Classifying Stocks using P-Trees and Investor Sentiment
Arijit Chatterjee
Dr.William Perrizo
Department of Computer Science
North Dakota State University
Fargo, ND 58012, USA
arijit.chatterjee@ndsu.edu
Department of Computer Science
North Dakota State University
Fargo, ND 58012, USA
william.perrizo@ndsu.edu
Abstract— For people who are not so exposed to the financial
markets, it is important for them to know which ticker symbols
to follow, based on which investment decisions can be made. In
this work, we propose how we can classify stock ticker symbols
from tweets vertically using P-Trees. The solution described in
this paper analyzes 3000 financial and news symbols vertically
from the Twitter platform and finds the ticker symbols which are
most frequently been discussed. It also provides an ability to scan
through the tweet texts associated with the common ticker
occurrences so that the context can be identified to help users
make better informed business decisions. The paper also
discusses on the bias of investors and the affect it has on the
volatility of the stocks in the market.
I. INTRODUCTION
Twitter is one of the most important social media platforms
in today’s world providing the unique ability for a user to
connect with almost anyone else in the world. The platform
supports 33 languages and has close to 288 million active users
and almost 500 million tweets are created every day. Investors
are day by day using Twitter platform to cite their opinions on
particular ticker symbols and share their market focused posts
and updates. But with so much of information in the platform it
is really difficult to find the information a particular user just
needs to reference to make an investment decision. In the realm
of stocks it is important to understand which ticker symbols to
follow based on which investment decisions can be made.
The solution described in the paper will provide them with
the ability to identify the ticker symbols effectively without
reading through huge corpuses of tweet texts. Now once those
ticker symbols with the most frequent occurrences from the
tweets are been classified, the paper also gives an insight into
how the sentiments of the investors make an impact on the
behavior of the stock in the market. The first section of this
paper introduces the programming around the Twitter platform
limitations, the second section of the paper introduces the
concept of P-Trees and how we can structure our data
vertically, the third section of the paper shows how we can
store the necessary information in the data cube model and
represent various views from the captured information. The
fourth section shows results on classifying ticker symbols from
the tweets of multiple investors and an insight to derive
sentiments of investors. The future direction of this work is
shown in the fifth section and we finally conclude in the sixth
section.
II. PROGRAMMING AROUND TWITTER PLATFORM
This section of the paper explains in details that how we
can programmatically retrieve the tweets from Twitter
platform. Twitter has a REST API that allows users to search
for tweets, users, timelines, or even post new messages. We use
Tweetinvi which is a C# based .net API which is been used to
access the Twitter API. A Twitter developer account needs to
be set up first with the necessary credentials to query the API
using Tweetinvi. The project is layered to keep the twitter
interactions, file management, application logic and P-Tree
based algorithms separate. Based on the sector we are
interested to follow, we first create a list of usernames (tweet
ID’s) from that particular sector whose tweets we would like to
analyze. For our analysis we grabbed a list of 3000 financial
and news symbol that we took from twitter lists and search
results. We also estimated when it was the best time to update
the users tweet based on their tweeting frequency.
The freshly downloaded tweets are serialized to JSON by
JSON.net and then written to an .xml based file one per twitter
username. The program is designed to download the maximum
historical tweets possible per user and then rechecking the
accounts for new tweets. Twitter limits the API requests to 300
requests per 15 minutes, and allows access to maximum of
3200 historical tweets. Considering the focus is on the financial
sector, we would not be missing much information as the
historical tweets will not have much significance as compared
to the present state of the markets. Additionally each request to
the platform can download a maximum of 200 tweets at a time.
So in order to maximize the productive use of the requests,
calculating the average time span from the user’s latest tweets
and setting the time the program should recheck for new tweets
is necessary. Also, when downloading the tweets we check if
we have already downloaded the tweets for this user. If there
are historical tweets for the user then we will need to download
only the updates. Each tweet has its own format and contains a
lot of information (ID, Text, Time, Retweets, Favorites, User,
and Followers). The new encoded tweets are written to a list
which is then written to a username.xml file.
III. THE P-TREE TECHNOLOGY
Tremendous volumes of data cause the cardinality problem
for conventional transaction based data mining algorithms. For
fast and efficient data processing, we transform the data into PTree, the loss-less, compressed, and data-mining-ready vertical
data structure.
The basic data structure exploited in the P-tree technology
[1] is the Predicate Count Tree2 (PC-Tree) or simply the P-tree.
Formally, P-trees are tree-like data structures that store
numeric-relational data (i.e. numeric data in relational format)
in column-wise, bit-compressed format by splitting each
attribute into bits (i.e. representing each attribute value by its
binary equivalent), grouping together all bits in each bit
position for all tuples, and representing each bit group by a Ptree. P-trees provide a lot of information and are structured to
facilitate data mining processes. After representing each
numeric attribute value by its bit representation, we store all
bits for each position separately. In other words, we group
together all the bit values at bit position x of each attribute for
all tuples t. Figure 1 shows a relational table made up of three
attributes and four tuples transformed from numeric to binary,
and highlights all the bits in the first three bit groups for the
first attribute, Attribute 1; each of those bit groups will form a
P-tree. Since each attribute value in our table is made up of 8
bits, 24 bit groups are generated in total with each attribute
generating 8 bit groups. Figure 2 shows a group of 16 bits
transformed into a P-tree after being divided into quadrants (i.e.
subgroups of 4). Each such tree is called a basic P-tree. In the
lower part of Figure 2, 7 is the total number of bits in the whole
bit group shown in the upper part. 4, 2, 1 and 0 are the number
of 1’s in the 1st, 2nd, 3rd and 4th quadrants respectively in the
bit group. Since the first quadrant (the node denoted by 4 on
the second level in the tree) is made up of “1” bits in its
entirety (we call it a pure-1 quadrant) no sub-trees for it are
needed. Similarly, quadrants made up entirely of “0” bits (the
node denoted by 0 on the second level in the tree) are called
pure-0 quadrants and have no sub-trees. As a matter of fact,
this is how compression is achieved3 [1]. Non-pure quadrants
such as nodes 2 and 1 on the second level in the tree are
recursively partitioned further into four quadrants with a node
for each quadrant. We stop the recursive partitioning of a node
when it becomes pure-1 or pure-0 (eventually we will reach a
point where the node is composed of a single bit only and is
pure because it is made up entirely of either only “1” bits or
“0” bits). P-tree algebra includes operations such as AND, OR,
NOT (or complement) and ROOTCOUNT (a count of the
number of “1”s in the tree). Details for those operations can be
found in [1]. The latest benchmark on P-trees ANDing has
shown a speed of 6 milliseconds for ANDing two P-trees
representing bit groups each containing 16 million bits. Speed
and compression aspects of P-Trees have been discussed in
greater details in [1]. [2], [4] and [5] give some applications
exploiting the P-tree technology. Once we have represented our
data using P-trees, no scans of the database are needed to
perform text categorization as we shall demonstrate later. In
fact, this is one of the important aspects of P-tree technology.
Fig. 1. Relational numeric data converted to binary format with the first three
bit groups in Attribute 1 highlighted.
2
3
Formerly known as the Peano Count Tree
Its worth noting that good P-Tree compression can be achieved
when the data is very sparse (which increases the chances of having
long sequences of “0” bits) or very dense (which increases the
chances of having long sequences of “1” bits)
Fig. 2. A 16 bit group converted to a P-Tree.
IV. DATA CUBE MODEL AND VIEWS
In this section we describe how we can represent the
captured tweets in the form of P-Trees and store the data
lossless in a 3-D data cube model.
In the term space model, a document is presented as a
vector in the term space where terms are used as features or
dimensions. The data structure resulting from representing all
the documents in a given collection as term vectors is referred
to as a document-by-term matrix. Given that the term space has
thousands of dimensions, most current text-mining algorithms
fail to scale-up. This very high dimensionality of the term
space is an idiosyncrasy of text mining and must be addressed
carefully in any text-mining application.
Within the term space model, many different
representations exist. On one extreme, there is the binary
representation in which a document is represented as a binary
vector where a 1 bit in slot i implies the existence of the
corresponding term ti in the document in position pj, and a 0 bit
implies its absence. This model is fast and efficient to
implement but clearly lacks the degree of accuracy needed
because most of the semantics are lost. On the other extreme,
there is the frequency representation where a document is
represented as a frequency vector. Many types of frequency
measures exist: term frequency (TF), term frequency by inverse
document frequency (TFxIDF), normalized TF, and the like.
This representation for term frequency is obviously more
accurate than the binary one but is not as easy and efficient to
implement. Our algorithm shows the term frequency (TF)
measure based on ticker symbol references in the Tweet texts
and is characterized by accuracy and space and time efficiency
because it is based on the P-Tree technology.
For our analysis we store the tweet ID, tweet Text, and
User Information as different dimensions of every tweet. We
also store time as a supplemental information which can be
used later in analysis. In a data cube model, the cubes can be
used to represent multidimensional data of different
dimensions. Each cube cells denote an event while the cube
edges stand for analysis dimensions. Each cube cell is given a
value of each measure. So far, we’ve created a binary matrix
similar to that depicted in Figure 1. We follow the same steps
presented in Section III to create the P-tree version of the
matrix as in Figure 2. For every bit position in every term ti we
will create a basic P-tree. Pi, j is the P-Tree representation of the
bits lying at jth position in ith term for all documents. Each Pi,j
will give the number of documents having a 1 bit in position j
for term i. This representation conveys a lot of information and
is structured to facilitate fast data mining processing. To get the
P-tree holding all documents having a certain value for some
term i, we can follow the steps given in the following example:
if the desired binary value for term i is 10, we calculate Pi,10 as
Pi,10 = Pi,1 AND P’i,0 where ’indicates the bit-complement or
the NOT operation (which is simply the count complement in
each quadrant).
A. P-Tree Term View
The term view P-Trees, for example, are then created by
bit-slicing the Term Table. They are based on the tweet ID
dimension and the position of occurrence of the term within the
tweet, a P-Tree for every term is been created.
For every tweet made by a user, we parse the tweet Text
and store all the unique words in a list. At the same pass, we
also find the max Position of the words in the tweet. Since
twitter has a character limitation of 140 for every tweet the max
Position in most cases from our tests have been <= 35. So
every user related data set can be captured as an aggregate of
tweet ID’s indexed on the unique word occurrences from their
tweets and the respective positions of these unique terms in the
tweets.
Fig. 4. Term View diagram showing an example of the term view of the
Term “How”.
B. P-Tree Position View
The Position view P-Trees are created by bit-slicing the
Position Table. They are based on the tweet ID dimension and
the unique term occurrences we find in each tweet ID, a P-Tree
for every position is been created.
Fig. 3. Data Cube diagram showing the dimension of Unique Term, Position
and Tweet ID’s.
The above cube shows the representation of a single tweet
text “Buy AAPL always and invest in TSLA” where based on
the unique terms and their positions we denote a 1 where there
is an occurrence else a 0. Now based on this cube there can be
different forms of P-Trees views which can be created based on
how we would like to slice the data cube. Intermediate to the
creation of P-Trees we view the data cube as tables three ways,
the Document Table (DT), the Term Table (TT) and the
Position Table (PT):
Document Table:
Doc T1P1…T1P7 . . . T9P1…T9P7
1
1
…
0
. . .
0
…
0
2
0
…
0
. . .
1
…
0
3
0
…
0
. . .
1
…
1
Term Table:
Term P1D1 P1D2 P1D3...P7D1…P7D3
1
1
..
.
0
1
... 0 …
Another view which can be created easily is the Document
view or tweet ID view by bit-slicing the Document Table. It is
based on the unique term and their position in each of the
tweets, a P-Tree for every tweet ID can be created.
The data has been stored redundantly in the form of three
different P-Tree view’s. The computational advantage of
processing the data in the form of these bitmaps becomes
significant when the data is very deep and also significantly
wide. From conventional horizontal processing, we have to
throw away data not because it is irrelevant but because the
massive amount of data results in data mining times that are
too much high. With P-Trees we would not ever need to throw
away the data due to the faster processing advantage.
0
V. CLASSIFICATION
9
0
…
0
. . .
1
…
1
Position Table
Pos T1D1 T1D2 T1D3...T9D1…T9D3
1
1
7
0
..
.
Fig. 5. Position View diagram showing an example of the position view of
the Position “1”.
0
…
1
0
... 0 …
. . .
1
…
0
1
A. TICKER SYMBOLS
Now with all the terms been stored in the term view PTrees list we can filter on the terms which only begin with a
“$” symbol. The term view P-Trees for every user generates
the term frequency based on the 1 occurrence of these terms.
The ticker symbol which has the highest frequency of 1occurrence is the most discussed amongst the investors. This
insight is helpful especially when a user needs to know which
stocks to invest in primarily and does not have much
knowledge on the markets. The system scans through 3000
different twitter user Names and retrieves this information on
the most frequent ticker symbol which is been discussed. The
system can also process a given number of latest tweets. Once
the most frequent occurrence of the ticker symbols is obtained,
the system generates an .xml based output containing the ticker
symbol frequency and the tweet Text associated with the ticker
symbol occurrence. Based on how we wish to process the text
from the tweets we can either use humans to read the final
generated .xml file to have an understanding on the ticker
symbols and derive sentiments or we can have a NLP tool to
process these generated .xml files. Using NLP to derive
sentiments from the Tweet Texts is outside the scope of this
paper.
The analysis has also been done with varied sample sizes
like studying the latest 100 tweets across 100 investors, 10
tweets across 500 investors and so on. A sample result with the
most frequent 10 ticker symbol occurrence from the latest 500
tweets across 25 most tweeted investors between 03/30/2015
and 04/03/2015 is shown below in Table. I.
TABLE I.
Ticker Symbol
10. $AXMM
% Price Changes
-15.2
The results show that $TRIL and $LBIO which had the
highest frequency of occurrence had risen close to 36.2% and
12.39% respectively in that time period.
Using P-Trees we not only find the most frequently
occurred ticker symbols in an efficient manner but we can also
re-construct the tweet texts which were assoicated for every
term and position for the most frequently occurring ticker
symbols. We are providing this information so that the end user
can understand the contexts based on which the investors had
made the tweets. Fig 6. shows below some of the sample tweet
texts which were associated for the ticker symbol “FB”
(Facebook Inc.).
TOP 10 TICKER SYMBOLS WITH FREQUENCY
Ticker Symbol
Frequency
1.
$TRIL
124
2.
$LBIO
76
3.
$CYBR
68
4.
$FEYE
61
5.
$JUNO
53
6.
$FB
44
7.
$CNAT
41
8.
$KRFT
39
9.
$SPY
39
10. $AXMM
37
We try to see the actual behavior of these stocks in the
market within the same time frame that the investors were
tweeting about these ticker symbols and the results are shown
in Table. II.
TABLE II.
TICKER SYMBOLS WITH % PRICE CHANGES
Ticker Symbol
% Price Changes
1.
$TRIL
36.2
2.
$LBIO
12.39
3.
$CYBR
0.29
4.
$FEYE
-2.74
5.
$JUNO
-4.86
6.
$FB
-.91
7.
$CNAT
-19.39
8.
$KRFT
-2.04
9.
$SPY
-.2
Fig. 6. Tweet Texts captured for “Facebook” from multiple investors.
Compared to any horizontal approach such as KNN to scan
for the term frequency, our approach shows much better results
in terms of speed and accuracy. The reason for the
improvement in speed is mainly due to the complexity of the
two algorithms. Usually, the high cost of KNN-based
algorithms is mainly associated with their selection phases. The
selection phase in our algorithm has a complexity of O(n)
where n is the number of dimensions (number of terms) while
the KNN approach has a complexity of O(mn) for its selection
phase where m is the size of the dataset (number of documents
or tuples) and n is the number of dimensions. Drastic
improvement is shown when the size of the matrix is very large
(the case of 5000x20000 matrix size in Table III). As for
accuracy, the KNN approach bases its judgment on the
similarity between two document vectors upon the angle
between those vectors regardless of the actual distance between
them. Our approach does a more sophisticated comparison by
using P-tree ANDing to compare the closeness of the value of
each term in the corresponding vectors, thus being able to
judge upon the distance between the two vectors and not only
the angle. Also, terms that seem to skew the result could have
been ignored in our algorithm unlike in the KNN approach
which has to include all the terms in the space during the
neighbor-selection process.
TIME COMPARISON TABLE
B. CLASSIFYING INVESTORS
With the globally most frequent ticker symbols now been
classified we would like to evaluate the sentiment of the
investors so that we can study their effect on certain ticker
symbols. Investors can safely be assumed to be sentiment
driven. Since we emphasize so heavily on the tweet texts it is
important to make sure that the investors are not underreacting
or overreacting for particular ticker symbols. The real
investors and markets are very complicated to be summarized
by a few selected biases and trading frictions. The top down
approach [] [] focuses on the measurement of reduced form,
aggregate sentiment and traces its effects to market returns and
individual stocks. The approach is based on two broad
undisputable assumptions of behavioral finance—sentiment
and the limits to arbitrage—to explain which stocks are likely
to be most affected by sentiment, rather than simply pointing
out that the level of stock prices in the aggregate depends on
sentiment. In particular, stocks of low capitalization, younger,
unprofitable, high volatility, non-dividend paying, growth
companies, or stocks of firms in financial distress, are likely to
be disproportionately sensitive to broad waves of investor
sentiment. In particular, stocks that are difficult to arbitrage or
to value are most affected by sentiment.
S2 denotes the standard deviation of the population above the
mean as shown in (1) and (2).
𝑆1 =
1
𝑛1 −1
∑𝑖𝑛1 𝑓1𝑖 (𝑥𝑖 – 𝑥1 ) 2
(1)
𝑆2 =
1
𝑛2 −1
∑𝑖𝑛2 𝑓2𝑖 (𝑥𝑖 – 𝑥2 ) 2
(2)
The composite standard deviation S of the population is
calculated as shown in (3).
𝑆=
𝑛1 .𝑆1 2 + 𝑛2 .𝑆2 2
(3)
𝑛1 +𝑛2 −1
Where 𝑛1 = ∑𝑖 𝑓1𝑖 and 𝑛2 = ∑𝑖 𝑓2𝑖
The weighted mean deviation about mean is shown in (4) and
it removes any bias from the measures of the tweet counts of
the investors.
1
𝑛1 + 𝑛2 −1
𝑛
𝑛
̂ | + ∑𝑖 2 𝑓2𝑖 | 𝑋2𝑖 − 𝑋
̂|)
( ∑𝑖 1 𝑓1𝑖 | 𝑋1𝑖 − 𝑋
̂=
Where 𝑋
1
𝑛1 + 𝑛2 −1
𝑛
(4)
𝑛
[∑𝑖 1 𝑋1𝑖 + ∑𝑖 2 𝑋2𝑖 ]
VI. FUTURE DIRECTION
With the twitter data now being accessible and loaded in
various P-Tree views, the future potential in this area can be
significant. P-Trees will help us analyze if necessary trillion
records deep. The main idea illustrated in this paper is solving
a classification problem to understand which ticker symbols we
would focus on depending on the tweets made by the investors.
Some users can also trade against this information based on
their investment pattern. The actual movement of the stocks in
the market in various time frames and their fluctuations can be
related with the information impact from this data. Investors
whose predictions have been in accordance with the stock
fluctuations can be assigned higher weightage values to further
classify ticker symbols.
Fig. 8. Cross-sectional effects of investor sentiment. Stocks that are
speculative and difficult to value and arbitrage will have higher relative
valuations when sentiment is high.
When sentiment is low, the average future returns of
speculative stocks exceed those of bond-like stocks. When
sentiment is high, the average future returns of speculative
stocks are on average lower than the returns of bond-like
stocks.
In our analysis, we focus on investors being sentiment
driven on particular ticker symbols based on their tweet
counts. The more is the heterogenity of the population of
investors tweeting on Ts, signifies Ts is been discused by a
wider population range. Let X: X1, X2,……….. , Xn be the
population of the investors who are tweeting on ticker symbol
Ts and f: f1, f2,……….. , fn denote the frequency of tweets made
by the investors. We use the median divisor principle as the
respective tweets are exhibiting two different patterns of
behavior based on the median value. In other words, below the
median, they will exhibit a certain pattern and above the
median, they exhibit a different pattern. So, we segregate them
in two subdivisions n1, n2 from the median where S1 denotes
the standard deviation of the population below the mean and
In our approach we believe that adding the third dimension,
namely term position in the tweet, offers us a wide range of
possible new decision supports, such as phrase analysis
(multiple juxtapose terms), such as “Buy AAPL”, the
evaluation of which could be done by shifting the “AAPL” PTree by one position bit, then AND’ing with the “Buy” P-Tree.
In addition to phrase analysis, the position dimension also
opens up the potential of discovering signals based on where in
a tweet, a particular term appears (early on, later, etc.). Of
course, introducing the third dimension of term position
massively expands the size of the data cube being considered
and
necessitates
effective
compression
techniques.
Fortunately, when converting to P-Trees in each of the three
dimensions, it is true that in all but one of the dimensions
(document dimension) each P-Tree is as sparse as it could
possibly be (a single one-bit) and therefore compresses
maximally. In the document dimension, by replicating single
one-bit P-Trees, instead of using links, the same advantage can
be realized. These advantages will be pursued in the future as
well.
We also plan to include this solution as a phone app which
will be commercially available to the end consumers on
Windows, Android and the iOS platforms.
VII. CONCLUSION AND LIMITATIONS
We have shown in this paper how using Twitter API and PTree’s we can provide insight to users who would like to invest
in the market but cannot identify which ticker symbols they
would like to invest in. They can use this solution which can
provide them insight to make business investment decisions.
We have also classified the investors based on their tweet
counts and have ensured that any bias from the measures is
removed. We have used classification as a decision support and
have not really used sentiment analysis in this approach. We
believe if the available information is provided in an easy
consumable manner, humans derive sentiments better than
NLP tools. The sentiment analysis derived from NLP solutions
have not always revealed accurate insights but if necessary we
would leverage NLP to derive sentiments from the tweet texts
when the generated output is considerably large to process by
humans.
[6]
[7]
[8]
[9]
[10]
[11]
[12]
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Cochrane Drive, Suite 300, Annapolis, Ma