwords utilized by Google search engine.
Algorithm 1 Heuristic Stopwords detection (HS) Input: Seed SW set, weekday trajectories of all words 1: From the seed set SW, compute the maximum DPS as UDPS, maximum DFIDF as UDFIDF, and minimum of DFIDF as LDFIDF.
2: for fi ∈ F do 3: Compute DFT for fi.
4: if Sfi ≤ UDPS and DFIDFfi ∈ [LDFIDF, UDFIDF] then 5: fi → SW 6: F = F − fi 7: end if 8: end for Overview of Feature Categorization After the SW set is generated, all stopwords are removed from F.
We then set the boundary between high and low DPS to be the upper bound of the SW set``s DPS.
An overview of all five feature sets is shown in Figure 7.
Figure 7: The 5 feature sets for events.
5.
IDENTIFYING BURSTS FOR FEATURES Since only features from HH, HL and LH are meaningful and could potentially be representative to some events, we pruned all other feature classified as LL or SW.
In this section, we describe how bursts can be identified from the remaining features.
Unlike Kleinberg``s burst identification algorithm [12], we can identify both significant and trivial bursts without the need to set any parameters.
5.1 Detecting Aperiodic Features'' Bursts For each feature in HH and HL, we truncate its trajectory by keeping only the bursty period, which is modeled with a Gaussian distribution.
For example, Figure 8 shows the word feature Iraq with a burst circa 09/06/1996 being modeled as a Gaussian.
Its bursty period is defined by [μf − σf , μf + σf ] as shown in Figure 8(b).
5.2 Detecting Periodic Features'' Bursts Since we have computed the DP for a periodic feature f, we can easily model its periodic feature trajectory yf using 0 0.2 0.4 0.6 0.8 8/20/96 12/8/96 3/28/97 7/16/97 (a) original DFIDF:time 0 0.2 0.4 0.6 0.8 8/20/96 12/8/96 3/28/97 7/16/97 burst= [μ-σ, μ+σ] (b) identifying burst Figure 8: Modeling Iraq``s time series as a truncated Gaussian with μ = 09/06/1996 and σ = 6.26.
a mixture of K = T/Pf Gaussians: f(yf = yf (t)|θf ) = K k=1 αk 1 2πσ2 k e − 1 2σ2 k (yf (t)−µk)2 , where the parameter set θf = {αk, μk, σk}K k=1 comprises: • αk is the probability of assigning yf into the kth Gaussian.
αk > 0, ∀k ∈ [1, K] and K k=1 αk = 1; • μk/σk is mean/standard deviation of the kth Gaussian.
The well known Expectation Maximization (EM) [8] algorithm is used to compute the mixing proportions αk, as well as the individual Gaussian density parameters μk and σK .
Each Gaussian represents one periodic event, and is modeled similarly as mentioned in Section 5.1.
6.
EVENTS FROM FEATURES After identifying and modeling bursts for all features, the next task is to paint a picture of the event with a potential set of representative features.
6.1 Feature Correlation If two features fi and fj are representative of the same event, they must satisfy the following necessary conditions: 1.
fi and fj are identically distributed: yfi ∼ yfj .
2.
fi and fj have a high document overlap.
Measuring Feature Distribution Similarity We measure the similarity between two features fi and fj using discrete KL-divergence defined as follows.
Definition 6.
(feature similarity) KL(fi, fj ) is given by max(KL(fi|fj ), KL(fj |fi)), where KL(fi|fj ) = T t=1 f(yfi (t)|θfi )log f(yfi (t)|θfi ) f(yfj (t)|θfj ) .
(1) Since KL-divergence is not symmetric, we define the similarity between between fi and fj as the maximum of KL(fi|fj ) and KL(fj |fi).
Further, the similarity between two aperiodic features can be computed using a closed form of the KL-divergence [16].
The same discrete KL-divergence formula of Eq.
1 is employed to compute the similarity between two periodic features, Next, we define the overal similarity among a set of features R using the maximum inter-feature KL-Divergence value as follows.
Definition 7.
(set``s similarity)KL(R) = max ∀fi,fj ∈R KL(fi, fj ).
Document Overlap Let Mi be the set of all documents containing feature fi.
Given two features fi and fj , the overlapping document set containing both features is Mi ∩ Mj .
Intuitively, the higher the |Mi ∩ Mj |, the more likelty that fi and fj will be highly correlated.
We define the degree of document overlap between two features fi and fj as follows.
Definition 8.
(Feature DF Overlap) d(fi, fj ) = |Mi∩Mj| min(|Mi|,|Mj|) .
Accordingly, the DF Overlap among a set of features R is also defined.
Definition 9.
(Set DF Overlap) d(R) = min ∀fi,fj ∈R d(fi, fj).
6.2 Unsupervised Greedy Event Detection We use features from HH to detect important aperiodic events, features from LH to detect less-reported/unimportant aperiodic events, and features from HL to detect periodic events.
All of them share the same algorithm.
Given bursty feature fi ∈ HH, the goal is to find highly correlated features from HH.
The set of features similar to fi can then collectively describe an event.
Specifically, we need to find a subset Ri of HH that minimizes the following cost function: C(Ri) = KL(Ri) d(Ri) fj ∈Ri Sfj , Ri ⊂ HH.
(2) The underlying event e (associated with the burst of fi) can be represented by Ri as y(e) = fj ∈Ri Sfj fu∈Ri Sfu yfj .
(3) The burst analysis for event e is exactly the same as the feature trajectory.
The cost in Eq.
2 can be minimized using our unsupervised greedy UG event detection algorithm, which is described in Algorithm 2.
The UG algorithm allows a feature Algorithm 2 Unsupervised Greedy event detection (UG).
Input: HH, document index for each feature.
1: Sort and select features in descending DPS order: Sf1 ≥ Sf2 ≥ ... ≥ Sf|HH| .
2: k = 0.
3: for fi ∈ HH do 4: k = k + 1.
5: Init: Ri ← fi, C(Ri) = 1/Sfi and HH = HH − fi.
6: while HH not empty do 7: m = arg min m C(Ri ∪ fm).
8: if C(Ri ∪ fm) < C(Ri) then 9: Ri ← fm and HH = HH − fm.
10: else 11: break while.
12: end if 13: end while 14: Output ek as Eq.
3.
15: end for to be contained in multiple events so that we can detect several events happening at the same time.
Furthermore, trivial events only containing year/month features (i.e., an event only containing 1 feature Aug could be identified over a 1year news stream) could be removed, although such events will have inherent high cost and should already be ranked very low.
Note that our UG algorithm only requires one data-dependant parameter, the boundary between high and low power spectrum, to be set once, and this parameter can be easily estimated using the HS algorithm (Algorithm 1).
7.
EXPERIMENTS In this section, we study the performances of our feature categorizing method and event detection algorithm.
We first introduce the dataset and experimental setup, then we subjectively evaluate the categorization of features for HH, HL, LH, LL and SW.
Finally, we study the (a)periodic event detection problem with Algorithm 2.
7.1 Dataset and Experimental Setup The Reuters Corpus contains 806,791 English news stories from 08/20/1996 to 08/19/1997 at a day resolution.
Version 2 of the open source Lucene software [1] was used to tokenize the news text content and generate the document-word vector.
In order to preserve the time-sensitive past/present/future tenses of verbs and the differences between lower case nouns and upper case named entities, no stemming was done.
Since dynamic stopword removal is one of the functionalities of our method, no stopword was removed.
We did remove nonEnglish characters, however, after which the number of word features amounts to 423,433.
All experiments were implemented in Java and conducted on a 3.2 GHz Pentium 4 PC running Windows 2003 Server with 1 GB of memory.
7.2 Categorizing Features We downloaded 34 well-known stopwords utilized by the Google search engine as our seed training features, which includes a, about, an, are, as, at, be, by, de, for, from, how, in, is, it, of, on, or, that, the, this, to, was, what, when, where, who, will, with, la, com, und, en and www.
We excluded the last five stopwords as they are uncommon in news stories.
By only analyzing news stories over 259 weekdays, we computed the upper bound of the power spectrum for stopwords at 11.18 and corresponding DFIDF ranges from 0.1182 to 0.3691.
Any feature f satisfying Sf <= 11.18 and 0.1182 <= DFIDFf <= 0.3691 over weekdays will be considered a stopword.
In this manner, 470 stopwords were found and removed as visualized in Figure 9.
Some detected stopwords are A (P = 65, S = 3.36, DFIDF = 0.3103), At (P = 259, S = 1.86, DFIDF = 0.1551), GMT (P = 130, S = 6.16, DFIDF = 0.1628) and much (P = 22, S = 0.80, DFIDF = 0.1865).
After the removal of these stopwords, the distribution of weekday and weekend news are more or less matched, and in the ensuing experiments, we shall make use of the full corpus (weekdays and weekends).
The upper bound power spectrum value of 11.18 for stopwords training was selected as the boundary between the high power and low power spectrum.
The boundary between high and low periodicity was set to 365/2 = 183.
All 422,963 (423433 − 470) word features were categorized into 4 feature sets: HH (69 features), HL (1,087 features), LH (83,471 features), and LL (338,806 features) as shown in Figure 10.
In Figure 10, each gray level denotes the relative density of features in a square region, measured by log10(1 + Dk), where Dk is the number of features within the k-th square region.
From the figure, we can make the 0 2 4 6 8 11.18 12879.82 1 65 100 130 259 S(f) P(f) LH HH LL HL Figure 9: Distribution of SW (stopwords) in the HH, HL, LH, and LL regions.
0 5 11.18 50 100 200 300 400 500 1000 12879.82 1 2 4 6 8 20 50 100 183 364 365 S(f) P(f) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 LH HH LL HL Figure 10: Distribution of categorized features over the four quadrants (shading in log scale).
following observations: 1.
Most features have low S and are easily distinguishable from those features having a much higher S, which allows us to detect important (a)periodic events from trivial events by selecting features with high S. 2.
Features in the HH and LH quadrants are aperiodic, which are nicely separated (big horizontal gap) from the periodic features.
This allows reliably detecting aperiodic events and periodic events independently.
3.
The (vertical) boundary between high and low power spectrum is not as clearcut and the exact value will be application specific.
By checking the scatter distribution of features from SW on HH, HL, LH, and LL as shown in Figure 9, we found that 87.02%(409/470) of the detected stopwords originated from LL.
The LL classification and high DFIDF scores of stopwords agree with the generally accepted notion that stopwords are equally frequent over all time.
Therefore, setting the boundary between high and low power spectrum using the upper bound Sf of SW is a reasonable heuristic.
7.3 Detecting Aperiodic Events We shall evaluate our two hypotheses, 1)important aperiodic events can be defined by a set of HH features, and 2)less reported aperiodic events can be defined by a set of LH features.
Since no benchmark news streams exist for event detection (TDT datasets are not proper streams), we evaluate the quality of the automatically detected events by comparing them to manually-confirmed events by searching through the corpus.
Among the 69 HH features, we detected 17 important aperiodic events as shown in Table 1 (e1 − e17).
Note that the entire identification took less than 1 second, after removing events containing only the month feature.
Among the 17 events, other than the overlaps between e3 and e4 (both describes the same hostage event), e11 and e16 (both about company reports), the 14 identified events are extremely accurate and correspond very well to the major events of the period.
For example, the defeat of Bob Dole, election of Tony Blair, Missile attack on Iraq, etc..
Recall that selecting the features for one event should minimize the cost in Eq.
2 such that 1) the number of features span different events, and 2) not all features relevant to an event will be selected, e.g., the feature Clinton is representative to e12 but since Clinton relates to many other events, its time domain signal is far different from those of other representative features like Dole and Bob.
The number of documents of a detected event is roughly estimated by the number of indexed documents containing the representative features.
We can see that all 17 important aperiodic events are popularly reported events.
After 742 minutes of computation time, we detected 23, 525 less reported aperiodic events from 83,471 LH features.
Table 1 lists the top 5 detected aperiodic events (e18 − e22) with respect to the cost.
We found that these 5 events are actually very trivial events with only a few news reports, and are usually subsumed by some larger topics.
For example, e22 is one of the rescue events in an airplane hijack topic.
One advantage of our UG Algorithm for discovering less-reported aperiodic events is that we are able to precisely detect the true event period.
7.4 Detecting Periodic Events Among the 1,087 HL features, 330 important periodic events were detected within 10 minutes of computing time.
Table 1 lists the top 5 detected periodic events with respect to the cost (e23 − e27).
All of the detected periodic events are indeed valid, and correspond to real life periodic events.
The GMM model is able to detect and estimate the bursty period nicely although it cannot distinguish the slight difference between every Monday-Friday and all weekdays as shown in e23.
We also notice that e26 is actually a subset of e27 (soccer game), which is acceptable since the Sheffield league results are announced independently every weekend.
8.
CONCLUSIONS This paper took a whole new perspective of analyzing feature trajectories as time domain signals.
By considering the word document frequencies in both time and frequency domains, we were able to derive many new characteristics about news streams that were previously unknown, e.g., the different distributions of stopwords during weekdays and weekends.
For the first time in the area of TDT, we applied a systematic approach to automatically detect important and less-reported, periodic and aperiodic events.
The key idea of our work lies in the observations that (a)periodic events have (a)periodic representative features and (un)important events have (in)active representative features, differentiated by their power spectrums and time periods.
To address the real event detection problem, a simple and effective mixture density-based approach was used to identify feature bursts and their associated bursty periods.
We also designed an unsupervised greedy algorithm to detect both aperiodic and periodic events, which was successful in detecting real events as shown in the evaluation on a real news stream.
Although we have not made any benchmark comparison against another approach, simply because there is no previous work in the addressed problem.
Future work includes evaluating the recall of detected events for a labeled news stream, and comparing our model against the closest equivalent methods, which currently are limited to the methods of Kleinberg [12] (which can only detect certain type of bursty events depending on parameter settings), Fung et al. [9], and Swan and Allan [18].
Nevertheless, we believe our simple and effective method will be useful for all TDT practitioners, and will be especially useful for the initial exploratory analysis of news streams.
9.
REFERENCES [1] Apache lucene-core 2.0.0, http://lucene.apache.org.
[2] Google news alerts, http://www.google.com/alerts.
[3] Reuters corpus, http://www.reuters.com/researchandstandards/corpus/.
[4] J. Allan.
Topic Detection and Tracking.
Event-based Information Organization.
Kluwer Academic Publishers, 2002.
[5] J. Allan, V. Lavrenko, and H. Jin.
First story detection in tdt is hard.
In CIKM, pages 374-381, 2000.
[6] J. Allan, C. Wade, and A. Bolivar.
Retrieval and novelty detection at the sentence level.
In SIGIR, pages 314-321, 2003.
[7] T. Brants, F. Chen, and A. Farahat.
A system for new event detection.
In SIGIR, pages 330-337, 2003.
[8] A. P. Dempster, N. M. Laird, and D. B. Rubin.
Maximum likelihood from incomplete data via the EM algorithm.
Journal of the Royal Statistical Society, 39(1):1-38, 1977.
[9] G. P. C. Fung, J. X. Yu, P. S. Yu, and H. Lu.
Parameter free bursty events detection in text streams.
In VLDB, pages 181-192, 2005.
[10] Q. He, K. Chang, and E.-P.
Lim.
A model for anticipatory event detection.
In ER, pages 168-181, 2006.
[11] Q. He, K. Chang, E.-P.
Lim, and J. Zhang.
Bursty feature reprensentation for clustering text streams.
In SDM, accepted, 2007.
[12] J. Kleinberg.
Bursty and hierarchical structure in streams.
In SIGKDD, pages 91-101, 2002.
[13] R. Kumar, J. Novak, P. Raghavan, and A. Tomkins.
On the bursty evolution of blogspace.
In WWW, pages 159-178, 2005.
[14] G. Kumaran and J. Allan.
Text classification and named entities for new event detection.
In SIGIR, pages 297-304, 2004.
[15] Q. Mei and C. Zhai.
Discovering evolutionary theme patterns from text: an exploration of temporal text mining.
In SIGKDD, pages 198-207, 2005.
[16] W. D. Penny.
Kullback-liebler divergences of normal, gamma, dirichlet and wishart densities.
Technical report, 2001.
[17] N. Stokes and J. Carthy.
Combining semantic and syntactic document classifiers to improve first story detection.
In SIGIR, pages 424-425, 2001.
[18] R. Swan and J. Allan.
Automatic generation of overview timelines.
In SIGIR, pages 49-56, 2000.
[19] M. Vlachos, C. Meek, Z. Vagena, and D. Gunopulos.
Identifying similarities, periodicities and bursts for online search queries.
In SIGMOD, pages 131-142, 2004.
[20] Y. Yang, T. Pierce, and J. Carbonell.
A study of retrospective and on-line event detection.
In SIGIR, pages 28-36, 1998.
[21] Y. Yang, J. Zhang, J. Carbonell, and C. Jin.
Topic-conditioned novelty detection.
In SIGKDD, pages 688-693, 2002.
Table 1: All important aperiodic events (e1 − e17), top 5 less-reported aperiodic events (e18 − e22) and top 5 important periodic events (e23 − e27).
Detected Event and Bursty Period Doc # True Event e1(Sali,Berisha,Albania,Albanian,March) 02/02/199705/29/1997 1409 Albanian``s president Sali Berisha lost in an early election and resigned, 12/1996-07/1997.
e2(Seko,Mobutu,Sese,Kabila) 03/22/1997-06/09/1997 2273 Zaire``s president Mobutu Sese coordinated the native rebellion and failed on 05/16/1997.
e3(Marxist,Peruvian) 11/19/1996-03/05/1997 824 Peru rebels (Tupac Amaru revolutionary Movement) led a hostage siege in Lima in early 1997.
e4(Movement,Tupac,Amaru,Lima,hostage,hostages) 11/16/1996-03/20/1997 824 The same as e3.
e5(Kinshasa,Kabila,Laurent,Congo) 03/26/199706/15/1997 1378 Zaire was renamed the Democratic Republic of Congo on 05/16/1997.
e6(Jospin,Lionel,June) 05/10/1997-07/09/1997 605 Following the early General Elections circa 06/1997, Lionel Jospin was appointed Prime Minister on 06/02/1997.
e7(Iraq,missile) 08/31/1996-09/13/1996 1262 U.S. fired missile at Iraq on 09/03/1996 and 09/04/1996.
e8(Kurdish,Baghdad,Iraqi) 08/29/1996-09/09/1996 1132 Iraqi troop fought with Kurdish faction circa 09/1996.
e9(May,Blair) 03/24/1997-07/04/1997 1049 Tony Blair became the Primary Minister of the United Kingdom on 05/02/1997.
e10(slalom,skiing) 12/05/1996-03/21/1997 253 Slalom Game of Alpine Skiing in 01/1997-02/1997.
e11(Interim,months) 09/24/1996-12/31/1996 3063 Tokyo released company interim results for the past several months in 09/1996-12/1996.
e12(Dole,Bob) 09/09/1996-11/24/1996 1599 Dole Bob lost the 1996 US presidential election.
e13(July,Sen) 06/25/1997-06/25/1997 344 Cambodia``s Prime Minister Hun Sen launched a bloody military coup in 07/1997.
e14(Hebron) 10/15/1996-02/14/1997 2098 Hebron was divided into two sectors in early 1997.
e15(April,Easter) 02/23/1997-05/04/1997 480 Easter feasts circa 04/1997 (for western and Orthodox).
e16(Diluted,Group) 04/27/1997-07/20/1997 1888 Tokyo released all 96/97 group results in 04/199707/1997.
e17(December,Christmas) 11/17/1996-01/26/1997 1326 Christmas feast in late 12/1997.
e18(Kolaceva,winter,Together,promenades,Zajedno, Slobodan,Belgrade,Serbian,Serbia,Draskovic,municipal, Kragujevac) 1/25/1997 3 University students organized a vigil on Kolaceva street against government on 1/25/1997.
e19(Tutsi,Luvengi,Burundi,Uvira,fuel,Banyamulenge, Burundian,Kivu,Kiliba,Runingo,Kagunga,Bwegera) 10/19/1996 6 Fresh fighting erupted around Uvira between Zaire armed forces and Banyamulengs Tutsi rebels on 10/19/1996.
e20(Malantacchi,Korea,Guy,Rider,Unions,labour, Trade,unions,Confederation,rammed,Geneva,stoppages, Virgin,hire,Myongdong,Metalworkers) 1/11/1997 2 Marcello Malantacchi secretary general of the International Metalworkers Federation and Guy Rider who heads the Geneva office of the International Confederation of Free Trade Unions attacked the new labour law of South Korea on 1/11/1997.
e21(DBS,Raﬄes) 8/17/1997 9 The list of the unit of Singapore DBS Land Raﬄes Holdings plans on 8/17/1997.
e22(preserver,fuel,Galawa,Huddle,Leul,Beausse) 11/24/1996 3 Rescued a woman and her baby during a hijacked Ethiopian plane that ran out of fuel and crashed into the sea near Le Galawa beach on 11/24/1996.
e23(PRICE,LISTING,MLN,MATURITY,COUPON, MOODY,AMT,FIRST,ISS,TYPE,PAY,BORROWER) Monday-Friday/week 7966 Announce bond price on all weekdays.
e24(Unaudited,Ended,Months,Weighted,Provision,Cost, Selling,Revenues,Loss,Income,except,Shrs,Revs) every season 2264 Net income-loss reports released by companies in every season.
e25(rating,Wall,Street,Ian) Monday-Friday/week 21767 Stock reports from Wall Street on all weekdays.
e26(Sheffield,league,scoring,goals,striker,games) every Friday, Saturday and Sunday 574 Match results of Sheffield soccer league were published on Friday, Saturday and Sunday 10 times than other 4 days.
e27(soccer,matches,Results,season,game,Cup,match, victory,beat,played,play,division) every Friday, Saturday and Sunday 2396 Soccer games held on Friday, Saturday and Sunday 7 times than other 4 days.

Analyzing Feature Trajectories for Event Detection
ABSTRACT
We consider the problem of analyzing word trajectories in both time and frequency domains, with the specific goal of identifying important and less-reported, periodic and aperiodic words.
A set of words with identical trends can be grouped together to reconstruct an event in a completely unsupervised manner.
The document frequency of each word across time is treated like a time series, where each element is the document frequency - inverse document frequency (DFIDF) score at one time point.
In this paper, we 1) first applied spectral analysis to categorize features for different event characteristics: important and less-reported, periodic and aperiodic; 2) modeled aperiodic features with Gaussian density and periodic features with Gaussian mixture densities, and subsequently detected each feature's burst by the truncated Gaussian approach; 3) proposed an unsupervised greedy event detection algorithm to detect both aperiodic and periodic events.
All of the above methods can be applied to time series data in general.
We extensively evaluated our methods on the 1-year Reuters News Corpus [3] and showed that they were able to uncover meaningful aperiodic and periodic events.
1.
INTRODUCTION
There are more than 4,000 online news sources in the world.
Manually monitoring all of them for important events has become difficult or practically impossible.
In fact, the topic detection and tracking (TDT) community has for many years been trying to come up with a practical solution to help people monitor news effectively.
Unfortunately, the holy grail is still elusive, because the vast majority of TDT
solutions proposed for event detection [20, 5, 17, 4, 21, 7, 14, 10] are either too simplistic (based on cosine similarity [5]) or impractical due to the need to tune a large number of parameters [9].
The ineffectiveness of current TDT technologies can be easily illustrated by subscribing to any of the many online news alerts services such as the industryleading Google News Alerts [2], which generates more than 50% false alarms [10].
As further proof, portals like Yahoo take a more pragmatic approach by requiring all machine generated news alerts to go through a human operator for confirmation before sending them out to subscribers.
Instead of attacking the problem with variations of the same hammer (cosine similarity and TFIDF), a fundamental understanding of the characteristics of news stream data is necessary before any major breakthroughs can be made in TDT.
Thus in this paper, we look at news stories and feature trends from the perspective of analyzing a time-series word signal.
Previous work like [9] has attempted to reconstruct an event with its representative features.
However, in many predictive event detection tasks (i.e., retrospective event detection), there is a vast set of potential features only for a fixed set of observations (i.e., the obvious bursts).
Of these features, often only a small number are expected to be useful.
In particular, we study the novel problem of analyzing feature trajectories for event detection, borrowing a well-known technique from signal processing: identifying distributional correlations among all features by spectral analysis.
To evaluate our method, we subsequently propose an unsupervised event detection algorithm for news streams.
Figure 1: Feature correlation (DFIDF: time) between a) Easter and April b) Unaudited and Ended.
As an illustrative example, consider the correlation between the words Easter and April from the Reuters Corpus'.
From the plot of their normalized DFIDF in Figure 1 (a), we observe the heavy overlap between the two words circa 04/1997, which means they probably both belong to the same event during that time (Easter feast).
In this example, the hidden event Easter feast is a typical important aperiodic event over 1-year data.
Another example is given by Figure 1 (b), where both the words Unaudited and Ended ` Reuters Corpus is the default dataset for all examples.
exhibit similar behaviour over periods of 3 months.
These two words actually originated from the same periodic event, net income-loss reports, which are released quarterly by publicly listed companies.
Other observations drawn from Figure 1 are: 1) the bursty period of April is much longer than Easter, which suggests that April may exist in other events during the same period; 2) Unaudited has a higher average DFIDF value than Ended, which indicates Unaudited to be more representative for the underlying event.
These two examples are but the tip of the iceberg among all word trends and correlations hidden in a news stream like Reuters.
If a large number of them can be uncovered, it could significantly aid TDT tasks.
In particular, it indicates the significance of mining correlating features for detecting corresponding events.
To summarize, we postulate that: 1) An event is described by its representative features.
A periodic event has a list of periodic features and an aperiodic event has a list of aperiodic features; 2) Representative features from the same event share similar distributions over time and are highly correlated; 3) An important event has a set of active (largely reported) representative features, whereas an unimportant event has a set of inactive (less-reported) representative features; 4) A feature may be included by several events with overlaps in time frames.
Based on these observations, we can either mine representative features given an event or detect an event from a list of highly correlated features.
In this paper, we focus on the latter, i.e., how correlated features can be uncovered to form an event in an unsupervised manner.
1.1 Contributions
This paper has three main contributions: 9 To the best of our knowledge, our approach is the first to categorize word features for heterogenous events.
Specifically, every word feature is categorized into one of the following five feature types based on its power spectrum strength and periodicity: 1) HH (high power and high/long periodicity): important aperiodic events, 2) HL (high power and low periodicity): important periodic events, 3) LH (low power and high periodicity): unimportant aperiodic events, 4) LL (low power and low periodicity): non-events, and 5) SW (stopwords), a higher power and periodicity subset of LL comprising stopwords, which contains no information.
9 We propose a simple and effective mixture densitybased approach to model and detect feature bursts.
9 We come up with an unsupervised event detection algorithm to detect both aperiodic and periodic events.
Our algorithm has been evaluated on a real news stream to show its effectiveness.
2.
RELATED WORK
This work is largely motivated by a broader family of problems collectively known as Topic Detection and Tracking (TDT) [20, 5, 17, 4, 21, 7, 14, 10].
Moreover, most TDT research so far has been concerned with clustering/classifying documents into topic types, identifying novel sentences [6] for new events, etc., without much regard to analyzing the word trajectory with respect to time.
Swan and Allan [18] first attempted using co-occuring terms to construct an event.
However, they only considered named entities and noun phrase pairs, without considering their periodicities.
On the contrary, our paper considers all of the above.
Recently, there has been significant interest in modeling an event in text streams as a "burst of activities" by incorporating temporal information.
Kleinberg's seminal work described how bursty features can be extracted from text streams using an infinite automaton model [12], which inspired a whole series of applications such as Kumar's identification of bursty communities from Weblog graphs [13], Mei's summarization of evolutionary themes in text streams [15], He's clustering of text streams using bursty features [11], etc. .
Nevertheless, none of the existing work specifically identified features for events, except for Fung et al. [9], who clustered busty features to identify various bursty events.
Our work differs from [9] in several ways: 1) we analyze every single feature, not only bursty features; 2) we classify features along two categorical dimensions (periodicity and power), yielding altogether five primary feature types; 3) we do not restrict each feature to exclusively belong to only one event.
Spectral analysis techniques have previously been used by Vlachos et al. [19] to identify periodicities and bursts from query logs.
Their focus was on detecting multiple periodicities from the power spectrum graph, which were then used to index words for "query-by-burst" search.
In this paper, we use spectral analysis to classify word features along two dimensions, namely periodicity and power spectrum, with the ultimate goal of identifying both periodic and aperiodic bursty events.
3.
DATA REPRESENTATION
3.1 Event Periodicity Classification
3.2 Representative Features
4.
IDENTIFYING FEATURES FOR EVENTS
4.1 Spectral Analysis for Dominant Period
4.2 Categorizing Features
Properties of Different Feature Sets
Stop Words (SW) Feature Set
5.
IDENTIFYING BURSTS FOR FEATURES
5.1 Detecting Aperiodic Features' Bursts
5.2 Detecting Periodic Features' Bursts
Document Overlap
6.
EVENTS FROM FEATURES
6.1 Feature Correlation
Measuring Feature Distribution Similarity
6.2 Unsupervised Greedy Event Detection
7.
EXPERIMENTS
7.1 Dataset and Experimental Setup
7.2 Categorizing Features
7.3 Detecting Aperiodic Events
7.4 Detecting Periodic Events
8.
CONCLUSIONS
This paper took a whole new perspective of analyzing feature trajectories as time domain signals.
By considering the word document frequencies in both time and frequency domains, we were able to derive many new characteristics about news streams that were previously unknown, e.g., the different distributions of stopwords during weekdays and weekends.
For the first time in the area of TDT, we applied a systematic approach to automatically detect important and less-reported, periodic and aperiodic events.
The key idea of our work lies in the observations that (a) periodic events have (a) periodic representative features and (un) important events have (in) active representative features, differentiated by their power spectrums and time periods.
To address the real event detection problem, a simple and effective mixture density-based approach was used to identify feature bursts and their associated bursty periods.
We also designed an unsupervised greedy algorithm to detect both aperiodic and periodic events, which was successful in detecting real events as shown in the evaluation on a real news stream.
Although we have not made any benchmark comparison against another approach, simply because there is no previous work in the addressed problem.
Future work includes evaluating the recall of detected events for a labeled news stream, and comparing our model against the closest equivalent methods, which currently are limited to the methods of Kleinberg [12] (which can only detect certain type of bursty events depending on parameter settings), Fung et al. [9], and Swan and Allan [18].
Nevertheless, we believe our simple and effective method will be useful for all TDT practitioners, and will be especially useful for the initial exploratory analysis of news streams.

Analyzing Feature Trajectories for Event Detection
ABSTRACT
We consider the problem of analyzing word trajectories in both time and frequency domains, with the specific goal of identifying important and less-reported, periodic and aperiodic words.
A set of words with identical trends can be grouped together to reconstruct an event in a completely unsupervised manner.
The document frequency of each word across time is treated like a time series, where each element is the document frequency - inverse document frequency (DFIDF) score at one time point.
In this paper, we 1) first applied spectral analysis to categorize features for different event characteristics: important and less-reported, periodic and aperiodic; 2) modeled aperiodic features with Gaussian density and periodic features with Gaussian mixture densities, and subsequently detected each feature's burst by the truncated Gaussian approach; 3) proposed an unsupervised greedy event detection algorithm to detect both aperiodic and periodic events.
All of the above methods can be applied to time series data in general.
We extensively evaluated our methods on the 1-year Reuters News Corpus [3] and showed that they were able to uncover meaningful aperiodic and periodic events.
1.
INTRODUCTION
There are more than 4,000 online news sources in the world.
Manually monitoring all of them for important events has become difficult or practically impossible.
In fact, the topic detection and tracking (TDT) community has for many years been trying to come up with a practical solution to help people monitor news effectively.
solutions proposed for event detection [20, 5, 17, 4, 21, 7, 14, 10] are either too simplistic (based on cosine similarity [5]) or impractical due to the need to tune a large number of parameters [9].
Thus in this paper, we look at news stories and feature trends from the perspective of analyzing a time-series word signal.
Previous work like [9] has attempted to reconstruct an event with its representative features.
However, in many predictive event detection tasks (i.e., retrospective event detection), there is a vast set of potential features only for a fixed set of observations (i.e., the obvious bursts).
Of these features, often only a small number are expected to be useful.
In particular, we study the novel problem of analyzing feature trajectories for event detection, borrowing a well-known technique from signal processing: identifying distributional correlations among all features by spectral analysis.
To evaluate our method, we subsequently propose an unsupervised event detection algorithm for news streams.
Figure 1: Feature correlation (DFIDF: time) between a) Easter and April b) Unaudited and Ended.
As an illustrative example, consider the correlation between the words Easter and April from the Reuters Corpus'.
From the plot of their normalized DFIDF in Figure 1 (a), we observe the heavy overlap between the two words circa 04/1997, which means they probably both belong to the same event during that time (Easter feast).
In this example, the hidden event Easter feast is a typical important aperiodic event over 1-year data.
Another example is given by Figure 1 (b), where both the words Unaudited and Ended ` Reuters Corpus is the default dataset for all examples.
exhibit similar behaviour over periods of 3 months.
These two words actually originated from the same periodic event, net income-loss reports, which are released quarterly by publicly listed companies.
Other observations drawn from Figure 1 are: 1) the bursty period of April is much longer than Easter, which suggests that April may exist in other events during the same period; 2) Unaudited has a higher average DFIDF value than Ended, which indicates Unaudited to be more representative for the underlying event.
These two examples are but the tip of the iceberg among all word trends and correlations hidden in a news stream like Reuters.
If a large number of them can be uncovered, it could significantly aid TDT tasks.
In particular, it indicates the significance of mining correlating features for detecting corresponding events.
To summarize, we postulate that: 1) An event is described by its representative features.
Based on these observations, we can either mine representative features given an event or detect an event from a list of highly correlated features.
In this paper, we focus on the latter, i.e., how correlated features can be uncovered to form an event in an unsupervised manner.
1.1 Contributions
This paper has three main contributions: 9 To the best of our knowledge, our approach is the first to categorize word features for heterogenous events.
9 We propose a simple and effective mixture densitybased approach to model and detect feature bursts.
9 We come up with an unsupervised event detection algorithm to detect both aperiodic and periodic events.
Our algorithm has been evaluated on a real news stream to show its effectiveness.
2.
RELATED WORK
Moreover, most TDT research so far has been concerned with clustering/classifying documents into topic types, identifying novel sentences [6] for new events, etc., without much regard to analyzing the word trajectory with respect to time.
Swan and Allan [18] first attempted using co-occuring terms to construct an event.
However, they only considered named entities and noun phrase pairs, without considering their periodicities.
On the contrary, our paper considers all of the above.
Recently, there has been significant interest in modeling an event in text streams as a "burst of activities" by incorporating temporal information.
Nevertheless, none of the existing work specifically identified features for events, except for Fung et al. [9], who clustered busty features to identify various bursty events.
Our work differs from [9] in several ways: 1) we analyze every single feature, not only bursty features; 2) we classify features along two categorical dimensions (periodicity and power), yielding altogether five primary feature types; 3) we do not restrict each feature to exclusively belong to only one event.
Spectral analysis techniques have previously been used by Vlachos et al. [19] to identify periodicities and bursts from query logs.
Their focus was on detecting multiple periodicities from the power spectrum graph, which were then used to index words for "query-by-burst" search.
In this paper, we use spectral analysis to classify word features along two dimensions, namely periodicity and power spectrum, with the ultimate goal of identifying both periodic and aperiodic bursty events.
8.
CONCLUSIONS
This paper took a whole new perspective of analyzing feature trajectories as time domain signals.
By considering the word document frequencies in both time and frequency domains, we were able to derive many new characteristics about news streams that were previously unknown, e.g., the different distributions of stopwords during weekdays and weekends.
For the first time in the area of TDT, we applied a systematic approach to automatically detect important and less-reported, periodic and aperiodic events.
The key idea of our work lies in the observations that (a) periodic events have (a) periodic representative features and (un) important events have (in) active representative features, differentiated by their power spectrums and time periods.
To address the real event detection problem, a simple and effective mixture density-based approach was used to identify feature bursts and their associated bursty periods.
We also designed an unsupervised greedy algorithm to detect both aperiodic and periodic events, which was successful in detecting real events as shown in the evaluation on a real news stream.
Although we have not made any benchmark comparison against another approach, simply because there is no previous work in the addressed problem.
Nevertheless, we believe our simple and effective method will be useful for all TDT practitioners, and will be especially useful for the initial exploratory analysis of news streams.

Analyzing Feature Trajectories for Event Detection
ABSTRACT
We consider the problem of analyzing word trajectories in both time and frequency domains, with the specific goal of identifying important and less-reported, periodic and aperiodic words.
A set of words with identical trends can be grouped together to reconstruct an event in a completely unsupervised manner.
The document frequency of each word across time is treated like a time series, where each element is the document frequency - inverse document frequency (DFIDF) score at one time point.
In this paper, we 1) first applied spectral analysis to categorize features for different event characteristics: important and less-reported, periodic and aperiodic; 2) modeled aperiodic features with Gaussian density and periodic features with Gaussian mixture densities, and subsequently detected each feature's burst by the truncated Gaussian approach; 3) proposed an unsupervised greedy event detection algorithm to detect both aperiodic and periodic events.
All of the above methods can be applied to time series data in general.
We extensively evaluated our methods on the 1-year Reuters News Corpus [3] and showed that they were able to uncover meaningful aperiodic and periodic events.
1.
INTRODUCTION
There are more than 4,000 online news sources in the world.
Manually monitoring all of them for important events has become difficult or practically impossible.
In fact, the topic detection and tracking (TDT) community has for many years been trying to come up with a practical solution to help people monitor news effectively.
Unfortunately, the holy grail is still elusive, because the vast majority of TDT
solutions proposed for event detection [20, 5, 17, 4, 21, 7, 14, 10] are either too simplistic (based on cosine similarity [5]) or impractical due to the need to tune a large number of parameters [9].
The ineffectiveness of current TDT technologies can be easily illustrated by subscribing to any of the many online news alerts services such as the industryleading Google News Alerts [2], which generates more than 50% false alarms [10].
As further proof, portals like Yahoo take a more pragmatic approach by requiring all machine generated news alerts to go through a human operator for confirmation before sending them out to subscribers.
Instead of attacking the problem with variations of the same hammer (cosine similarity and TFIDF), a fundamental understanding of the characteristics of news stream data is necessary before any major breakthroughs can be made in TDT.
Thus in this paper, we look at news stories and feature trends from the perspective of analyzing a time-series word signal.
Previous work like [9] has attempted to reconstruct an event with its representative features.
However, in many predictive event detection tasks (i.e., retrospective event detection), there is a vast set of potential features only for a fixed set of observations (i.e., the obvious bursts).
Of these features, often only a small number are expected to be useful.
In particular, we study the novel problem of analyzing feature trajectories for event detection, borrowing a well-known technique from signal processing: identifying distributional correlations among all features by spectral analysis.
To evaluate our method, we subsequently propose an unsupervised event detection algorithm for news streams.
Figure 1: Feature correlation (DFIDF: time) between a) Easter and April b) Unaudited and Ended.
As an illustrative example, consider the correlation between the words Easter and April from the Reuters Corpus'.
From the plot of their normalized DFIDF in Figure 1 (a), we observe the heavy overlap between the two words circa 04/1997, which means they probably both belong to the same event during that time (Easter feast).
In this example, the hidden event Easter feast is a typical important aperiodic event over 1-year data.
Another example is given by Figure 1 (b), where both the words Unaudited and Ended ` Reuters Corpus is the default dataset for all examples.
exhibit similar behaviour over periods of 3 months.
These two words actually originated from the same periodic event, net income-loss reports, which are released quarterly by publicly listed companies.
Other observations drawn from Figure 1 are: 1) the bursty period of April is much longer than Easter, which suggests that April may exist in other events during the same period; 2) Unaudited has a higher average DFIDF value than Ended, which indicates Unaudited to be more representative for the underlying event.
These two examples are but the tip of the iceberg among all word trends and correlations hidden in a news stream like Reuters.
If a large number of them can be uncovered, it could significantly aid TDT tasks.
In particular, it indicates the significance of mining correlating features for detecting corresponding events.
To summarize, we postulate that: 1) An event is described by its representative features.
A periodic event has a list of periodic features and an aperiodic event has a list of aperiodic features; 2) Representative features from the same event share similar distributions over time and are highly correlated; 3) An important event has a set of active (largely reported) representative features, whereas an unimportant event has a set of inactive (less-reported) representative features; 4) A feature may be included by several events with overlaps in time frames.
Based on these observations, we can either mine representative features given an event or detect an event from a list of highly correlated features.
In this paper, we focus on the latter, i.e., how correlated features can be uncovered to form an event in an unsupervised manner.
1.1 Contributions
This paper has three main contributions: 9 To the best of our knowledge, our approach is the first to categorize word features for heterogenous events.
Specifically, every word feature is categorized into one of the following five feature types based on its power spectrum strength and periodicity: 1) HH (high power and high/long periodicity): important aperiodic events, 2) HL (high power and low periodicity): important periodic events, 3) LH (low power and high periodicity): unimportant aperiodic events, 4) LL (low power and low periodicity): non-events, and 5) SW (stopwords), a higher power and periodicity subset of LL comprising stopwords, which contains no information.
9 We propose a simple and effective mixture densitybased approach to model and detect feature bursts.
9 We come up with an unsupervised event detection algorithm to detect both aperiodic and periodic events.
Our algorithm has been evaluated on a real news stream to show its effectiveness.
2.
RELATED WORK
This work is largely motivated by a broader family of problems collectively known as Topic Detection and Tracking (TDT) [20, 5, 17, 4, 21, 7, 14, 10].
Moreover, most TDT research so far has been concerned with clustering/classifying documents into topic types, identifying novel sentences [6] for new events, etc., without much regard to analyzing the word trajectory with respect to time.
Swan and Allan [18] first attempted using co-occuring terms to construct an event.
However, they only considered named entities and noun phrase pairs, without considering their periodicities.
On the contrary, our paper considers all of the above.
Recently, there has been significant interest in modeling an event in text streams as a "burst of activities" by incorporating temporal information.
Kleinberg's seminal work described how bursty features can be extracted from text streams using an infinite automaton model [12], which inspired a whole series of applications such as Kumar's identification of bursty communities from Weblog graphs [13], Mei's summarization of evolutionary themes in text streams [15], He's clustering of text streams using bursty features [11], etc. .
Nevertheless, none of the existing work specifically identified features for events, except for Fung et al. [9], who clustered busty features to identify various bursty events.
Our work differs from [9] in several ways: 1) we analyze every single feature, not only bursty features; 2) we classify features along two categorical dimensions (periodicity and power), yielding altogether five primary feature types; 3) we do not restrict each feature to exclusively belong to only one event.
Spectral analysis techniques have previously been used by Vlachos et al. [19] to identify periodicities and bursts from query logs.
Their focus was on detecting multiple periodicities from the power spectrum graph, which were then used to index words for "query-by-burst" search.
In this paper, we use spectral analysis to classify word features along two dimensions, namely periodicity and power spectrum, with the ultimate goal of identifying both periodic and aperiodic bursty events.
3.
DATA REPRESENTATION
Let T be the duration/period (in days) of a news stream, and F represents the complete word feature space in the classical static Vector Space Model (VSM).
3.1 Event Periodicity Classification
Within T, there may exist certain events that occur only once, e.g., Tony Blair elected as Prime Minister of U.K., and other recurring events of various periodicities, e.g., weekly soccer matches.
We thus categorize all events into two types: aperiodic and periodic, defined as follows.
genre occur regularly with a fixed periodicity P <[T/2], we say that this particular event genre is periodic, with each member event qualified as a periodic event.
Note that the definition of "aperiodic" is relative, i.e., it is true only for a given T, and may be invalid for any other T'> T. For example, the event Christmas feast is aperiodic for T <365 but periodic for T> 730.
3.2 Representative Features
Intuitively, an event can be described very concisely by a few discriminative and representative word features and vice-versa, e.g., "hurricane", "sweep", and "strike" could be representative features of a Hurricane genre event.
Likewise, a set of strongly correlated features could be used to reconstruct an event description, assuming that strongly correlated features are representative.
The representation vector of a word feature is defined as follows:
yf = [yf (1), yf (2),..., yf (T)], where each element yf (t) is a measure of feature f at time t, which could be defined using the normalized DFIDF score2
where DFf (t) is the number of documents (local DF) containing feature f at day t, DFf is the total number of documents (global DF) containing feature f over T, N (t) is the number of documents for day t, and N is the total number of documents over T.
4.
IDENTIFYING FEATURES FOR EVENTS
In this section, we show how representative features can be extracted for (un) important or (a) periodic events.
4.1 Spectral Analysis for Dominant Period
Given a feature f, we decompose its feature trajectory yf = [yf (1), yf (2),..., yf (T)] into the sequence of T complex numbers [X1,..., XT] via the discrete Fourier transform (DFT):
DFT can represent the original time series as a linear combination of complex sinusoids, which is illustrated by the inverse discrete Fourier transform (IDFT):, t = 1, 2,..., T, where the Fourier coefficient Xk denotes the amplitude of the sinusoid with frequency k/T.
The original trajectory can be reconstructed with just the dominant frequencies, which can be determined from the power spectrum using the popular periodogram estimator.
The periodogram is a sequence of the squared magnitude of the Fourier coefficients, 11Xk112, k = 1, 2,..., [T/2], which indicates the signal power at frequency k/T in the spectrum.
From the power spectrum, the dominant period is chosen as the inverse of the frequency with the highest power spectrum, as follows.
DEFINITION 4.
(Dominant Period) The dominant period (DP) of a given feature f is Pf = T / arg max 11Xk112.
Accordingly, we have DEFINITION 5.
(Dominant Power Spectrum) The dominant power spectrum (DPS) of a given feature f is Sf = 11Xk112, with 11Xk112 11Xj 112, dj = ~ k.
4.2 Categorizing Features
The DPS of a feature trajectory is a strong indicator of its activeness at the specified frequency; the higher the DPS, the more likely for the feature to be bursty.
Combining DPS with DP, we therefore categorize all features into four types: 2We normalize yf (t) as y' f (t) = yf (t) / ET i = 1 yf (i) so that it could be interpreted as a probability.
• HH: high Sf, aperiodic or long-term periodic (Pf> [T/2]); • HL: high Sf, short-term periodic (Pf <[T/2]); • LH: low Sf, aperiodic or long-term periodic; • LL: low Sf, short-term periodic.
The boundary between long-term and short-term periodic is set to [T/2].
However, distinguishing between a high and low DPS is not straightforward, which will be tackled later.
Properties of Different Feature Sets
To better understand the properties of HH, HL, LH and LL, we select four features, Christmas, soccer, DBS and your as illustrative examples.
Since the boundary between high and low power spectrum is unclear, these chosen examples have relative wide range of power spectrum values.
Figure 2 (a) shows the DFIDF trajectory for Christmas with a distinct burst around Christmas day.
For the 1-year Reuters dataset, "Christmas" is classified as a typical aperiodic event with Pf = 365 and Sf = 135.68, as shown in Figure 2 (b).
Clearly, the value of Sf = 135.68 is reasonable for a well-known bursty event like Christmas.
Figure 2: Feature "Christmas" with relative high Sf and long-term Pf.
The DFIDF trajectory for soccer is shown in Figure 3 (a), from which we can observe that there is a regular burst every 7 days, which is again verified by its computed value of Pf = 7, as shown in Figure 3 (b).
Using the domain knowledge that soccer games have more matches every Saturday, which makes it a typical and heavily reported periodic event, we thus consider the value of Sf = 155.13 to be high.
Figure 3: Feature "soccer" with relative high Sf and short-term Pf.
From the DFIDF trajectory for DBS in Figure 4 (a), we can immediately deduce DBS to be an infrequent word with a trivial burst on 08/17/1997 corresponding to DBS Land Raffles Holdings plans.
This is confirmed by the long period of Pf = 365 and low power of Sf = 0.3084 as shown in Figure 4 (b).
Moreover, since this aperiodic event is only reported in a few news stories over a very short time of few days, we therefore say that its low power value of Sf = 0.3084 is representative of unimportant events.
The most confusing example is shown in Figure 5 for the word feature your, which looks very similar to the graph for soccer in Figure 3.
At first glance, we may be tempted to group both your and soccer into the same category of HL or LL since both distributions look similar and have the same dominant period of approximately a week.
However, further
Figure 4: Feature "DBS" with relative low Sf and long-term Pf.
analysis indicates that the periodicity of your is due to the differences in document counts for weekdays (average 2,919 per day) and weekends3 (average 479 per day).
One would have expected the "periodicity" of a stopword like your to be a day.
Moreover, despite our DFIDF normalization, the weekday/weekend imbalance still prevailed; stopwords occur 4 times more frequently on weekends than on weekdays.
Thus, the DPS remains the only distinguishing factor between your (Sf = 9.42) and soccer (Sf = 155.13).
However, it is very dangerous to simply conclude that a power value of S = 9.42 corresponds to a stopword feature.
The SW set is initially seeded with a small set of 29 popular stopwords utilized by Google search engine.
Algorithm 1 Heuristic Stopwords detection (HS) Input: Seed SW set, weekday trajectories of all words
1: From the seed set SW, compute the maximum DPS as UDPS, maximum DFIDF as UDFIDF, and minimum of DFIDF as LDFIDF.
2: for fi E F do 3: Compute DFT for fi.
4: if Sfi <UDPS and DFIDFfi E [LDFIDF, UDFIDF] then 5: fi--+ SW 6: F = F
Figure 5: Feature "your" as an example confusing with feature "soccer".
Before introducing our solution to this problem, let's look at another LL example as shown in Figure 6 for beenb, which is actually a confirmed typo.
We therefore classify beenb as a noisy feature that does not contribute to any event.
Clearly, the trajectory of your is very different from beenb, which means that the former has to be considered separately.
Figure 6: Feature "beenb" with relative low Sf and short-term Pf.
Stop Words (SW) Feature Set
Based on the above analysis, we realize that there must be another feature set between HL and LL that corresponds to the set of stopwords.
Features from this set has moderate DPS and low but known dominant period.
Since it is hard to distinguish this feature set from HL and LL only based on DPS, we introduce another factor called average DFIDF (DFIDF).
As shown in Figure 5, features like your usually have a lower DPS than a HL feature like soccer, but have a much higher DFIDF than another LL noisy feature such as beenb.
Since such properties are usually characteristics of stopwords, we group features like your into the newly defined stopword (SW) feature set.
Since setting the DPS and DFIDF thresholds for identifying stopwords is more of an art than science, we proposed a heuristic HS algorithm, Algorithm 1.
The basic idea is to only use news stories from weekdays to identify stopwords.
Figure 7: The 5 feature sets for events.
5.
IDENTIFYING BURSTS FOR FEATURES
Since only features from HH, HL and LH are meaningful and could potentially be representative to some events, we pruned all other feature classified as LL or SW.
In this section, we describe how bursts can be identified from the remaining features.
Unlike Kleinberg's burst identification algorithm [12], we can identify both significant and trivial bursts without the need to set any parameters.
5.1 Detecting Aperiodic Features' Bursts
For each feature in HH and HL, we truncate its trajectory by keeping only the bursty period, which is modeled with a Gaussian distribution.
For example, Figure 8 shows the word feature Iraq with a burst circa 09/06/1996 being modeled as a Gaussian.
Its bursty period is defined by [μf - σf, μf + σf] as shown in Figure 8 (b).
5.2 Detecting Periodic Features' Bursts
Since we have computed the DP for a periodic feature f, we can easily model its periodic feature trajectory yf using
Figure 8: Modeling Iraq's time series as a truncated Gaussian with μ = 09/06/1996 and σ = 6.26.
Document Overlap
Let Mi be the set of all documents containing feature fi.
Given two features fi and fj, the overlapping document set containing both features is Mi fn Mj.
Intuitively, the higher the | Mi fn Mj |, the more likelty that fi and fj will be highly correlated.
We define the degree of document overlap between two features fi and fj as follows.
where the parameter set θf = {αk, μk, σk} Kk = 1 comprises:
• αk is the probability of assigning yf into the kth Gaussian.
αk> 0, ` dk E [1, K] and EKk = 1 αk = 1; • μk / σk is mean/standard deviation of the kth Gaussian.
The well known Expectation Maximization (EM) [8] algorithm is used to compute the mixing proportions αk, as well as the individual Gaussian density parameters μk and σK.
Each Gaussian represents one periodic event, and is modeled similarly as mentioned in Section 5.1.
6.
EVENTS FROM FEATURES
After identifying and modeling bursts for all features, the next task is to paint a picture of the event with a potential set of representative features.
6.1 Feature Correlation
If two features fi and fj are representative of the same event, they must satisfy the following necessary conditions:
1.
fi and fj are identically distributed: yfi ∼ yfj.
2.
fi and fj have a high document overlap.
Measuring Feature Distribution Similarity
We measure the similarity between two features fi and fj using discrete KL-divergence defined as follows.
Since KL-divergence is not symmetric, we define the similarity between between fi and fj as the maximum of KL (fi | fj) and KL (fj | fi).
Further, the similarity between two aperiodic features can be computed using a closed form of the KL-divergence [16].
The same discrete KL-divergence formula of Eq.
1 is employed to compute the similarity between two periodic features, Next, we define the overal similarity among a set of features R using the maximum inter-feature KL-Divergence value as follows.
6.2 Unsupervised Greedy Event Detection
We use features from HH to detect important aperiodic events, features from LH to detect less-reported/unimportant aperiodic events, and features from HL to detect periodic events.
All of them share the same algorithm.
Given bursty feature fi E HH, the goal is to find highly correlated features from HH.
The set of features similar to fi can then collectively describe an event.
Specifically, we need to find a subset Ri of HH that minimizes the following cost function:
The underlying event e (associated with the burst of fi) can be represented by Ri as
The burst analysis for event e is exactly the same as the feature trajectory.
The cost in Eq.
2 can be minimized using our unsupervised greedy UG event detection algorithm, which is described in Algorithm 2.
The UG algorithm allows a feature Algorithm 2 Unsupervised Greedy event detection (UG).
Input: HH, document index for each feature.
1: Sort and select features in descending DPS order: Sf1> Sf2>...> Sf | HH |.
2: k = 0.
3: for fi E HH do 4: k = k + 1.
5: Init: Ri + - fi, C (Ri) = 1/Sfi and HH = HH − fi.
6: while HH not empty do 7: m = arg min C (Ri U fm).
m 8: if C (Ri U fm) <C (Ri) then 9: Ri + - fm and HH = HH − fm.
10: else 11: break while.
12: end if 13: end while 14: Output ek as Eq.
3.
15: end for
Sfj DEFINITION 7.
(set's similarity) KL (R) = max KL (fi, fj).
to be contained in multiple events so that we can detect sevVfi, fjER eral events happening at the same time.
Furthermore, trivial events only containing year/month features (i.e., an event
only containing 1 feature Aug could be identified over a 1year news stream) could be removed, although such events will have inherent high cost and should already be ranked very low.
Note that our UG algorithm only requires one data-dependant parameter, the boundary between high and low power spectrum, to be set once, and this parameter can be easily estimated using the HS algorithm (Algorithm 1).
7.
EXPERIMENTS
In this section, we study the performances of our feature categorizing method and event detection algorithm.
We first introduce the dataset and experimental setup, then we subjectively evaluate the categorization of features for HH, HL, LH, LL and SW.
Finally, we study the (a) periodic event detection problem with Algorithm 2.
7.1 Dataset and Experimental Setup
The Reuters Corpus contains 806,791 English news stories from 08/20/1996 to 08/19/1997 at a day resolution.
Version 2 of the open source Lucene software [1] was used to tokenize the news text content and generate the document-word vector.
In order to preserve the time-sensitive past/present/future tenses of verbs and the differences between lower case nouns and upper case named entities, no stemming was done.
Since dynamic stopword removal is one of the functionalities of our method, no stopword was removed.
We did remove nonEnglish characters, however, after which the number of word features amounts to 423,433.
All experiments were implemented in Java and conducted on a 3.2 GHz Pentium 4 PC running Windows 2003 Server with 1 GB of memory.
7.2 Categorizing Features
We downloaded 34 well-known stopwords utilized by the Google search engine as our seed training features, which includes a, about, an, are, as, at, be, by, de, for, from, how, in, is, it, of, on, or, that, the, this, to, was, what, when, where, who, will, with, la, com, und, en and www.
We excluded the last five stopwords as they are uncommon in news stories.
By only analyzing news stories over 259 weekdays, we computed the upper bound of the power spectrum for stopwords at 11.18 and corresponding DFIDF ranges from 0.1182 to 0.3691.
Any feature f satisfying Sf <= 11.18 and 0.1182 <= DFIDFf <= 0.3691 over weekdays will be considered a stopword.
In this manner, 470 stopwords were found and removed as visualized in Figure 9.
Some detected stopwords are A (P = 65, S = 3.36, DFIDF = 0.3103), At (P = 259, S = 1.86, DFIDF = 0.1551), GMT (P = 130, S = 6.16, DFIDF = 0.1628) and much (P = 22, S = 0.80, DFIDF = 0.1865).
After the removal of these stopwords, the distribution of weekday and weekend news are more or less matched, and in the ensuing experiments, we shall make use of the full corpus (weekdays and weekends).
The upper bound power spectrum value of 11.18 for stopwords training was selected as the boundary between the high power and low power spectrum.
The boundary between high and low periodicity was set to [365/2] = 183.
All 422,963 (423433 − 470) word features were categorized into 4 feature sets: HH (69 features), HL (1,087 features), LH (83,471 features), and LL (338,806 features) as shown in Figure 10.
In Figure 10, each gray level denotes the relative density of features in a square region, measured by log10 (1 + Dk), where Dk is the number of features within the k-th square region.
From the figure, we can make the
Figure 9: Distribution of SW (stopwords) in the HH, HL, LH, and LL regions.
Figure 10: Distribution of categorized features over the four quadrants (shading in log scale).
following observations:
1.
Most features have low S and are easily distinguishable from those features having a much higher S, which allows us to detect important (a) periodic events from trivial events by selecting features with high S. 2.
Features in the HH and LH quadrants are aperiodic, which are nicely separated (big horizontal gap) from the periodic features.
This allows reliably detecting aperiodic events and periodic events independently.
3.
The (vertical) boundary between high and low power spectrum is not as clearcut and the exact value will be application specific.
By checking the scatter distribution of features from SW on HH, HL, LH, and LL as shown in Figure 9, we found that 87.02% (409/470) of the detected stopwords originated from LL.
The LL classification and high DFIDF scores of stopwords agree with the generally accepted notion that stopwords are equally frequent over all time.
Therefore, setting the boundary between high and low power spectrum using the upper bound Sf of SW is a reasonable heuristic.
7.3 Detecting Aperiodic Events
We shall evaluate our two hypotheses, 1) important aperiodic events can be defined by a set of HH features, and 2) less reported aperiodic events can be defined by a set of LH features.
Since no benchmark news streams exist for event detection (TDT datasets are not proper streams), we evaluate the quality of the automatically detected events by comparing them to manually-confirmed events by searching through the corpus.
Among the 69 HH features, we detected 17 important aperiodic events as shown in Table 1 (e1 − e17).
Note that the entire identification took less than 1 second, after removing events containing only the month feature.
Among the 17 events, other than the overlaps between e3 and e4 (both describes the same hostage event), e11 and e16 (both about company reports), the 14 identified events are extremely accurate and correspond very well to the major events of the period.
For example, the defeat of Bob Dole, election of Tony Blair, Missile attack on Iraq, etc. .
Recall that selecting the features for one event should minimize the cost in Eq.
2 such that 1) the number of features span different events, and 2) not all features relevant to an event will be selected, e.g., the feature Clinton is representative to e12 but since Clinton relates to many other events, its time domain signal is far different from those of other representative features like Dole and Bob.
The number of documents of a detected event is roughly estimated by the number of indexed documents containing the representative features.
We can see that all 17 important aperiodic events are popularly reported events.
After 742 minutes of computation time, we detected 23, 525 less reported aperiodic events from 83,471 LH features.
Table 1 lists the top 5 detected aperiodic events (e18 − e22) with respect to the cost.
We found that these 5 events are actually very trivial events with only a few news reports, and are usually subsumed by some larger topics.
For example, e22 is one of the rescue events in an airplane hijack topic.
One advantage of our UG Algorithm for discovering less-reported aperiodic events is that we are able to precisely detect the true event period.
7.4 Detecting Periodic Events
Among the 1,087 HL features, 330 important periodic events were detected within 10 minutes of computing time.
Table 1 lists the top 5 detected periodic events with respect to the cost (e23 − e27).
All of the detected periodic events are indeed valid, and correspond to real life periodic events.
The GMM model is able to detect and estimate the bursty period nicely although it cannot distinguish the slight difference between every Monday-Friday and all weekdays as shown in e23.
We also notice that e26 is actually a subset of e27 (soccer game), which is acceptable since the Sheffield league results are announced independently every weekend.
8.
CONCLUSIONS
This paper took a whole new perspective of analyzing feature trajectories as time domain signals.
By considering the word document frequencies in both time and frequency domains, we were able to derive many new characteristics about news streams that were previously unknown, e.g., the different distributions of stopwords during weekdays and weekends.
For the first time in the area of TDT, we applied a systematic approach to automatically detect important and less-reported, periodic and aperiodic events.
The key idea of our work lies in the observations that (a) periodic events have (a) periodic representative features and (un) important events have (in) active representative features, differentiated by their power spectrums and time periods.
To address the real event detection problem, a simple and effective mixture density-based approach was used to identify feature bursts and their associated bursty periods.
We also designed an unsupervised greedy algorithm to detect both aperiodic and periodic events, which was successful in detecting real events as shown in the evaluation on a real news stream.
Although we have not made any benchmark comparison against another approach, simply because there is no previous work in the addressed problem.
Future work includes evaluating the recall of detected events for a labeled news stream, and comparing our model against the closest equivalent methods, which currently are limited to the methods of Kleinberg [12] (which can only detect certain type of bursty events depending on parameter settings), Fung et al. [9], and Swan and Allan [18].
Nevertheless, we believe our simple and effective method will be useful for all TDT practitioners, and will be especially useful for the initial exploratory analysis of news streams.