The multi-layered method we will make use of for cancer diagnosis has a combinatorially rich architecture which gets empowered with every new algorithm incorporated into it. Let’s explain this architecture which has several building blocks, namely, filtering, selection, classification and simulation/forecasting, a relational sketch of which is as follows (Fig. 1).
2.1 Filtering: Cancerous tissues have certain physical, chemical and biological properties/featureswhich could be decomposed into two main categories: image-based features and non-image-based features. For the purposes of this article, we will focus on image-based features involving geometrically or physically describable morphological and other properties such as color, tone, size, shape/texture and related intricate details concerning curvature, kinks, (dis)continuities, degree of fuzziness, irregularity, asymmetry, possible rupture and non-convexity, broken or diffracted edges or segments, structures of interconnectedness as well as convoluted differentiation, overlapping patterns etc. Image filters are designed to extract mathematically-represented (quantifiable) features from the images. Filter-based/scrutinized mathematical representation of morphological, topological and other features of images could bring into light hidden patterns or structures embodied in images. Patterns revealed through such filters make it possible to more accurately diagnose the cancerous tissues, thus facilitating the proper discrimination of benign tissues from the cancerous ones or the discrimination of tissues at advanced cancerous stages from the early stage ones.Features extracted through image filters make it possible to distinguish between different types or subtypes of cancer as well.
Cancerous tissues appear to display a range of features including various kinds of heterogeneity, irregularity and possible complex differentiation and connectedness, the patterns of which could be captured by nano, micro or macro level images that could be effectively used in distinguishing cancereous tissues/lesions from the non-cancereous ones. Clearly, if the existing image filter algorithms (or algorithms that can be designed for specific image analyses) enable us to extract, from images, quantifiable (real-valued) features that properly represent the intricate details of those images embodying cancer-signifying information, we can use those quantifiable features, via further algorithms, to accurately identify whether a tissue is cancereous or not. Similarly, properly designed image filters may help identify features that facilitate the detection of early signs for cancer tendencies before the critical or metastatic stage, allowing a time-specific classification of cancer-prone tissues.
In this paper, we will make use of a subset of the image filter algorithms built in the machine learning program, “Waikato Environment for Knowledge Analysis” (WEKA), which are named, in a suggestive manner, as “Auto Color Correlogram Filter”, “Binary Patterns Pyramid Filter”, “Color Layout Filter”, “Edge Histogram Filter”, “Fuzzy Color and Texture Histogram Filter” (FCTH Filter), “Fuzzy Opponent Histogram Filter”, “Gabor Filter”, “JPEG Coefficient Filter”, “Pyramid Histogram Oriented Gradients Filter” and “Simple Color Histogram Filter”. Some of these filters extract color information from the images, some extract texture information and some do both. The procedures through which these algorithms extract information/features from images are beyond the scope of this paper. Without getting into the mathematical descriptions of these algorithms, we will incorporate the filter-extracted quantified features into a selection algorithm which we which we will point out next.
2.2 Selection:Through image-filters, we can extract/construct hundreds (and sometimes thousands) of quantified features representing the images. Features may direct us in different directions and using all those features in the classification process need not always lead to the best results. Instead, it would often be better to construct a subset of features that are most suitable for classification purposes. For that reason, we will use a “feature selection algorithm” to select the best features for the classification target. There are a number of algorithms ranging from “Cfs Subset Eval” to “Correlation Attribute Eval” that can be used for selection purposes. We will choose Cfs Subset Eval algorithm, which is based on the predictive abilities of the individual features, for the task of selecting the best subset of the image-based features.
The list of features we consider for overall analysis need not consist only of image-based features. We can enlarge the list of finally-chosen features for overall analysis by adding, to the image-based subset, those non-image-based features the current medical knowledge considers to be important for diagnostic purposes.
2.3. Classification: Following the steps of extracting features from images (filtering) and forming a best subset of features (selection), we can choose algorithms to identify the nature of the tissues/lesions (classification). That is to say, through classification algorithms based on image-filtered and properly selected features, we can determine whether a tissue is cancereous or not or we can classify, with a reasonably high degree of accuracy, the types, subtypes, degrees or stages of cancer. The classification algorithms we can use in the diagnostic process ranges from “multiobjective evolutionary fuzzy classifier” to “deep learning”, the performances (or successes) of which are likely to depend, among other things, on the particular targeted classification problem. The set of criteria that are used to measure the performances/successes of these algorithms include many metrics such as “accuracy rate”, “sensitivity”, “specificity”, “F measure” and “AUC” (area under the ROC curve).
The performance evaluation problem of the classification algorithms or the overall chain of diagnosis-targeting algorithms is a particularly complicated or sensitive matter in the context of our paper, precisely because we use a hybrid method that incorporates image filters and selection algorithms beforehand. In other words, the classification procedures we use in this paper are image filter-integrated and best feature-selected artificial intelligence algorithms, the performance of which resides not only in the classification process itself but also in the filtering and selection processes and perhaps combination of all three processes. We conjecture that image-filtering and feature-selection improve the performance of the classification algorithms they are integrated with, but the dependence of the classification task on the filtering and selection tasks renders the classification performance sensitive to the filtering and selection performances. Certain combinations of filtering, selection and classification may well prove to be highly successful for the identification of certain types of cancer. The question of which combinations of image filters and classification algorithms work better for the identification of what types of cancer is, we think, a fruitful and sophisticated mathematical topic with powerful practical implications/consequences for cancer diagnosis. In the third (“the results”) section of this paper, without delving into the mathematical details, we will try to find combinations of image-filters and classification algorithms that yield a high degree of accuracy.
2.4. Simulation/forecasting of future trends: The above-described triadic method based on filtering, selection and classification is, as we will show in the context of a concrete case in the next section, very successful at cancer diagnosis at a point in time. This is, if the phrase is appropriate, “a successin static contexts”. Can this success in static contexts be generalized to dynamic contexts? The answer to this question is, I think, a “qualified yes”. The answer is qualified because of the multidimensionally intricate cases with complicated feedback relations that might render the cancer trajectories difficult to predict over time. Despite the challenging difficulties, artificial intelligence methods, if properly combined with appropriate simulation paradigms, could produce a significant success in dynamic contexts as well. For an illustrative description, let us begin with a relatively simple case (example) where we can diagnose whether a tissue is cancerous at different points in time, using the triadic method explained above. Using the obtained estimates at different points in time, we can form a time series implicitly characterizing the cancer trajectory over time. We can then use artificial intelligence algorithms to undertake a time series forecasting of the future trends. This can be done with different programs including the WEKA mentioned above. The forecasting algorithms could also enable us to incorporate the effects of different factors on the trajectory, assuming that the data about those factors are available. This way we can, for instance, forecast the effects of possible interventions (involving drugs, radiation etc.) on the cancer trajectories. Some versions of these types of forecasting could also be carried out via ARIMA (Auto Regressive Integrated Moving Average)-type models which could be run with computer programs such as EVIEWS.
Artificial intelligence-based possibilities in dynamic contexts are not limited to the time series forecasting. We can construct simulation models where we can incorporate artificial intelligence algorithms - models that enable us to formulate the feedback relations characterizing cancer processes and take into account a multiplicity of possibly interconnected or interwoven factors, delays or interdependencies in the microenvironment. Such multiple factors and the web of interactions among those factors could be modeled with the methods of “system dynamics” or “agent-based modeling” or a combination of both. These simulation paradigms present possibilities which cancer practitioners can take advantage of in dealing with or analyzing cancer-related phenomena such as metastatic potential and recurrence, not to mention the possibilities involving the timing and magnitude of intervention to limit cancer progression. And as such, the simulative framework is highly suitable for innovative exploration and experimentation of a wide range of dynamic structures in cancer research.
[1]For some features of malignant tumors, see (Prabhu et al. 2022).
[2]The WEKA program provides descriptions/brief accounts of these algorithms.
[3]Different features may be crucial to detecting different types of cancer. The features extracted through image filters may need to be classified in terms of their instrumental role in cancer diagnosis. Color-centered filters may be more successful in some cases than others. Similarlyfilters extracting some topological features or shape-related features would be more conducive to successful diagnosis in cases where these features play a more distinguishing role. So a study of filters and taxonomy of them might be useful.