Alliance Beats Isolation: Unifying Heterogeneous Allied Datasets Improves Classifier Performance

# 1Introduction
Source: [https://arxiv.org/html/2609.19748](https://arxiv.org/html/2609.19748)
††graphicalabstract:![[Uncaptioned image]](https://arxiv.org/html/2609.19748v1/fig_data_unification.png)††highlights:Defines the notion of allied datasets, having data about similar objects, similar class\-labels and overlapping but otherwise heterogeneous feature\-spaces Proposes a method to merge the feature\-spaces into a single feature\-space for a pair of allied datasets Uses a matrix completion method to create a unified dataset based on the merged feature\-space Hypothesizes that merged representation facilitates transfer of classification knowledge from one dataset to another Experimentally demonstrates that any classifier trained on the unified representation always outperforms classifiers separately trained on the constituent allied datasets on several pairs of allied datasets###### Abstract

In many application domains, such as student dropout, insurance fraud, loan approval, and machine failures, several labelled public datasets are available where \(i\) data is about the same type of objects but the set of actual underlying objects are disjoint; and \(ii\) the class labels are same; and \(iii\) the feature spaces of the datasets are largely distinct \(heterogeneous\), with a few shared features\. We call such datasets asallied\. A single classifier cannot be trained on both datasets together, and one classifier trained on one dataset cannot be tested on the other\. In this paper, we propose a method to merge the feature\-spaces into a single feature\-space for a pair of given allied heterogeneous datasets\. We then use a matrix completion method to create a unified dataset based on the merged feature\-space\. The hypothesis is that the merged representation facilitates the transfer of classification knowledge from one dataset to another\. We conduct experiments on several pairs of allied, heterogeneous datasets and several classifiers to demonstrate that any classifier trained on the unified representation always outperforms classifiers separately trained on the constituent allied datasets on several pairs of allied datasets\. This work provides an easy way to substantially improve classifier performance by unifying and using multiple allied datasets together\.

###### Keywords:

Data unification , Matrix Completion , Classification , Machine Learning

## 1Introduction

In many domains, several labelled public datasets are available with the following characteristics: \(i\) data is about the same type of objects but the set of actual underlying objects are disjoint; and \(ii\) the class labels are same; and \(iii\) the feature spaces of the datasets are largely distinct, with a few shared features\. We call such datasets asallied\. For simplicity, we assume that the class labels are binary\{0,1\}\\\{0,1\\\}, with11denoting the minority class of interest \(e\.g\., a dropped out student, or a fraudulent claim\)\. Generalization to more than two class labels is simple\. For simplicity, we assume that we are given two allied, heterogeneous datasets, denotedD1D\_\{1\}andD2D\_\{2\}, each as a single table\. Generalization to more than two allied constituent datasets is simple and discussed later\. If the dataset is split across multiple tables, we assume it can be brought into a single table form, say by denormalization\.

Table 1:Examples of Allied Datasets- 0All values in this table are based on pre\-processed dataset versions aligned with each other
- 1Rows having class labelEnrolledwere removed
- 2kaggle\.com/datasets/shivamb/vehicle\-claim\-fraud\-detection
- 3https://data\.mendeley\.com/datasets/992mh7dk9y/2
- 4kaggle\.com/datasets/mmumairkhattak/loan\-approval\-dataset\-2026\-credit\-risk\-and\-bank\-a
- 5kaggle\.com/datasets/mytalkwithyou/bank\-loan\-approval\-dataset
- 6kaggle\.com/datasets/saquib7hussain/machine\-failure\-prediction\-dataset?select=machine\_failure\_data\.csv
- 7kaggle\.com/datasets/zara2099/iiot\-sensor\-data\-for\-predictive\-maintenance

Table[1](https://arxiv.org/html/2609.19748#S1.T1)shows some allied public datasets, each with twoconstituent datasets\. One example has two constituent datasets about student attrition \(OULAD\[[7](https://arxiv.org/html/2609.19748#bib.bib10)\]and HEPSR\[[8](https://arxiv.org/html/2609.19748#bib.bib6)\]\), where the objects are students and the courses they are enrolled in and the class label is about whether the student completed the course or dropped out of it\. The individual students in the two datasets are unrelated and disjoint\. Both datasets share some common features \(with possibly different names\) but the other features are specific to each dataset\. These datasets are inherentlyheterogeneousi\.e\., they differ in terms of feature spaces, schema representations, and data distributions\. Another example shows two constituent datasets about automobile insurance claims, where the main objects are claims, insurance policies, vehicles and policy\-holders, and the class label indicates whether the claim was fraudulent or not\. The claims in the two datasets are unrelated \(different\)\. The feature spaces are heterogeneous\.

Such allied labelled datasets in a domain are collected independently by different teams and their data elements \(e\.g\., rows\) refer todifferent, unrelatedobjects\. Because of these differences, such allied datasets cannot be directly merged to create a larger,unifieddataset for training\. A common way to use these allied datasets in ML is to train and evaluatedifferentprediction models, one for each of the allied datasets\. Consequently, each such model is tailored only to the characteristics of a dataset\. Each dataset\-specific model discards the non\-common attributes, and completely ignores the challenges posed by the heterogeneous feature spaces and different data distributions\. Such approaches lead to information loss and fail to exploit the complementary knowledge available across multiple datasets\. The models exhibit limited generalizability when it is desired to be applied to other allied datasets\. In fact, a model trained on, sayD1D\_\{1\}cannot even be directly tested onD2D\_\{2\}because of the presence of non\-shared attributes inD2D\_\{2\}which were not available when the model was trained onD1D\_\{1\}\.

The research questions addressed in this paper are:

1. 1\.Super\-Dataset \(Dataset Unification\): How canD1D\_\{1\}andD2D\_\{2\}beunified\(synthesized\) into asuper\-datasetD12D\_\{12\}, which effectively combines the information \(and knowledge\) hidden in the two constituent datasetsD1D\_\{1\}andD2D\_\{2\}and which minimizes the information loss? Any proposed data unification method should handle disjoint underlying objects, feature\-space heterogeneity, data distribution differences, and domain differences\. What would be the attributes inD12D\_\{12\}? How to construct the rows inD12D\_\{12\}from rows inD1D\_\{1\}andD2D\_\{2\}?
2. 2\.Would any standard predictive ML model trained on the unified datasetD12D\_\{12\}be more accurate than individual models \(of the same type\)M1M\_\{1\}andM2M\_\{2\}trained onD1D\_\{1\}andD2D\_\{2\}respectively? The model should be capable of providing robust and transferable predictions across multiple data contexts\.

We answer both questions affirmatively in this paper\.

There is limited research onconstructing a unified super\-dataset from multiple allied datasets while preserving both shared and dataset\-specific information\. As a result, it is not clear how a generalized ML model can learn from such allied datasets and accurately make predictions for objects already within either of the constituent datasets, or for unseen objects that may come in the format of data inD1D\_\{1\}or inD2D\_\{2\}\. Therefore, there is a need of developing an integrated framework that allows the user to building super\-classifiers from allied datasets\. This integrated framework would enable the development of a scalable, institution\-independent unified datasets and associated classification \(predictive\) models\. The idea is to leverage the diversity of heterogeneous allied data sources to improve prediction accuracy, robustness, and generalizability\.

This paper is organized as follows\. Section[2](https://arxiv.org/html/2609.19748#S2)formalizes the problem of unification of allied datasets\. Section[3](https://arxiv.org/html/2609.19748#S3)discusses relevant research work\. Section[4](https://arxiv.org/html/2609.19748#S4)gives details of the data unification procedure which can use any suitable matrix completion method\. Section[5](https://arxiv.org/html/2609.19748#S5)gives experimental results and provides some insights derived from them\. Section[6](https://arxiv.org/html/2609.19748#S6)provides conclusions and discusses some future work\.

## 2Problem Formalization

![Refer to caption](https://arxiv.org/html/2609.19748v1/fig_data_unification.png)Figure 1:Steps in creating a unified dataset from constituent allied datasets\.LetD1D\_\{1\}andD2D\_\{2\}be two given aligned datasets, both having data about the same type of objects, having disjoint sets of underlying objects, having some shared \(common\) features and otherwise heterogeneous features, and having the same binary class labels\. Fig\.[1](https://arxiv.org/html/2609.19748#S2.F1)shows the steps involved in creating a unified representation from constituent datasetsD1D\_\{1\}andD2D\_\{2\}\. In the first step, wealign\(orclean\) these two given allied datasets:

1. 1\.Ensure all columns shared between the two datasets have the same names \(change names, if required\)\. Ensure that each shared attribute has exactly the same meaning and similar values in both datasets; e\.g\., consistently mapping value in columnGenderin both datasets, or convertingDOBtoAge\)\.
2. 2\.Remove columns that are the primary keys for the table \(e\.g\.,Student\_ID, orClaim\_ID\)\.
3. 3\.Replace values in every categorical column with numbers\.
4. 4\.Ensure each shared categorical column has the same set of possible values\.
5. 5\.Ensure the class labels are binary\{0,1\}\\\{0,1\\\}in both tables, with11denoting the minority class of interest \(e\.g\., a dropped out student, or a fradulent claim\)\.
6. 6\.Move all shared columns to the beginning of the table, with the shared class label column as the first\.
7. 7\.If required, add simplederived attributesif they can be shared between the datasets\.
8. 8\.Remove columns which are unsuitable for any simple conversion to numbers, e\.g\.,Address\.
9. 9\.Remove redundant columns; e\.g\., removeDOBif a new converted columnAgeis added\.

Formally, let𝐃a​l​l​i​e​d=\{D1,D2\}\\mathbf\{D\}\_\{allied\}=\\\{D\_\{1\},D\_\{2\}\\\}denote a collection of \(for simplicity\) two given allied and aligned \(cleaned\) datasetsD1D\_\{1\}andD2D\_\{2\}\. We further assume that each dataset is a single table, where each row refers to a specific type of object, such as a student or an insurance claim\. In general, the two sets of underlying objects forD1D\_\{1\}andD2D\_\{2\}are completely disjoint\. Let the two datasets havekkcommon, shared attributes𝐂=\{C1,C2,…,Ck\}\\mathbf\{C\}=\\\{C\_\{1\},C\_\{2\},\\ldots,C\_\{k\}\\\}having the same meaning in both\. Let𝐀𝟏=\{C1,C2,…,Ck,A1\(1\),A2\(1\),…,An1\(1\)\}\\mathbf\{A\_\{1\}\}=\\\{C\_\{1\},C\_\{2\},\\ldots,C\_\{k\},A^\{\(1\)\}\_\{1\},A^\{\(1\)\}\_\{2\},\\ldots,A^\{\(1\)\}\_\{n\_\{1\}\}\\\}and𝐀𝟐=\{C1,C2,…,Ck,A1\(2\),A2\(2\),…,An2\(2\)\}\\mathbf\{A\_\{2\}\}=\\\{C\_\{1\},C\_\{2\},\\ldots,C\_\{k\},A^\{\(2\)\}\_\{1\},A^\{\(2\)\}\_\{2\},\\ldots,A^\{\(2\)\}\_\{n\_\{2\}\}\\\}denote the sets of attributes of these two datasets \(n1\+kn\_\{1\}\+kandn2\+kn\_\{2\}\+kattributes respectively\), each including the common attributes\.

The alliedstudent\_dropoutdatasets OULAD and HEPSR are about completely disjoint sets of students and only a few features are shared between them \(Table[2](https://arxiv.org/html/2609.19748#S2.T2)\)\. Similar is the case for the two allied datasets on automobile insurance claims\. In HEPSR dataset, we have used the feature namesC1andC2to refer to curricular units that the student was approved for enrollment in the first and second semester respectively\. The featureimd\_bandin OULAD is comparable to the combined value of 3 features in HEPSR\. Thus, some pre\-processing and standardization is often necessary to make the values in these common features comparable across the two allied datasets\.

Table 2:Common Attributes in Two Allied Datasets\.
## 3Related Work

Data integration is a well\-known problem in data management, whose aim is to provide simple, coherent, perspective\-specific views of large and diverse data sources\. It is often formulated as mapping queries between a global \(mediated\) schema and various source schemas\. Techniques such asExtract, Transform, Load \(ETL\)and technologies such asData Warehousing\[[4](https://arxiv.org/html/2609.19748#bib.bib1)\]andData Lakes111https://www\.pwc\.com/us/en/technology\-forecast/2014/cloud\-computing/assets/pdf/pwc\-technology\-forecast\-data\-lakes\.pdfare widely used for these tasks\. In contrast, the aim in this paper is to unify allied datasets for improving classfication\. The task in Data imputation\[[3](https://arxiv.org/html/2609.19748#bib.bib2)\]is to estimate the missing values in given data\. This paper has proposed a novel application of the data imputation techniques of matrix completion for the purpose of data unification\.

Many methods have been devised formatrix completion\[[9](https://arxiv.org/html/2609.19748#bib.bib9)\],\[[5](https://arxiv.org/html/2609.19748#bib.bib8)\],\[[10](https://arxiv.org/html/2609.19748#bib.bib7)\]\. Matrix completion involves reconstructing a matrix from only a small subset of its observed entries\. This problem is important in many applications \- e\.g\., recommender systems, collaborative filtering, and compressed sensing \- where collecting all entries of the data matrix is usually too costly\. Matrix completion methods are broadly divided into two types: passive and adaptive\. Passive methods are widely used in machine learning\. Many of these methods assume that the unknown matrix has a low\-rank structure, and then pose an optimization problem to find the lowest rank matrix which matches with the observed entries in the given incomplete matrix\.Nuclear norm minimizationmethods are a convex version of rank minimization and use the sum of singular values to identify low\-rank solutions\.Alternating minimizationmethods factorize the unknown target matrix into a product of two smaller low\-rank matricesX=U​VTX=UV^\{T\}and alternate the optimization steps between them\.Iterative principal component analysis \(PCA\)methods fills missing entries with initial guesses, run PCA approximations, update the cells, and repeat until convergence\.

Federated Learning\[[6](https://arxiv.org/html/2609.19748#bib.bib3)\]is another related line of research, where broadly the task is privacy\-preserving, decentralized ML, involving issues of local training, model distribution, update sharing and aggregating to construct the global ML model\. Related techniques ofkk\-anonymity, and differential privacy inPrivacy\-Preserving Data Mining\[[1](https://arxiv.org/html/2609.19748#bib.bib4)\]aim to learn useful patterns in data while protecting identification and leakage of sensitive information\. In this paper, we are not attempting distributed ML nor privacy preservation\.

Finally,co\-training\[[2](https://arxiv.org/html/2609.19748#bib.bib5)\]is a closely related semi\-supervised ML algorithm, which splits given lalelled data into two feature\-spaces, learns separate classifiers on each view, and then uses their predictions on given unlabelled data to automatically create more labelled data\. Crucial assumptions in co\-training are \(i\) that the two feature sets of each instance are conditionally independent given the class\-label; \(ii\) each view is sufficient to predict the class accurately\. In this paper, we are not proposing a new ML algorithm, and we are also not learning two separate classifiers on two datasets\. We also do not need any unlabelled data\. Our goal is to systematically unify the datasets to improve classification accuracy ofanyclassifier\. We are also not making any independence assumptions between the two feature\-spaces; in fact, we have assumed that the two feature\-spaces share at least a few features\.

## 4Unifying Allied Datasets into a Super\-Dataset

### 4\.1Merged Data Matrix

M=\[D1,1\(1\)…D1,k\(1\)D1,k\+1\(1\)…D1,k\+n1\(1\)N​A…N​A………………………DN1,1\(1\)…DN1,k\(1\)DN1,k\+1\(1\)…DN1,k\+n1\(1\)N​A…N​AD1,1\(2\)…D1,k\(2\)N​A…N​AD1,k\+1\(2\)…D1,k\+n2\(2\)………………………DN2,1\(2\)…DN2,k\(2\)N​A…N​ADN2,k\+1\(2\)…DN2,k\+n2\(2\)\]M=\\left\[\\begin\{array\}\[\]\{ccc\|ccc\|ccc\}D^\{\(1\)\}\_\{1,1\}&\\ldots&D^\{\(1\)\}\_\{1,k\}&D^\{\(1\)\}\_\{1,k\+1\}&\\ldots&D^\{\(1\)\}\_\{1,k\+n\_\{1\}\}&NA&\\ldots&NA\\\\ \\ldots&\\ldots&\\ldots&\\ldots&\\ldots&\\ldots&\\ldots&\\ldots&\\ldots\\\\ D^\{\(1\)\}\_\{N\_\{1\},1\}&\\ldots&D^\{\(1\)\}\_\{N\_\{1\},k\}&D^\{\(1\)\}\_\{N\_\{1\},k\+1\}&\\ldots&D^\{\(1\)\}\_\{N\_\{1\},k\+n\_\{1\}\}&NA&\\ldots&NA\\\\ \\hline\\cr D^\{\(2\)\}\_\{1,1\}&\\ldots&D^\{\(2\)\}\_\{1,k\}&NA&\\ldots&NA&D^\{\(2\)\}\_\{1,k\+1\}&\\ldots&D^\{\(2\)\}\_\{1,k\+n\_\{2\}\}\\\\ \\ldots&\\ldots&\\ldots&\\ldots&\\ldots&\\ldots&\\ldots&\\ldots&\\ldots\\\\ D^\{\(2\)\}\_\{N\_\{2\},1\}&\\ldots&D^\{\(2\)\}\_\{N\_\{2\},k\}&NA&\\ldots&NA&D^\{\(2\)\}\_\{N\_\{2\},k\+1\}&\\ldots&D^\{\(2\)\}\_\{N\_\{2\},k\+n\_\{2\}\}\\\\ \\end\{array\}\\right\]Figure 2:Merged data matrix representation for two aligned \(cleaned\) allied datasetsD1D\_\{1\}andD2D\_\{2\}\.The first step to unify the two allied, and aligned datasetsD1D\_\{1\}andD2D\_\{2\}is to construct a merged data matrixMM\(Fig\.[2](https://arxiv.org/html/2609.19748#S4.F2)\), as follows\.

1. 1\.Construct a combined feature set𝐀c​o​m​b=C∪An​o​n​s​h​a​r​e​d\(1\)∪An​o​n​s​h​a​r​e​d\(2\)\\mathbf\{A\}\_\{comb\}=C\\cup A^\{\(1\)\}\_\{nonshared\}\\cup A^\{\(2\)\}\_\{nonshared\}, where𝐂\\mathbf\{C\}is the shared common attributes and𝐀n​o​n​s​h​a​r​e​d\(1\)=\{A1\(1\),A2\(1\),…,An1\(1\)\}\\mathbf\{A\}^\{\(1\)\}\_\{nonshared\}=\\\{A^\{\(1\)\}\_\{1\},A^\{\(1\)\}\_\{2\},\\ldots,A^\{\(1\)\}\_\{n\_\{1\}\}\\\}is the set of features present inD1D\_\{1\}but not inD2D\_\{2\}\.𝐀n​o​n​s​h​a​r​e​d\(2\)\\mathbf\{A\}^\{\(2\)\}\_\{nonshared\}is similarly defined\.
2. 2\.Construct a combined \(merged\) data matrixMMwithN1\+N2N\_\{1\}\+N\_\{2\}rows and\|Ac​o​m​b\|=k\+n1\+n2\|A\_\{comb\}\|=k\+n\_\{1\}\+n\_\{2\}columns, whereN1N\_\{1\}andN2N\_\{2\}are the number of rows inD1D\_\{1\}andD2D\_\{2\}respectively\. For theii\-th row,1≤i≤N11\\leq i\\leq N\_\{1\}, their firstk\+n1k\+n\_\{1\}columns are filled with the corresponding values in theii\-th row inD1D\_\{1\}and the nextn2n\_\{2\}columns are filled withN​ANAvalues\. Then for theN1\+jN\_\{1\}\+j\-th row,1≤j≤N21\\leq j\\leq N\_\{2\}, their firstkkcolumns are filled with the corresponding shared columns inD2D\_\{2\}, nextn1n\_\{1\}columns are filled withN​ANAvalues, and the lastn2n\_\{2\}columns are filled with the corresponding values in thejj\-th row inD2D\_\{2\}\. Here,N​ANAindicates a missing value\. We have assumed that in bothD1D\_\{1\}andD2D\_\{2\}the firstkkcolumns are the shared ones\.

Here,Di,p\(1\)D^\{\(1\)\}\_\{i,p\}\(Di,p\(2\)D^\{\(2\)\}\_\{i,p\}\) denotes the value in theii\-th row andpp\-th column in datasetD1D\_\{1\}\(respectively, datasetD2D\_\{2\}\)\.

### 4\.2Matrix Completion

Given the merged data matrix representationMMfor two allied, aligned datasets, the problem of constructing the unified datasetDu​n​i​f​i​e​dD\_\{unified\}can now be posed as the problem of completing the merged data matrixMMi\.e\., estimating the missing values denoted byN​ANA\. There areN1×n2\+N2×n1N\_\{1\}\\times n\_\{2\}\+N\_\{2\}\\times n\_\{1\}missing entries in the matrixMM, out of a total of\(N1\+N2\)×\(k\+n1\+n2\)\(N\_\{1\}\+N\_\{2\}\)\\times\(k\+n\_\{1\}\+n\_\{2\}\)entries\.

Many methods have been devised formatrix completion\[[9](https://arxiv.org/html/2609.19748#bib.bib9)\],\[[5](https://arxiv.org/html/2609.19748#bib.bib8)\],\[[10](https://arxiv.org/html/2609.19748#bib.bib7)\]\. We used theiterative SVDmethod of matrix completion, which works well when the number of rows is much greater than the number of columns, to unify the two allied and aligned datasets i\.e\., to estimate theN​ANAvalues in the merged data matrix representation\.

As an example, for OULAD and HEPSR allied datasets \(after alignment\),N1=32593,n1=20,N2=3630,n2=28,k=7N\_\{1\}=32593,n\_\{1\}=20,N\_\{2\}=3630,n\_\{2\}=28,k=7\. The total number of entries in the merged data matrix is\(32593\+3630\)×\(7\+20\+28\)=1992265\(32593\+3630\)\\times\(7\+20\+28\)=1992265, out of which the number of missing entries is32593×28\+3630×20=98520432593\\times 28\+3630\\times 20=985204\(49\.4549\.45%\)\. Specifically,n2n\_\{2\}entries are missing in each of the firstN1N\_\{1\}rows \(for OULAD students\) andn1n\_\{1\}entries are missing in each of the nextN2N\_\{2\}rows after the firstN1N\_\{1\}rows \(for HEPSR students\)\. These missing entries are estimated and the unified data matrix is created very efficiently by the iterative SVD matrix completion method\.

## 5Empirical Results

Table 3:Classifier Performance on Allied Datasets in Various ScenariosTrainingTestXGBoostRFSVMKNNPrec\.Recall𝐅𝟏\\mathbf\{F\_\{1\}\}1𝐅𝟏\\mathbf\{F\_\{1\}\}𝐅𝟏\\mathbf\{F\_\{1\}\}𝐅𝟏\\mathbf\{F\_\{1\}\}oulad\_ cleaned2−\-0\.75350\.75350\.77830\.77610\.79380\.7351hepsr\_ cleaned−\-0\.91360\.91360\.87410\.86840\.87300\.7641oulad\_ extended3−\-0\.95410\.95410\.95160\.86870\.99290\.8165hepsr\_ extended−\-1\.00001\.00000\.99890\.99960\.99510\.9822student\_dropout\_ unified4−\-0\.96100\.96100\.95680\.88290\.99230\.8244student\_dropout\_ unifiedoulad\_ extended1\.00000\.99991\.00001\.00000\.99711\.0000student\_dropout\_ unifiedhepsr\_ extended1\.00001\.00001\.00001\.00001\.00001\.0000oulad\_ extendedhepsr\_ extended0\.87980\.71080\.78630\.81020\.00000\.6408hepsr\_ extendedoulad\_ extended0\.52860\.95960\.68170\.71460\.77720\.7102oracle\_ cleaned−\-0\.34680\.34680\.11290\.00220\.22830\.0507mendeley\_ cleaned−\-0\.55680\.55680\.47190\.13480\.34570\.1502oracle\_ extended−\-0\.99890\.99890\.97150\.84630\.99010\.7479mendeley\_ extended−\-0\.99150\.99150\.96440\.87181\.00000\.3881auto\_fraud\_ unified−\-0\.98470\.98470\.95410\.78140\.87350\.3441auto\_fraud\_ unifiedoracle\_ extended1\.00001\.00001\.00001\.00001\.00001\.0000auto\_fraud\_ unifiedmendeley\_ extended1\.00001\.00001\.00001\.00001\.00001\.0000oracle\_ extendedmendeley\_ extended0\.30830\.16600\.21580\.32030\.00000\.2081mendeley\_ extendedoracle\_ extended0\.11180\.11700\.11430\.08780\.00210\.0160umair\_ cleaned−\-1\.00001\.00001\.00001\.00000\.99250\.8735sharma\_ cleaned−\-0\.98500\.98500\.98010\.97240\.91610\.8601umair\_ extended−\-1\.00001\.00001\.00001\.00000\.99880\.8936sharma\_ extended−\-1\.00001\.00000\.99880\.99881\.00000\.9975loan\_approval\_ unified−\-1\.00001\.00000\.99970\.99960\.99770\.8944loan\_approval\_ unifiedumair\_ extended1\.00001\.00001\.00001\.00000\.99931\.0000loan\_approval\_ unifiedsharma\_ extended1\.00001\.00001\.00001\.00000\.99751\.0000umair\_ extendedsharma\_ extended1\.00000\.39430\.56560\.56110\.54950\.5564sharma\_ extendedumair\_ extended0\.89710\.55840\.68840\.75330\.00000\.6276saquib\_ cleaned−\-0\.16140\.16140\.04090\.00670\.15920\.0288iiot\_ cleaned−\-0\.41690\.41690\.26640\.09710\.33990\.1069saquib\_ extended−\-1\.00001\.00000\.99831\.00001\.00001\.0000iiot\_ extended−\-0\.41690\.41690\.26640\.09710\.33990\.1069machine\_failure\_ unified−\-0\.88160\.88160\.78670\.79150\.77720\.7744machine\_failure\_ unifiedsaquib\_ extended1\.00001\.00001\.00001\.00001\.00001\.0000machine\_failure\_ unifiediiot\_ extended1\.00001\.00001\.00001\.00000\.95011\.0000saquib\_ extendediiot\_ extended0\.24660\.33950\.28570\.33200\.00000\.3619iiot\_ extendedsaquib\_ extended0\.15710\.17450\.16530\.01920\.34450\.16111When the test dataset is not specified, theP,R,F1P,R,F\_\{1\}numbers refer to55\-fold cross\-validation on training dataset\. Moreover, they are for the minority class11\.2cleaned: original rows and columns \(after pre\-processing and alignment\)3extended: original rows and columns \(after pre\-processing and alignment\) \+ extended columns3unified: union of all rows \+ all extended columns![Refer to caption](https://arxiv.org/html/2609.19748v1/fig_exp_scenarios.png)Figure 3:Nine different experimental scenarios\.For each pair of allied, and aligned datasets \(Table[1](https://arxiv.org/html/2609.19748#S1.T1)\), we performed experiments under several scenarios \(Fig\.[3](https://arxiv.org/html/2609.19748#S5.F3)\), where we trained several classical ML models \(classifiers\) and computed the associated performance measures such as Precision, Recall andF1F\_\{1\}\. We did not do any feature engineering, except standardizing all numeric features\. We have also not performed any hyper\-parameter tuning, and used only the default values for the hyper\-parameters \(e\.g\., RBF kernel andC=1C=1forSVM,k=5k=5forKNNetc\.\)\. Table[3](https://arxiv.org/html/2609.19748#S5.T3)shows the results for four classifiersXGBoost, RandomForest, SVM, KNN; results for other classifiers were similar\. We used the classifier implementations in Python’sscikit\-learnpackage\. Using classifier implementations inpyCaretpackage gave similar results\. Since both the datasetsD1D\_\{1\}andD2D\_\{2\}now have thesamefeature\-space in the cleaned, extended and unified versions, we are free to try various combinations, such as \(i\) train a classifier on one extended dataset and test thesameclassifier on the other extended dataset, or \(ii\) train a classifier on the unified dataset and test it oneachconstituent extended dataset, as shown in the Table\. Broad observations about the results are as follows:

1. 1\.Numbers inredare the baselineF1F\_\{1\}\-measures \(5\-fold cross\-validation\) on the cleaned and aligned versions of the datasets\. Numbers inblueare theF1F\_\{1\}\-measures \(5\-fold cross\-validation\) on the extended versions, where more columns were added to each constituent dataset and whose values were estimated using matrix completion\. The training and testing was only on the constituent dataset, but with extended columns\. As seen, adding extended columns has clearly improved the performance of all classifiers for all allied datasets, as compared to the baselines \(which used the original cleaned, aligned data butwithoutextended columns\)\. Thus we can unambiguously infer that adding extended column to one dataset, which were computed from the other, allied dataset is clearly beneficial\. For OULAD, the baselineF1F\_\{1\}\-measure on the cleaned, aligned dataset is0\.77830\.7783\(55\-fold cross\-validation\) forXGBoost, whereas when using the cleaned,andextended OULAD dataset, theF1F\_\{1\}value forXGBoostimproves to0\.95160\.9516\(Δ=0\.1733\\Delta=0\.1733, a clear22\.322\.3% improvement\)\. For HEPSR, the corresponding numbers are:0\.87410\.8741\(XGBooston cleaned\),0\.99890\.9989\(XGBooston extended\),Δ=0\.1248\\Delta=0\.1248\(14\.314\.3% improvement\)\. TheF1F\_\{1\}and hence the improvement level is more forRandomForeston extended OULAD dataset\. The same trend is seen on all pairs of allied datasets and all classifiers that we have tried\.Only adding the extended columns to the original dataset improves the classifier cross\-validation performance\.Since the values in the extended columns forD1D\_\{1\}are estimated using rows inbothD1D\_\{1\}andD2D\_\{2\}, this clearly shows that the knowledge fromD2D\_\{2\}is transferred and learned by the classifier trained only onD1D\_\{1\}extended, even though the rows forD2D\_\{2\}arenotused in the training on extendedD1D\_\{1\}\.
2. 2\.Training and testing on the entire unified dataset \(which has rows from both datasets and all extended columns\) yields very good performance\. These numbers are always better than the baselines, though not necessarily the best\. For example, trainingXGBooston theauto\_fraud\_unifieddataset, yields the 5\-fold cross validationF1=0\.9541F\_\{1\}=0\.9541, much better than the baselines\. Thustraining a classifier on the entire unified dataset yields very good cross\-validation performance, better than the corresponding numbers on only the cleaned constituent datasets\.
3. 3\.As seen, for all the classifiers and all allied datasets, training on the unified dataset and testing on the extended subsets \(corresponding to extended constituent datasets\) yields perfectF1F\_\{1\}scores \(1\.01\.0, or very close\), shown inbold\. This may be attributed perhaps to the classifiers memorizing the data, since the test dataset is a subset of the unified dataset on which the classifier was trained\.
4. 4\.Interestingly, if a classifier is trained on the entireunifieddataset \(rows from both datasets and all extended columns\), and tested on constituent extended datasets, the performance always improves, but not necessarily yielding the most improvement\. For instance, theXGBoostclassifier trained on theauto\_fraud\_unifieddataset showsF1=0\.8872F\_\{1\}=0\.8872andF1=0\.8872F\_\{1\}=0\.8872respectively when tested onoracle\_extendedandmendeley\_extendeddatasets\. While these numbers are much improved over the baseline figures of0\.08890\.0889and0\.44970\.4497on the two corresponding cleaned datasets, they are less than the best numbers0\.96600\.9660\(trained onmendeley\_extendedand tested onoracle\_extended\) and0\.97720\.9772\(trained onoracle\_extendedand tested onmendeley\_extended\)\. This shows that the knowledge transfer is sometimes better from one constituent extended dataset to another, rather than from the unified dataset to constituent extended dataset\. In either case, the extended columns are playing a critical role as carriers of knowledge, leading to substantial improvements\.
5. 5\.In theloan\_approvaldatasets, the cleaned versions already deliver an extremely high performance, even without the extended columns\. However, adding the extended columns does lead to tiny improvements, and certainly does notreducethe original perfoemance figures\. This shows that adding extended columns is always likely to be beneficial\.

For standalone original OULAD data, the performance of theXGBoost\(Extreme Gradient Boosting\) classifier isP=0\.7553,R=0\.8260,F1=0\.7889P=0\.7553,R=0\.8260,F\_\{1\}=0\.7889, with1010\-fold cross\-validation\. For theRandom Forestclassifier, the performance on the same data isP=0\.7588,R=07982,F1=0\.7778P=0\.7588,R=07982,F\_\{1\}=0\.7778\. When using the full unified data \(rows in OULAD as well as HEPSR data, along with all extended columns i\.e\., estimated values for all missing entries\), the performance of theXGBoostclassifier jumps toP=0\.9632,R=0\.9547,F1=0\.9589P=0\.9632,R=0\.9547,F\_\{1\}=0\.9589and forRandom Forestclassifier it jumps toP=0\.8765,R=0\.8717,F1=0\.8740P=0\.8765,R=0\.8717,F\_\{1\}=0\.8740, showing a substantial improvement\. Similar substantial jumps are observed in all classifiers that we tried\. Clearly, the knowledge hidden in both the OULAD and HEPSR data has also been learnt simultaneously by the classifier trained on the unified data, since rows for both OULAD and HEPSR data are present in the unified data and the extended columns added for OULAD rows \(HEPSR rows\) explicitly model information derived from original HEPSR data \(respectively, original OULAD data\)\.

Using only the firstN1=32593N\_\{1\}=32593rows corresponding to OULAD students, Fig\.[4](https://arxiv.org/html/2609.19748#S5.F4)shows the change inF1F\_\{1\}of two classifiers against the number of extended columns used\. Clearly, for both classifiers, the performance keeps improving as more extended columns are used, even though the rows corresponding to HEPSR students are not used in the training\. A similar improvement pattern is observed for HEPSR data\. Note that the improvement for OULAD students is less forRandomForestthanXGBoost, even when all extended columns are used\. Moreover, as already shown, the performance of both classifiers improves on OULAD students, when using all extended columns and all rows \(OULAD as well as HEPSR\), demonstrating that the the classifier is learning from both sets of students\. Dropping one set of students from training mildly reduces the size of the jump in the performance \(for both classifiers\)\.

![Refer to caption](https://arxiv.org/html/2609.19748v1/F1_unified_data_fig1.png)
![Refer to caption](https://arxiv.org/html/2609.19748v1/F1_unified_data_fig2.png)

Figure 4:Change inF1F\_\{1\}\-measure vs\. the number of extended columns used for \(a\) OULAD students \(b\) HEPSR students\.![Refer to caption](https://arxiv.org/html/2609.19748v1/fig_chart3.png)Figure 5:Summary statistics forF1F\_\{1\}\-measure versus number of shared columns dropped fromauto\_fraud\_unifieddataset \.In another experiment, out ofkkshared columns, we systematically dropped subsets of sizejj,1≤j≤k−11\\leq j\\leq k\-1\(column 0 is the class label\) and computed the minimum, maximum and averageF1F\_\{1\}for each unified dataset\. Fig\.[5](https://arxiv.org/html/2609.19748#S5.F5)shows the result forauto\_fraud\_unifieddataset \(k=13k=13\)\. As seen, the minimum and averageF1F\_\{1\}values \(in 5\-fold cross\-validation\) keep reducing as the number of dropped shared columns increases\. Similar results are seen for other datasets and also when even more shared columns are dropped\. Dropping all shared columns \(other than the class label\) yields the minimum, maximum and averageF1F\_\{1\}as 0\.0, 0\.0 and 0\.0 respectively\. This shows that the shared columns have important influence on the classifier performance in the unified data\. This makes sesnse because as the number of shared columns is reduced, the number of filled\-up entries in the merged data matrix reduces and consequently, the matrix completion algorithm does a poorer job of estimating the missing data values\.

## 6Conclusions and Further Work

In this paper, we defined the notion ofallieddatasets, which are labelled datasets with same class\-labels, overlapping but otherwise distinct feature\-spaces and related but distinct objects within the domain\. We identified forur pairs of such allied datasets in diverse application domains: student dropout, insurance fraud, loan approval, and machine failures\. In this paper, we have provided one way to directly transfer the classification knowledge from one dataset to another, or even unify such knowledge into a single whole\. We proposed a method to merge the overlapping feature\-spaces into a single feature\-space for a pair of given allied heterogeneous datasets\. We then used a matrix completion method to create a unified dataset based on the merged feature\-space\. We conducted experiments under different scenarios on these 4 pairs of allied, heterogeneous datasets and 4 different classifiers \(XGBoost, RandomForest, SVM, KNN\)\. The experiments conclusively demonstrated that these classifiers, when trained on the unified representation,alwaysoutperformed classifiers, trained separately on the constituent allied datasets forallthese pairs of allied datasets\.

This work provides an easy way to substantially improve classifier performance by unifying and using multiple allied datasets together\. Since the datasets are independently created by different organizations on different domain objects, this approach allows to integrate them into a unified dataset, and build high\-quality classification models that can be seamlessly applied to data in either format\.

We are working on applying the approach to several more pairs of allied datasets and also trying out more classifiers, including neural network models\. We are also working on a GAN\-like encoder\-decoder based approach that maps the two distinct feature\-spaces to a common latent space\. The approach in this paper can be easily extended to unify, say, 3 allied datasets; the only constraint is that the shared attributes must be present in all 3 allied datasets\. We are working on demonstrating the benefits of and evaluating any limitations of this larger data unification scheme\. Another problem we are working on is evaluating the quality and interpretability of the newly added data values, estimated using various matrix completion algorithms i\.e\., theoretically modelling the data unification process \(e\.g\., how does the performance vary per the number of shared columns?\) and identifying true reasons for the substantially improved classification performance\. One possibility is that the allied datasets share \(hidden\) reasons for producing the class label for a given data record, which the unified representatons are implicitly capturing through the extended columns\. For example, almost certainly there are shared reasons why students drop\-out in both OULAD and HEPSR datasets\. It would be interesting to verify this hypothesis; currently the actual reasons as to why students drop out are not explicitly known in either dataset\.

The current experiments show improvements in classifier performance under cross\-validation\. An interesting scenario would be to test the unified model \- trained on unification of two allied datasetsD1D\_\{1\}andD2D\_\{2\}\- on a third “unseen” allied datasetD3D\_\{3\}\. For this, we are working out the scheme for estimating extended attributes based onD3D\_\{3\}, without they being “seen” by the classifier trained onD1D\_\{1\}andD2D\_\{2\}\.

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