Recent advances in rotation-invariant (RI) learning for 3D point clouds typically replace raw coordinates with handcrafted RI features to ensure robustness under arbitrary rotations. However, these approaches often suffer from the loss of global pose information, making them incapable of distinguishing geometrically similar but spatially distinct structures. We identify that this limitation stems from the restricted receptive field in existing RI methods, leading to Wing–tip feature collapse, a failure to differentiate symmetric components (e.g., left and right airplane wings) due to indistinguishable local geometries. To overcome this challenge, we introduce the Shadow-informed Pose Feature (SiPF), which augments local RI descriptors with a globally consistent reference point (referred to as the “shadow”) derived from a learned shared rotation. This mechanism enables the model to preserve global pose awareness while maintaining rotation invariance. We further propose Rotation-invariant Attention Convolution (RIAttnConv), an attention-based operator that integrates SiPFs into the feature aggregation process, thereby enhancing the model’s capacity to distinguish structurally similar components. Additionally, we design a task-adaptive shadow locating module based on the Bingham distribution over unit quaternions, which dynamically learns the optimal global rotation for constructing consistent shadows. Extensive experiments on 3D classification and part segmentation benchmarks demonstrate that our approach substantially outperforms existing RI methods, particularly in tasks requiring fine-grained spatial discrimination under arbitrary rotations.

Timely fault detection in HVAC systems is crucial for preventing energy waste and maintaining thermal comfort in commercial buildings. This paper introduces the adaptive adversarial autoencoder (AdaAAE), an innovative anomaly detection approach designed for unsupervised fault detection within air handling units (AHUs) of HVAC systems. By combining the adversarial autoencoder (AAE) with deep support vector data description (DSVDD), AdaAAE efficiently trains the reconstruction, regularization, and compactness phases to produce a spherical and compact latent representation of the training data, enabling effective fault detection within the latent space. A key feature of AdaAAE is its ability to accurately determine the anomaly threshold at the end of the training phase, which is particularly beneficial in scenarios where there is no prior knowledge of the anomaly ratio for test instances—a common challenge in real-world applications. AdaAAE’s performance was evaluated on a real-world AHU system developed as part of the ASHRAE research project 1312 (RP-1312). Experimental results, especially with regard to AUC-ROC and AUC-PR, highlight AdaAAE’s superior fault detection capabilities across AHU datasets with varying complexities. Notably, AdaAAE achieved outstanding performance, with an average AUC-ROC of 97.5% and AUC-PR of 94.4%, significantly outperforming the baseline methods in this study. Additionally, the experimental findings demonstrate AdaAAE’s proficiency in accurately estimating the anomaly threshold without prior knowledge, with minimal performance degradation when shifting from a scenario with a known anomaly ratio to one requiring estimation.Note to Practitioners—The concept of anomaly detection through subspace learning has attracted significant interest, with a focus on achieving a compact latent distribution. In this study, we introduce a new anomaly detection technique called AdaAAE, which is designed to produce a spherical and compact latent representation of training data. This feature enhances the method’s ability to identify anomalies within the latent space. Moreover, AdaAAE offers a distinct advantage in accurately determining the anomaly threshold at the end of the training phase, which is especially useful in practical scenarios where prior information about anomaly ratios for test instances is unavailable. To ensure reproducibility and allow for future enhancements by other researchers, the entire source code for this study is available in the following repository: https://github.com/viettra-xai/Ada-AAE.

In recent years, axial data, where observations are treated as axes of direction, has gained prominence in a range of complex tasks, including gene expression data clustering, blind speech separation, and depth image analysis. However, prevailing methods for axial data modeling mainly rely on shallow probabilistic models, which often overlook the hidden and hierarchical dependencies in the latent space. These methods also require a separate, human-engineered feature extractor to obtain features from raw axial data for downstream tasks. This work introduces a novel framework, Axial Variational Autoencoders (AVAEs), for modeling and representation learning of axial data by leveraging a deep generative model, the Variational Autoencoder (VAE). Unlike existing approaches, our method can autonomously learn more expressive representations from axial data by designing a VAE that uses the Watson distribution as the latent prior. Furthermore, we introduce a tailored reparameterization technique to support stable training. We validate the effectiveness of our model through experiments on simulated axial datasets and a real-world application.

Occupancy estimation (OE) and activity recognition (AR), predicted using Internet of Things (IoT) sensor data, are among the most important outcomes of artificial intelligence (AI) applied to buildings. The unavailability of enough labeled data is a serious problem for building researchers which is why they came up with domain adaptation (DA). Unsupervised domain adaptation (UDA) solves the problem of the unavailability of labeled data in target domains. In this research, we present a novel application for OE and AR that considers UDA methods. We have adapted 3 UDA methods called Joint Adaptation Networks (JAN), Deep Adaptation Networks (DAN), and Deep Correlation Alignment (D-CORAL). Our research application offers a practical solution for smart building management, enabling accurate OE and AR using adapted UDA techniques.

Clustering high-dimensional directional data (i.e., L2 normalized vectors) presents significant challenges due to the intricate spherical representations of latent embeddings and the limitations of classical (non-deep) clustering techniques. Moreover, dynamically inferring the number of clusters remains a fundamental issue in existing deep clustering methods, especially those involving complex model-selection criteria. This paper addresses these challenges by introducing a novel deep nonparametric clustering framework that employs hyperspherical latent embeddings within a Variational Autoencoder architecture, enhanced by an infinite Von Mises-Fisher Mixture Model as a dynamic prior. This approach enables automatic adaptation of cluster numbers during training, eliminating the need for predefined clusters and traditional model selection processes. Our scalable architecture effectively integrates In-vMFMM with hyperspherical embeddings to tackle the complexities of directional data. Utilizing a joint training strategy, our method alternates between updating neural network parameters and adjusting mixture model priors via nonparametric variational Bayes. Empirical evaluations on benchmark datasets, including complex ImageNet-50, demonstrate that our approach significantly outperforms state-of-the-art deep nonparametric clustering methods. It also robustly estimates the number of clusters, showcasing its effectiveness and versatility in handling high-dimensional directional data.

Accurate electric power load forecasting is critical for power utility companies as it increases control over the relevant infrastructure, resulting in significant improvements in energy management and scheduling. However, point forecasting appears to fall short of providing these businesses with enough information to prepare for the worst. This paper proposes an encoder–decoder model that takes advantage of the expressiveness of Transformer-based encoders to produce probabilistic forecasts, i.e., a distribution over future predictions. Two real-world datasets are utilized to incorporate the performance of the proposed model on two different types of data: hourly load data from the power supply company of the city of Johor in Malaysia and hourly load consumption data from one of Grenoble Institute of Technology’s buildings. The former represents aggregated data, which makes identifying patterns and trends easier, but the latter was taken from a single building (non-aggregated), which increases the difficulty of forecasts. The model’s performance is discussed across multiple time horizons, including 24-hour, 1-week, and 1-month predictions. It achieved notable improvements compared to the used baseline, Amazon DeepAr. For 24 h ahead forecasting, accuracy was increased from 87.2 percent to 96.2 percent for Malaysian data and from 52.3 percent to 68.2 percent for Grenoble data. And for 1 month ahead forecasting, it was improved from 84.7 percent to 89.7 percent for Malaysian data, and from 45.5 percent to 57.2 percent for Grenoble data.

This paper tackles the pressing challenge of load forecasting in smart buildings, aiming to enhance energy management in the light of the sector’s substantial energy consumption. Specifically, we focus on overcoming the issue of historical data being insufficient to train effective deep learning models. To this end, we introduce a federated load forecasting framework to exploit data from multiple buildings while maintaining the privacy of their load information, ensuring that data remains within each building’s local environment. Acknowledging the diverse load profiles shaped by factors like size, location, and user behavior, we investigate existing techniques to personalize the global model to accommodate each building’s specific characteristics. We perform a series of experiments across diverse datasets to compare and interpret the results of each personalization mechanism. Our findings indicate that federated learning significantly enhances forecasting accuracy across different buildings, with personalized federated learning providing even more substantial improvements.

This article proposes a novel deep clustering model based on the variational autoencoder (VAE), named GamMM-VAE, which can learn latent representations of training data for clustering in an unsupervised manner. Most existing VAE-based deep clustering methods use the Gaussian mixture model (GMM) as a prior on the latent space. We employ a more flexible asymmetric Gamma mixture model to achieve higher quality embeddings of the data latent space. Second, since the Gamma is defined for strictly positive variables, in order to exploit the reparameterization trick of VAE, we propose a transformation method from Gaussian distribution to Gamma distribution. This method can also be considered a Gamma distribution reparameterization trick, allows gradients to be backpropagated through the sampling process in the VAE. Finally, we derive the evidence lower bound (ELBO) based on the Gamma mixture model in an effective way for the stochastic gradient variational Bayesian (SGVB) estimator to optimize the proposed model. ELBO, a variational inference objective, ensures the maximization of the approximation of the posterior distribution, while SGVB is a method used to perform efficient inference and learning in VAEs. We validate the effectiveness of our model through quantitative comparisons with other state-of-the-art deep clustering models on six benchmark datasets. Moreover, due to the generative nature of VAEs, the proposed model can generate highly realistic samples of specific classes without supervised information.

In this paper, we propose a Human-Machine Inter-face offering an efficient and privacy-conscious approach to train Occupancy Estimation Machine Learning models by interacting with users to request the occupancy level of a room. Although there are existing works that optimize the frequency of interactions, these techniques assume that the data is clean. Hence, anomalies in sensor measurements may lead to unnecessary interactions with users, resulting in their disengagement. To address this problem, we employ an Autoencoder neural network to detect anomalies in univariate time series sensor data using the reconstruction error. Furthermore, we tackle the autoencoder architecture selection challenge by utilizing a Reinforcement Learning-based Neural Architecture Search (RLNAS) approach, where an agent explores a predefined search space and identifies the optimal neural configuration by learning through trial and error. Experiments conducted on a custom anomaly detection dataset demonstrate competitive performance, and illustrate how this technique discovers effective architectures that may not be immediately apparent or intuitive.

Abstract Latent Dirichlet allocation (LDA) is one of the major models used for topic modelling. A number of models have been proposed extending the basic LDA model. There has also been interesting research to replace the Dirichlet prior of LDA with other pliable distributions like generalized Dirichlet, Beta‐Liouville and so forth. Owing to the proven efficiency of using generalized Dirichlet (GD) and Beta‐Liouville (BL) priors in topic models, we use these versions of topic models in our paper. Furthermore, to enhance the support of respective topics, we integrate mixture components which gives rise to generalized Dirichlet mixture allocation and Beta‐Liouville mixture allocation models respectively. In order to improve the modelling capabilities, we use variational inference method for estimating the parameters. Additionally, we also introduce an online variational approach to cater to specific applications involving streaming data. We evaluate our models based on its performance on applications related to text classification, image categorization and genome sequence classification using a supervised approach where the labels are used as an observed variable within the model.

The proliferation of Internet of Things (IoT) sensors in smart buildings has generated vast amounts of time series data, offering valuable insights when properly leveraged. We propose to use this data to identify abnormal behaviors and deviations in temporal data which will enable the detection of anomalies related to power consumption, control system failures, and sensor malfunctions. To achieve this, we propose a reconstruction-based anomaly detection framework utilizing autoencoders where we train the model on anomaly-free samples, minimizing the error between the original and reconstructed sequences. Then, by setting a threshold on the reconstruction error, abnormal sequences can be distinguished from the predominant regular patterns observed in the majority of the time windows. Moreover, to address the challenge of selecting a suitable autoencoder architecture, a Reinforcement Learning-based Neural Architecture Search (RLNAS) approach is employed to explore a manually defined search space and discover the best neural configuration by learning through trial and error. Experimental results on two custom anomaly detection datasets demonstrate competitive performance, showcasing the effectiveness of this approach in discovering effective architectures that may not be immediately apparent or intuitive.

Incomplete data is the most common but tricky problem for data-driven energy and building solutions. Due to sensor errors or communication failures, raw building data with missing data points are rarely satisfactory for fault detection and diagnosis (FDD) applications. In this paper, a new framework named a deep variational mixture of principal component analyzers (DV-MPPCA) is proposed to address the building FDD problem with incomplete data. DV-MPPCA is the combination of a variational autoencoder (VAE) model for data compression and a mixture of principal component analyzers (MPPCA) for density estimation. To construct an integrated framework comprising both VAE and MPPCA, we introduce a novel methodology that represents the algebraic model of MPPCA within the architecture of a neural network. This innovative architecture undergoes optimization through the minimization of a designated loss function. Subsequently, the refined and optimized framework is harnessed as an unsupervised fault detection model for a real-world air handling unit (AHU) system designed by the ASHRAE research project 1312 (RP-1312). Furthermore, by incorporating the modified evidence lower bound (ELBO) loss function within the VAE, the resulting DV-MPPCA framework exhibits exceptional performance when confronted with incomplete AHU datasets, even with high missing rates. Empirical findings substantiate the supremacy of DV-MPPCA over other contemporary classic and deep models. Impressively, even with a missing rate as modest as 10%, DV-MPPCA consistently delivers outstanding performance, achieving F1-scores of 98.10%, 93.50%, and 81.57% for the Summer, Winter, and Spring datasets, respectively.Note to Practitioners—This article was motivated by the fact that raw building data with missing data points are not qualitative enough for direct use in fault detection and diagnosis (FDD) applications. To resolve this problem, existing studies manipulated imputation algorithms in the preprocessing step to prepare the data for constructing FDD models and impute missing points in test instances during the online monitoring process. However, this step makes an overall FDD framework cumbersome. Therefore, instead of utilizing a data imputation method as a separately operating model, we adopt VAE in our framework to exclude the contribution of missing points during the offline modeling and online monitoring processes. This modification of VAE helps our framework be immune to incomplete data. For reproducibility and future improvement by other researchers, the complete source code of this study is provided in the following repository: https://github.com/viettra-xai/DV-MPPCA.

We introduce a mixture of mixtures of bounded asymmetric generalized Gaussian and uniform distributions. Based on this framework, we propose model-based classification and model-based clustering algorithms. We develop an objective function for the minimum message length (MML) model selection criterion to discover the optimal number of clusters for the unsupervised approach of our proposed model. Given the crucial attention received by Explainable AI (XAI) in recent years, we introduce a method to interpret the predictions obtained from the proposed model in both learning settings by defining their boundaries in terms of the crucial features. Integrating Explainability within our proposed algorithm increases the credibility of the algorithm’s predictions since it would be explainable to the user’s perspective through simple If-Then statements using a small binary decision tree. In this paper, the proposed algorithm proves its reliability and superiority to several state-of-the-art machine learning algorithms within the following real-world applications: fault detection and diagnosis (FDD) in chillers, occupancy estimation and categorization of residential energy consumers.

We consider the problem of anomaly detection in proportional data by investigating the Libby-Novick Beta-Liouville distribution, a novel distribution merging the salient characteristics of Liouville and Libby-Novick Beta distributions. Its main benefit, compared to the typical distributions dedicated to proportional data such as Dirichlet and Beta-Liouville, is its adaptability and explanatory power when dealing with this kind of data. Our goal is to exploit this appropriateness for modeling proportional data to achieve great performance in the anomaly detection task. First, we develop generative models, namely finite mixture models of Libby-Novick Beta-Liouville distributions. Then, we propose two discriminative techniques: Normality scores based on selecting the given distribution to approximate the softmax output vector of a deep classifier and an improved version of Support Vector Machine (SVM) by suggesting a feature mapping approach. We demonstrate the benefits of the presented approaches through a variety of experiments on both image and non-image datasets. The results demonstrate that the proposed anomaly detectors based on the Libby-Novick Beta-Liouville distribution outperform the classical distributions as well as the baseline techniques.

Human action recognition (HAR) is a crucial research field that necessitates the implementation of advanced mathematical concepts to recognize human activities from sequences of observations. This paper presents a novel framework employing a mixture-based Hidden Markov Model (HMM) that capitalizes on the advantages of asymmetric modeling, bounded support, and robustness in sensor-based HAR. To accommodate variations in observations within each human activity class, we propose an asymmetric generalized Gaussian mixture model (AGGM) to model the emission probabilities. Subsequently, we propose incorporating the bounded asymmetric generalized Gaussian mixture model (BAGGM) to address the constraints inherent in real-life data. The parameters of the corresponding HMM are estimated using the Baum-Welch algorithm, and the most probable sequence of hidden states is inferred using the Viterbi algorithm. We validate our proposed framework using four datasets for human activities. Experimental results demonstrate that our proposed model outperforms all state-of-the-art HAR models that are HMM-based, thereby emphasizing the superiority of our proposed frameworks in HAR systems to understand behaviours, predict potential actions, and facilitate sports applications for the general population and independent living applications for vulnerable populations.

The widespread deployment of smart meters in residential settings has led to a wealth of high-resolution electrical power consumption data, providing the opportunity to discover valuable insights into energy consumption patterns. Mixture models are essential for revealing hidden patterns in data, enabling accurate insights and informed decision-making across diverse applications. In this paper, we introduce the mixture of mixtures of bounded asymmetric generalized Gaussian and Uniform distributions (BAGGUMM) and investigate its potential for characterizing residential energy users, thereby enhancing energy management applications, including demand response and energy efficiency programs. We investigate the potential for improved clustering efficacy by incorporating an inner mixture containing the Uniform distribution to enhance robustness against outliers. Additionally, we integrate a decision tree algorithm for model explainability to define pattern boundaries using if-then statements. We validate our proposed model using three real-life datasets. Additionally, The performance of BAGGUMM is compared against several state-of-the-art mixture models.

Nonparametric mixture models are a powerful and flexible approach to data clustering; they account for uncertainty by using Bayesian inference to obtain a posterior distribution over the model's parameters and a better fit to the data. Additionally, nonparametric mixture models can adaptively adjust the number of components to fit the data. Incorporating asymmetric generalized Gaussian distribution (AGGD) within the mixture framework extends the capabilities of the widely used Gaussian mixture model (GMM) by adding parameters that control the shape and the skewness of the per-component distribution, which enables the model to capture diverse and complex data patterns. Furthermore, we incorporate explainability within our proposed infinite asymmetric generalized Gaussian mixture model (IAGGMM) to provide interpretable insights into the clustering results, enhancing the model's practicality and transparency. This integration facilitates a deeper understanding of the underlying data structures and the rationale behind the model's decisions, fostering trust and promoting the adoption of our approach in various real-world scenarios. In this study, we explore the application of occupancy estimation for optimizing energy efficiency and facility management in smart buildings. Our approach demonstrates superior performance in modelling complex and asymmetric data distributions, resulting in improved accuracy and adaptability for occupancy level estimation. Therefore, we achieve the optimal trade-off between model complexity and accuracy.

In this work, we propose a novel anomaly detection approach in images based on normality scores using transformations. By applying various transformations to the input image such as rotation and flipping, we train a classifier to predict the transformation label applied to the images. Then, we represent the output of the classifier by a softmax vector. Thanks to the flexibility of multivariate Beta in fitting the data compared to other conventional distributions such as the Dirichlet distribution, we approximate the softmax vector by this general form of the Beta distribution to construct the normality scores. Moreover, we use the Maximum Likelihood to estimate the parameters of the proposed distribution. To show the power and the effectiveness of our approach, we conduct experiments of detecting anomalies in various public datasets. Furthermore, the proposed method is compared with state-of-the-art techniques and results demonstrate its superiority in terms of Area Under Receiver Operating characteristics (AUROC).

In this article, we propose a predictive model based on Beta-Liouville (BL) and inverted BL (IBL) mixture models for occupancy estimation in smart buildings. This model gives better results than point estimate methods, when the training data is small, because it is based on data-driven predictive distribution. The Liouville-based mixture models were chosen because of their flexibility in fitting symmetric and asymmetric distributions. However, the large number of parameters of BL and IBL increases the uncertainty in approximating the upper bound of the predictive distribution, hence we propose an optimization scheme in which reliability is investigated and verified. In addition, we extend our work presented by giving more details about the predictive model and by studying the occupancy estimation in smart buildings problems in depth. Indeed, different occupancy scenarios are considered to show the merits of our predictive framework. This article aims to address the problem of occupancy estimation with a focus on scenarios where small training data sets are available. By developing robust predictive models that can generalize well with limited data, this research seeks to facilitate the early adoption and practical application of occupancy models in various domains.

Bayesian non-negative matrix factorization (BNMF) has been widely used in different applications. In this article, we propose a novel BNMF technique dedicated to semibounded data where each entry of the observed matrix is supposed to follow an Inverted Beta distribution. The model has two parameter matrices with the same size as the observation matrix which we factorize into a product of excitation and basis matrices. Entries of the corresponding basis and excitation matrices follow a Gamma prior. To estimate the parameters of the model, variational Bayesian inference is used. A lower bound approximation for the objective function is used to find an analytically tractable solution for the model. An online extension of the algorithm is also proposed for more scalability and to adapt to streaming data. The model is evaluated on five different applications: part-based decomposition, collaborative filtering, market basket analysis, transactions prediction and items classification, topic mining, and graph embedding on biomedical networks.

In topic models, collections are organized as documents where they arise as mixtures over latent clusters called topics. A topic is a distribution over the vocabulary. In large-scale applications, parametric or finite topic mixture models such as LDA (latent Dirichlet allocation) and its variants are very restrictive in performance due to their reduced hypothesis space. In this article, we address the problem related to model selection and sharing ability of topics across multiple documents in standard parametric topic models. We propose as an alternative a BNP (Bayesian nonparametric) topic model where the HDP (hierarchical Dirichlet process) prior models documents topic mixtures through their multinomials on infinite simplex. We, therefore, propose asymmetric BL (Beta-Liouville) as a diffuse base measure at the corpus level DP (Dirichlet process) over a measurable space. This step illustrates the highly heterogeneous structure in the set of all topics that describes the corpus probability measure. For consistency in posterior inference and predictive distributions, we efficiently characterize random probability measures whose limits are the global and local DPs to approximate the HDP from the stick-breaking formulation with the GEM (Griffiths-Engen-McCloskey) random variables. Due to the diffuse measure with the BL prior as conjugate to the count data distribution, we obtain an improved version of the standard HDP that is usually based on symmetric Dirichlet (Dir). In addition, to improve coordinate ascent framework while taking advantage of its deterministic nature, our model implements an online optimization method based on stochastic, at document level, variational inference to accommodate fast topic learning when processing large collections of text documents with natural gradient. The high value in the predictive likelihood per document obtained when compared to the performance of its competitors is also consistent with the robustness of our fully asymmetric BL-based HDP. While insuring the predictive accuracy of the model using the probability of the held-out documents, we also added a combination of metrics such as the topic coherence and topic diversity to improve the quality and interpretability of the topics discovered. We also compared the performance of our model using these metrics against the standard symmetric LDA. We show that online HDP-LBLA (Latent BL Allocation)’s performance is the asymptote for parametric topic models. The accuracy in the results (improved predictive distributions of the held out) is a product of the model’s ability to efficiently characterize dependency between documents (topic correlation) as now they can easily share topics, resulting in a much robust and realistic compression algorithm for information modeling.

Variational inference approaches are gaining more and more success and are applied in various data mining applications. In this work, we present a variational learning framework for the Shifted Scaled Dirichlet finite mixture model. Furthermore, we introduce component splitting based on Entropy approximation to estimate the number of components in our model along with the parameters of the distribution. We test the performance of this model on two real-life datasets, both related to human activity recognition.

Computer network technology is developing quickly, and the advancement of internet techniques is growing faster. Furthermore, people and companies have became more aware of the importance of network security. To protect the network from different attacks, it is necessary to instantly detect intrusions with significantly low False-Positive Rates (FPRs). Many Anomaly-based Detection Systems (ADS) have been proposed in the past. The performance of these systems depends on many factors such as features selection or extraction, missing or inaccurate records in data, over-fitting, under-fitting, high bias, and variance in data. Thus, it is important to take all these factors into account. Recently, a novel Geometric Area Analysis (GAA) technique based on Trapezoidal Area Estimation (TAE) has been proposed based on the Beta Mixture Model (BMM). In this work, we evaluate GAA and TAE techniques using other flexible mixture models based on inverted Beta, generalized Dirichlet, and generalized inverted Dirichlet distributions. The evaluation of this work is performed on two datasets, namely the NSL-KDD and UNSW-NB15. The results have shown the efficiency of the proposed ADS demonstrated by obtaining high accuracy and low false-positive rates in all attack types.

Nowadays a massive amount of data is generated as the development of technology and services has accelerated. Therefore, the demand for data clustering in order to gain knowledge has increased in many sectors such as medical sciences, risk assessment and product sales. Moreover, binary data has been widely used in various applications including market basket data and text documents. While applying classic widely used k-means method is inappropriate to cluster binary data, this work proposes an improvement of K-medoids algorithm using binary similarity measures instead of Euclidean distance which is generally deployed in clustering algorithms. We have considered two challenging applications, namely; text clustering and binary images categorization to show the merits of the proposed framework.

A novel regression algorithm has been proposed, Beta-Liouville regression, to solve regression of compositional data, where the prediction is multi-dimensional and sums to unity. Applications include market-share data mining in relation to its score in Google-trends and smart building occupancy estimation. The study of Google-trends in relation to market-shares gives a good estimate of whether the company's investment in advertisements have yielded any results in improving their market-shares. Secondly, occupant behaviour in buildings gives useful insights on the required levels of air conditioning, lighting and even initiating help during emergency. Sensors to estimate the occupancy of a smart building include microphone, door/window positions, motion detection, power consumption. The Beta-Liouville regression algorithm is compared to ordinary least squares regression with compositional transformations and Dirichlet regression.

A new kind of supervised learning approach is proposed to determine the number of occupants in a room in order to use these estimate for improved energy management. It introduces the concept of Parametrized classifier. It relies on the predetermined structure of supervised learning classifiers, where any classifier could be used to evaluate this approach. The parameters will be adjusted according to the incoming data sensors (i.e CO2 concentration, acoustic pressure, ...) using a tuning mechanism depends on an optimization process. This paper provides different supervised learning methods (i.e decision tree random forest) to determine the required structure in order to be used in parametrized classifier approach. The structure of decision tree has been chosen which represents the classification rules and limit the depth of the tree to facilitate the generalization process. In order to evaluate the generalization possibilities of a supervised learning approach (i.e. decision tree), it has been chosen to extrapolate results from office H358 to another similar office H355. The knowledge has been extracted from a decision tree built on H358 office then applied and tuned for H355 using parameterized classifier approach. Moreover, experiments implement occupancy estimations and hot water productions control show that energy efficiency can be increased by about 6% over known optimal control techniques and more than 26% over rule-based control besides maintaining the occupant comfort standards. The building efficiency gain is strongly connected with the occupancy estimation accuracy.